# Optical Spectra of Candidate International Celestial Reference Frame (ICRF)
Flat-Spectrum Radio Sources

O. Titov  Geoscience Australia, PO Box 378, Canberra, ACT 2601, Australia
<EMAIL_ADDRESS>Laura M. Stanford  Geoscience Australia, PO Box 378,
Canberra, ACT 2601, Australia  Helen M. Johnston  Sydney Institute for
Astronomy, School of Physics, University of Sydney, NSW 2006, Australia  T.
Pursimo  Nordic Optical Telescope, Nordic Optical Telescope Apartado
474E-38700 Santa Cruz de La Palma, Santa Cruz de Tenerife, Spain  Richard W.
Hunstead  Sydney Institute for Astronomy, School of Physics, University of
Sydney, NSW 2006, Australia  David L. Jauncey  CSIRO Astronomy and Space
Science, ATNF & Research School of Astronomy & Astrophysics, Australian
National University, Canberra, ACT 2611, Australia  K. Maslennikov  The
Central Astronomical Observatory at Pulkovo, Pulkovskoye Shosse, 65/1, 196140,
St.Petersburg, Russia  A. Boldycheva  Ioffe Physical Technical Institute, 26
Polytekhnicheskaya, St. Petersburg, 194021, Russia

###### Abstract

Continuing our program of spectroscopic observations of ICRF sources, we
present redshifts for 120 quasars and radio galaxies. Data were obtained with
five telescopes: the 3.58 m ESO New Technology Telescope (NTT), the two 8.2 m
Gemini telescopes, the 2.5 m Nordic Optical Telescope (NOT), and the 6.0 m Big
Azimuthal Telescope (BTA) of the Special Astrophysical Observatory in Russia.

The targets were selected from the International VLBI Service for Geodesy &
Astrometry (IVS) candidate International Celestial Reference Catalogue which
forms part of an observational VLBI program to strengthen the celestial
reference frame. We obtained spectra of the potential optical counterparts of
more than 150 compact flat-spectrum radio sources, and measured redshifts of
120 emission-line objects, together with 19 BL Lac objects. These
identifications add significantly to the precise radio–optical frame tie to be
undertaken by Gaia, due to be launched in 2013, and to the existing data
available for analysing source proper motions over the celestial sphere. We
show that the distribution of redshifts for ICRF sources is consistent with
the much larger sample drawn from FIRST and SDSS, implying that the ultra-
compact VLBI sources are not distinguished from the overall radio-loud quasar
population.

In addition, we obtained NOT spectra for five radio sources from the FIRST and
NVSS catalogs, selected on the basis of their red colors, which yielded three
quasars with $z>4$.

reference systems – galaxies: active – quasars: emission lines – BL Lacertae
objects: general – radio continuum: general

##  1 Introduction

The coming astrometric space mission, Gaia (Perryman et al., 2001; Mignard &
Klioner, 2012), to be launched in 2013 by the European Space Agency, will
measure high precision positions ($\sim 26\mu$as for $V=15$ mag, $\sim
300\mu$as for $V=20$ mag, (de Bruijne,, 2012)) and proper motions of
$\sim$500,000 quasars brighter than $m_{v}=20$. This new optical astrometric
catalog will be linked with the current radio astrometric catalog, ICRF2, the
second realization of the International Celestial Reference Frame (Fey et al.,
2009). Optical counterparts of the extragalactic sources are being sought to
confirm their identification as quasars.

This paper is the second in our series aimed at investigating the optical
spectra of radio sources in the International VLBI Service for Geodesy &
Astrometry (IVS) Reference Catalog; see Schlüter & Behrend (2007) for a
description of the IVS history. Astrometric Very Long Baseline Interferometry
(VLBI) measures the differences in arrival times of radio waves from ultra-
compact, flat-spectrum radio sources at telescopes positioned large distances
apart. This procedure determines the positions of such sources to
milliarcsecond precision.

The International Celestial Reference System (ICRS) (Arias et al., 1995) was
adopted by the International Astronomical Union (IAU) as a reference system
with its origin at the barycentre of the Solar system (MacCarthy & Petit,
2004), and axes fixed by the positions of selected extragalactic radio
sources. The first realization of the International Celestial Reference Frame
(ICRF1) was used to establish the orientation of the ICRS axes (Ma et al.,
1998). The current International Celestial Reference Frame, known as ICRF2, is
based on a catalog of 295 ‘defining’ soures. The formal weighted errors in the
radio positions are reported by Fey et al. (2009) to have an upper limit to
the noise floor of $41~{}\mu$as.

The IVS astrometric program has a total catalog of $>6000$ radio sources,
where $\sim 1200$ are observed on a regular basis. In the Southern Hemisphere,
there is a significant deficit in candidate sources as well as a lack of
optical identifications. By 2012 February, of the 3257 objects with measured
redshifts only 1213 are in the southern hemisphere and only 287 have
declinations south of $-40\arcdeg$. This paucity of redshifts in the south
leads to problems in the analysis of apparent proper motions of the reference
radio sources (Titov & Malkin, 2009). To address this issue, an extensive
program was started in 2010 to find optical counterparts and determine
redshifts for southern IVS sources (Titov et al., 2011).

The quasars at high redshift ($z\geq 2$) will be used for more intensive
observations at the VLBI facilities in the southern hemisphere. VLBI
observations of weak sources will be undertaken with the 64-meter telescope in
Parkes, Australia, and two 26-meter telescopes in Hobart (Australia) and
HartRAO (South Africa). Stronger radio sources (flux density $\geq$400 mJy)
will be monitored with four 12-meter telescopes recently installed in
Australia: the AuScope network comprising Hobart, Yarragadee and Katherine in
Australia (Titov et al., 2013) and Warkworth in New Zealand. Several quasars
found during the first observing run with the NTT in 2010 August (Titov et
al., 2011) have now been tracked with the AuScope radio telescopes in
2011–2012.

In this paper we continue our spectroscopic observations of the optical
counterparts of southern IVS sources, in particular those with a long VLBI
observational history. Some strong radio sources from the northern hemisphere
have also been observed. Optical identifications were sought initially from
the image and catalog data from the SuperCOSMOS Sky Surveys on the grounds of
their small digitization pixel scale and excellent astrometric accuracy
(Hambly et al., 2001). We also took advantage of the Sloan Digital Sky Survey
(SDSS; York et al. 2000) DR8 data release in the regions where it was
available. This improved the identification process, especially in regions of
high stellar density.

In addition, we observed five weaker radio sources from the NVSS (NRAO VLA Sky
Survey; Condon et al. 1998) and FIRST catalogs (Faint Images of the Radio Sky
at Twenty cm; Becker et al. 1995) that we identified with objects from the
SDSS whose colors were typical of high redshift quasars. Such high redshift
quasars provide unique information about the early stages of the Universe. The
number of known radio sources with $z\geq 4$ is small, and we are exploiting
this technique in an attempt to increase their number.

The observations and data reduction procedures are described in Section 2 and
we report our results, along with detailed comments on individual objects, in
Section 3.

##  2 Observations

Spectroscopic observations were carried out at five optical facilities.

ESO NTT: We had a 5-night observing run in Visitor Mode at the European
Southern Observatory (ESO) 3.58-meter New Technology Telescope at La Silla in
2011 December (088.A-0021 (A)) using the ESO Faint Object Spectrograph and
Camera (EFOSC) system with grism #13 covering the wavelength range 3685–9315
Å. The seeing during observations was typically $0\farcs{5}-1\farcs{5}$, with
a wavelength resolution 21.2 Å. Exposure times varied from 10 minutes to 1
hour depending on the magnitude of each target and current sky conditions.
Wavelength calibration was performed using the spectra of a HeNeAr comparison
lamp, resulting in an rms accuracy of 0.5 Å.

Gemini: A large number of targets were observed in Service Mode at the Gemini
North and Gemini South 8.2-meter telescopes through the Poor Weather Program
(GS-2011A-Q-89, GN-2011B-Q-109, GS-2011A-Q-94) using the Gemini Multi-Object
Spectrograph (GMOS) system with grating R400. This grating covers 4500 Å
centered either at 5200 Å or 6500 Å. As expected, the seeing and weather
conditions were variable but the program overall was very successful. The
wavelength resolution was $\sim$15 Å, and an exposure time of 20 minutes was
used for all targets. Wavelength calibration was performed using the spectra
of a CuAr lamp, resulting in an rms accuracy of $\sim$0.3 Å.

NOT: Observations with the 2.5-meter Nordic Optical Telescope on La Palma were
carried out using the Andalucia Faint Object Spectrograph and Camera (ALFOSC)
spectrograph, either with grism #5, or grism #4 with the WG345 blocking
filter. The nominal wavelength range for grism #4 is 3200–9100 Å, with the
second-order blocking filter cutting below 3560 Å. The red end of the detector
suffers fringing, so the effective long-wavelength limit is about 8000 Å. For
grism #5 the nominal range is 5000–10250 Å. The slit width was $1\farcs{0}$ or
$1\farcs{3}$ depending on the seeing. The typical integration time was between
20 and 40 minutes. The longer integrations were divided into two and the
target was offset along the slit in order to improve the fringe correction.
For the single integrations, internal halogen lamp images were taken before
and after the science frame. Wavelength calibration was based on a HeNe lamp
exposure taken before the science frame(s), resulting in an rms accuracy of
$\sim$0.5 Å.

BTA: Two objects were observed in Visitor Mode at the 6-meter Big Azimuthal
Telescope (BTA) telescope, of the Special Astrophysical Observatory in Russia
in 2011 August, using the SCORPIO multi-mode focal reducer with GR300 grism
covering the wavelength range 3500–9500 Å. The seeing during observations was
about $2\arcsec$. Spectral resolution was typically 20 Å.

Data reduction was performed with the iraf software suite111IRAF is
distributed by the National Optical Astronomical Observatories, which are
operated by the Association of Universities for Research in Astronomy, Inc.,
under contract to the National Science Foundation. using standard procedures
for spectral analysis. We removed the bias and pixel-to-pixel gain variations
from each frame and then removed cosmic rays using the IRAF task szap. Where
more than one exposure was obtained, the separate exposures were combined.
Spectrum extraction, sky subtraction and wavelength calibration were then
carried out and the final one-dimensional spectra were flux-calibrated with a
spectrophotometric standard observed with the same instrumental setup. Because
the conditions were often non-photometric, especially for observations made
through the Gemini Poor Weather Program, the flux calibration should be taken
as approximate.

##  3 Results

Spectra of 120 IVS objects are shown in Fig. 1, along with the line
identifications. A blue, dashed line indicates lines that were used for
redshift calculation, while a red, dot-dashed line indicates lines that were
detected, generally at a low signal-to-noise ratio (S/N), but not used in
determining the mean redshift.

Table 1 lists the IVS sources with their ICRF2 coordinates (which refer to the
epoch J2000.0), the telescope used for each spectrum, the identified emission
lines with their rest and observed wavelengths, the mean redshift and error,
and brief notes on individual sources. More detailed notes on individual
sources (indicated by an asterisk in the final column) are given in section
3.2.

The quoted errors $\Delta z$ in the mean redshift $\overline{z}$ are given by

$\Delta
z=\\{[(\sigma_{z})^{2}+(\Delta\lambda/\overline{\lambda_{0}})^{2}]/N\\}^{1/2},$

where $\sigma_{z}$ is the measured standard deviation among the independent
estimates of $z$, $\Delta\lambda$ is the rms error in the wavelength
calibration (typically 0.5 Å), and $\overline{\lambda_{0}}$ is the mean rest
wavelength of the $N$ lines used to measure $\overline{z}$. Single-line
redshifts (mostly Mg II) are assigned a conservative error of 0.001 if the
signal-to-noise ratio is high and the line is symmetric. If the signal-to-
noise ratio is low or the line is broad or asymmetric an (arbitrary) error of
0.002 has been assigned; in two extreme cases where the signal-to-noise ratio
is low and the line is broad or asymmetric (IVS B0633$-$26B and B1129$-$161)
the redshift is given with a colon(:) appended and no error.

Nineteen objects, listed in Table 2 with their ICRF2 positions (Fey et al.,
2009), were found to have a good signal-to-noise ratio (typically S/N$\sim
60-110$) but featureless spectra and hence are identified as probable BL Lac
objects. Their spectra are shown in Fig. 2.

A further 18 targets had spectra with a signal-to-noise ratio that was too low
for confident spectral classification; these are listed in Table 3 with their
ICRF2 positions.

There were five IVS targets that returned stellar spectra. This was assumed to
be the result of foreground obscuration and, in most cases, small but
significant offsets between SuperCOSMOS optical and ICRF2 radio positions. In
two cases the correct identification was found when the fields were reobserved
in excellent seeing. Further discussion of these five objects is given in
Section 3.1.

###  3.1 Separation of close objects

Occasionally, Galactic stars are found close on the sky to the radio position,
leading to possible misidentification. Here we note several cases that were
encountered during the observing runs.

  * •

IVS B0900$-$664—the spectrum obtained was that of a red M star, which is
offset by $0\farcs{52}$ from the ICRF position. A faint counterpart was seen
in the NTT B-band acquisition image, but a much longer integration in good
seeing will be needed to secure a redshift.

  * •

IVS B0905$-$202—the nearest object, as seen by SuperCOSMOS, was a $R=14.6^{\rm
m}$ stellar object located $1\farcs{55}$ from the radio position. Our NTT
acquisition image, taken in $0\farcs{6}$ seeing, showed a faint object at the
radio position, but on the limb of the stellar disk. Spectroscopy of this
faint $R\sim 22$ object did not reveal any clear emission lines.

  * •

IVS B1657$-$261—located in a very crowded star field in the Galactic bulge at
a latitude of $b=9\fdg{7}$. Identification of the optical counterpart may not
be feasible.

  * •

IVS B1946$-$582—based on the SuperCOSMOS optical position, the radio minus
optical position difference is only $0\farcs{06}$ in right ascension and
$-0\farcs{04}$ in declination, but the Gemini South observation of this $R\sim
19$ object showed a typical stellar spectrum. The radio source has a flat
spectrum with flux density 200–300 mJy at cm wavelengths.

  * •

IVS B2300$-$307—the obscuration of the optical field of this source by a
foreground star was discussed previously (Titov et al., 2011). However, a
later 80 s image in $0\farcs{6}$ seeing (Fig. 3) revealed a faint $R\sim 22$
object coincident with the radio position. Our spectroscopy yielded a redshift
of $1.039\pm 0.002$ based on weak C III] and Mg II emission.

Figure 3: Two acquisition images of the sky field around the quasar IVS
B2300$-$307 made at the NTT in 2010 August (left: seeing $2^{\prime\prime}$)
and 2011 December (right: seeing $0\farcs{6}$). Each image is 50′′ on a side;
north is up and east to the left. The foreground star in the centre of the
left image completely obscures the quasar due to its large seeing disk. In the
right image the much better seeing reveals the faint quasar ($R\sim$22, marked
between the bars), separated by $3\farcs{7}$ from the star. (The diagonal step
in contrast in the right image is an artefact of fast readout using two
amplifiers for the acquisition image.)

###  3.2 Notes on individual targets

  * •

IVS B0233$-$478—the broad feature attributed to Al III and C III] may also
include Si III $\lambda$1890.

  * •

IVS B0417$-$302—prominent Fe II multiplet emission; intervening Mg II doublet
absorption at $z_{\rm abs}=0.8395\pm 0.0005$.

  * •

IVS B0447$-$507—possible double-peaked C III] line and prominent Fe II
multiplet bands.

  * •

IVS B0448$-$482—poor redshift match to C III] may indicate the presence of Si
III $\lambda$1890; prominent Fe II multiplet bands.

  * •

IVS B0521$-$262—strong associated absorption in the Ly $\alpha$ emission line
and a clear detection of the Lyman limit at the emission redshift.

  * •

IVS B0529$-$031—faint optical counterpart with a very red spectrum, showing a
single broad emission line identified as Mg II with associated Mg II
absorption at $z_{\rm abs}=1.8744\pm 0.0004$, corresponding to a relative
blue-shift of $\sim$1500 km s-1; a further absorption line, at 8182.1 Å
remains unidentified. Given the low signal blueward of 6000 Å, together with
the faint SDSS blue magnitudes ($u=24.41,\ g=21.93$), it is not surprising
that C III] and C IV are not detected.

  * •

IVS B0548$-$527—redshift in Table 1 is for the forbidden lines; the permitted
lines of Mg II and H $\beta$ show a redshift systematically higher by $830\pm
80$ km s-1.

  * •

IVS B0554+242—narrow self-absorption in Ly $\alpha$ and C IV at $z_{\rm
abs}=3.2319\pm 0.0010$.

  * •

IVS B0608$-$230—wavelengths for C III] and C IV are not consistent, suggesting
the presence of additional lines or asymmetric structure; in addition, the Ly
$\alpha$ wavelength is likely to be affected by absorption in the blue wing.

  * •

IVS B0633$-$26B—a very faint galaxy; a low signal-to-noise ratio spectrum,
with a single broad emission line, assumed to be Mg II.

  * •

IVS B0810$-$180—very broad line wings in C IV and Ly $\alpha$, extending
$\sim$30,000 km s-1 redward of the line peaks.

  * •

IVS B0828$-$064—poor consistency in redshift between C IV and C III], possibly
due to associated absorption in the blue wing of C IV. Mg II is present with a
low signal-to-noise ratio just redward of the atmospheric A-band.

  * •

IVS B0844$-$557—redshift in Table 1 is for the forbidden lines; permitted
lines Mg II and H $\beta$ are displaced $\sim$1000 km s-1 to higher redshift.

  * •

IVS B0948$-$860—single emission line, assumed to be Ly $\alpha$; the adopted
redshift, $z=3.696$, is consistent with the 40% continuum depression blueward
of the emission line due to the Ly $\alpha$ forest, and the possible detection
of C IV at the red edge of the spectrum.

  * •

IVS B0952$-$185—associated absorption at the emission redshift in both Ly
$\alpha$ and C IV.

  * •

IVS B0956$-$409—Ly $\alpha$ is strongly self-absorbed.

  * •

IVS B1004$-$125—reported as having $z=0.24$ in Simbad (no reference given),
clearly inconsistent with our Gemini spectrum; strong intervening heavy-
element system at $z_{\rm abs}=1.5786\pm 0.0002$ based on Fe II
$\lambda\lambda$2344, 2382, 2586, 2600 and Mg II $\lambda\lambda$2796, 2803
absorption.

  * •

IVS B1020+270—extended red wing in C IV; C III] is not detected due to strong
CCD fringing.

  * •

IVS B1039$-$474—Si IV, C IV and C III] emission lines all show strongly
extended blue wings; redshift is based on the peak positions of the lines.

  * •

IVS B1127$-$443—single-line redshift is supported by stellar absorption
features (G-band, Mg Ib) noted in the plotted spectrum.

  * •

IVS B1143$-$696—spectrum is very similar to that of 3C 273, with strong Fe II
multiplet emission in the region around H $\beta$ (Wampler & Oke, 1967).

  * •

IVS B1722+562—strong associated absorption system at $z_{\rm abs}=2.2463\pm
0.0002$ seen in C IV, Si IV, N V and Ly $\alpha$. This has led to a relatively
large uncertainty in emission redshift.

  * •

IVS B2235$-$556—strong self-absorption in the red wing of C IV.

  * •

IVS B2334$-$525—broad Mg II, possibly double-peaked with an extended red wing.

  * •

IVS B2341+295—very blue object based on POSS II sky survey images; rise in the
spectrum redward of 7000 Å may be due to the underlying galaxy or an unrelated
object on the spectrograph slit. Intervening Mg II absorber at $z=0.8644\pm
0.0004$.

###  3.3 Spectra of color-selected quasars

In an attempt to find more high-redshift radio quasars for our VLBI proper
motion studies as a function of redshift, we selected five weak radio sources
from the FIRST and NVSS catalogs for which the SDSS colors suggested the
likelihood of $u$\- or $g$-band dropouts and the possibility of high
redshifts. Spectra were obtained at the NOT on the nights of 2012 May 24–26.
The SDSS colors, wavelengths and redshifts for the five color-selected radio
quasars are given in Table 4. The ‘bluest’ of the five, NVSS J125944+240707,
was a $z=1.139$ radio galaxy, but the other four proved to be broad emission-
line quasars with redshifts in excess of 3.5, including three with $z>4$. This
is an excellent return for our search and a striking result from the NOT, the
smallest of the telescopes used in this program. The five spectra are shown in
Fig. 4 and further information is given in Table 4. Redshifts for the $z>4$
quasars are based on estimated wavelengths for Ly$\alpha$ (and, in one case,
Ly$\beta$) and are very uncertain because of strong absorption in the blue
wing of the line.

A comparison between the FIRST and NVSS flux densities at 1.4 GHz for the five
sources showed that one, NVSS J145459+110928, appeared to show evidence of
variability, with $S_{\rm NVSS}=9.8\pm 0.5$ mJy and $S_{\rm FIRST}=15.07\pm
0.14$ mJy. This is also the only source that is unresolved in FIRST. The other
four sources all show minor extension at the $1\arcsec$ level.

Figure 4: Spectra of the five color-selected quasars from NVSS/FIRST and SDSS.
Dashed lines (blue) indicate emission lines used for redshift determination;
dot-dashed lines (red) indicate lines detected at a lower signal-to-noise
ratio or blended. Further details are given in Table 4.

##  4 Redshift distributions

Together with the 31 redshifts reported in Titov et al. (2011), we have now
accumulated over 150 redshifts for IVS sources, mostly in the south. Their
optical counterparts are systematically fainter than those in the Titov &
Malkin (2009) compilation. Since the IVS selection process is directed at
compact, milliarcsecond radio quasars, it is important to test whether their
redshift distribution differs from that of the FIRST-SDSS quasar sample
(Kimball et al., 2011), which is selected without regard to morphology,
spectral index or angular size and extends to much lower flux densities.

The redshift distribution of the sources from this paper and Titov et al.
(2011) is shown in Figure 5(a). For comparison, Figure 5(b) shows the
distribution of 1594 point sources with known redshifts from ICRF2, using
redshift data from Titov & Malkin (2009). The SuperCOSMOS Hambly et al. (2001)
morphological classification was used to remove galaxies from the Titov &
Malkin (2009) list, and the sample was further restricted to those with radio-
optical offsets $<1^{\prime\prime}$ and Galactic latitudes $>10^{\circ}$
(Schaefer et al. 2013, in prep.).

The redshift distribution for the sources from this paper and the earlier
paper (Titov et al., 2011) is completely consistent with having been drawn
from the same redshift distribution as FIRST-SDSS quasars (Kimball et al.,
2011), with a Kolmogorov-Smirnov test giving a probability $p=0.84$ of the two
samples being drawn from the same distribution. Thus the sharp drop-off that
we see in the number of quasars at $z\gtrsim 2$ is a reflection of the
underlying quasar distribution, and not a selection effect of the IVS
candidate sources. While the K-S plot for the ICRF2 sample shows an apparent
excess of low-redshift sources compared with FIRST-SDSS, the difference is not
significant, with a K-S probability of $p=0.24$. We attribute this excess to
selection effects arising from the redshifts in (Titov & Malkin, 2009) being
drawn from the literature, and therefore likely to be biased towards brighter,
lower-redshift quasars.

(a) (b)

Figure 5: (a) Distribution of redshifts among the $\sim$150 IVS sources from
this paper and the previous paper (Titov et al., 2011, abbreviated above as
T11). The lower panel shows the cumulative redshift distribution (K-S test)
compared with the FIRST-SDSS sample (Kimball et al., 2011). (b) Corresponding
redshift distribution and K-S test for 1594 ICRF2 quasars from Titov & Malkin
(2009); see text.

##  5 Summary and conclusion

We present redshifts and spectra for 120 emission-line objects identified with
radio sources from the candidate International Celestial Reference Catalog.
Most of the target objects are in the south and many had not previously been
optically identified. While redshifts were usually based on two or more lines,
those for 22 objects were based on a single emission line, in most cases
assumed to be Mg II; many of these single-line redshifts were supported by
other spectral information and most are considered reliable. In addition, we
classed 19 sources as probable BL Lac objects, based on a high signal-to-noise
ratio but featureless spectra. A further 18 targets were considered to have a
signal-to-noise ratio too low for confident spectral classification.

The distribution of redshifts from this paper, together with those from our
earlier paper (Titov et al., 2011), is consistent with the much larger sample
drawn from FIRST and SDSS (Kimball et al., 2011). This implies that the ultra-
compact, flat-spectrum sources that make up the IVS Reference Catalog are not
distinguished from the radio quasar population at large. On the other hand,
the distribution of redshifts from the much larger sample drawn from ICRF2
(Titov & Malkin, 2009) has a small, but not significant excess of low-redshift
quasars, almost certainly the result of observational selection.

##  6 Acknowledgments

This paper is based on observations collected at five telescopes:

1\. ESO New Technology Telescope, under the European Organisation for
Astronomical Research in the Southern Hemisphere, Chile under program
088.A-0021(A).

2\. Two Gemini Observatories, which are operated by the Association of
Universities for Research in Astronomy, Inc., under a cooperative agreement
with the National Science Foundation on behalf of the Gemini partnership: the
National Science Foundation (United States), the Science and Technology
Facilities Council (United Kingdom), the National Research Council (Canada),
CONICYT (Chile), the Australian Research Council (Australia), Ministurio da
Ciuncia, Tecnologia e Inovacio (Brazil) and Ministerio de Ciencia, Tecnologia
e Innovacion Productiva (Argentina) under programs GS-2011A-Q-89 and
GS-2011B-Q-94 (Gemini South), and GN-2011B-Q-109 (Gemini North).

3\. Six-meter Big Azimuthal Telescope (BTA) operated by the Special
Astrophysical Observatory (Russia)

4\. Nordic Optical Telescope, operated on the island of La Palma jointly by
Denmark, Finland, Iceland, Norway and Sweden, in the Spanish Observatorio del
Roque de los Muchachos of the Instituto de Astrofisica de Canarias.

Two of us, Titov and Jauncey, were supported by a travel grant from the
Australian Nuclear Science Technology Organisation (ANSTO) in their Access to
Major Research Facilities Program (AMRFP) (reference number AMRFP 10/11-O-31)
to travel to the BTA telescope in Russia.

Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the
Participating Institutions, the National Science Foundation and the U.S.
Department of Energy Office of Science. The SDSS-III web site is
http://www.sdss3.org/.

SDSS-III is managed by the Astrophysical Research Consortium for the
Participating Institutions of the SDSS-III Collaboration including the
University of Arizona, the Brazilian Participation Group, Brookhaven National
Laboratory, University of Cambridge, Carnegie Mellon University, University of
Florida, the French Participation Group, the German Participation Group,
Harvard University, the Instituto de Astrofisica de Canarias, the Michigan
State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence
Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max
Planck Institute for Extraterrestrial Physics, New Mexico State University,
New York University, Ohio State University, Pennsylvania State University,
University of Portsmouth, Princeton University, the Spanish Participation
Group, University of Tokyo, University of Utah, Vanderbilt University,
University of Virginia, University of Washington, and Yale University.

AuScope is funded under the National Collaborative Research Infrastructure
Strategy (NCRIS), an Australian Commonwealth Government Programme.

This paper is published with the permission of the CEO, Geoscience Australia.

© Commonwealth of Australia (Geoscience Australia) 2013. This product is
released under the Creative Commons Attribution 3.0 Australia Licence.
http://creativecommons.org/licenses/by/3.0/au/deed.en

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Table 1: Observed emission lines  Source | RA (J2000)aaICRF2 radio position | Dec (J2000)aaICRF2 radio position | TelescopebbTelescope abbreviations: BTA = Big Azimuthal Telescope, GS = Gemini North, NOT = Nordic Optical Telescope, NTT = ESO New Technology Telescope | Line | Rest $\lambda$ | Obs $\lambda$ccSquare brackets indicate the line was not used for redshift determination | $\overline{z}$ | Notedd“S” denotes a single-line redshift; * indicates a note in Section 3.2. Previously determined redshifts are from: [A09] Afanas’ev et al. (2009); [S12] Shaw et al. (2012); [S] Simbad database; [6dF] 6dF survey, Jones et al. (2009)
---|---|---|---|---|---|---|---|---
IVS B0022$-$227 | 00 25 24.2474 |  $-$22 27 47.596 | GS | Mg ii | 2799.9 | 5136.3 | $0.834\pm 0.001$ |  S
IVS B0032$+$276 | 00 34 43.4861 |  $+$27 54 25.721 | BTA | Ly $\alpha$ | 1215.7 | 4820.4 |  |
|  |  |  | N v | 1240.1 | [4921.7] |  |
|  |  |  | Si iv | 1398.3 | [5545.9] |  |
|  |  |  | C iv | 1549.5 | 6141.2 | $2.9642\pm 0.0009$ |
IVS B0044$-$846 | 00 44 26.6883 |  $-$84 22 39.988 | GS | Mg ii | 2799.9 | 5697.2 | $1.035\pm 0.001$ |  S $z=1.032$ [S12]
IVS B0205$-$619 | 02 06 40.0029 |  $-$61 43 32.206 | NTT | C ii] | 2326.9 | [4032.5] |  |
|  |  |  | Mg ii | 2799.9 | 4855.9 |  |
|  |  |  | [O ii] | 3726.8 | 6454.0 |  |
|  |  |  | [Ne iii] | 3868.7 | 6694.0 |  |
|  |  |  | [O iii] | 5006.8 | 8661.5 | $0.7316\pm 0.0010$ |
IVS B0206$-$625 | 02 08 01.1713 |  $-$62 16 35.533 | GS/NTT | Ly $\alpha$ | 1215.7 | 4114.9 |  |
|  |  |  | N v | 1240.1 | [4198.6] |  |
|  |  |  | Si iv | 1398.3 | [4733.6] |  |
|  |  |  | C iv | 1549.5 | 5237.6 |  |
|  |  |  | C iii] | 1908.7 | 6451.8 | $2.3817\pm 0.0016$ |
IVS B0213$-$015 | 02 16 05.6638 |  $-$01 18 03.397 | GS | Ly $\alpha$ | 1215.7 | 4624.9 |  |
|  |  |  | N v | 1240.1 | [4720.2] |  |
|  |  |  | Si iv | 1398.3 | [5326.7] |  |
|  |  |  | C iv | 1549.5 | 5887.3 |  |
|  |  |  | C iii] | 1908.7 | 7261.7 | $2.8028\pm 0.0017$ |
IVS B0219$-$637 | 02 20 54.1727 |  $-$63 30 19.387 | GS | C iii] | 1908.7 | 4730.2 |  |
|  |  |  | Mg ii | 2799.9 | 6937.4 | $1.4780\pm 0.0003$ |
IVS B0226$-$375 | 02 28 33.7343 |  $-$37 19 56.338 | NTT | Ly $\alpha$ | 1215.7 | 3842.4 |  |
|  |  |  | Si iv | 1398.3 | [4408.5] |  |
|  |  |  | C iv | 1549.5 | 4881.0 |  |
|  |  |  | C iii] | 1908.7 | 6014.0 | $2.1538\pm 0.0034$ |
IVS B0233$-$478 | 02 35 06.4235 |  $-$47 37 10.574 | GS | Al iii | 1858.8 | [4692.1] |  |
|  |  |  | C iii] | 1908.7 | [4784.9] |  |
|  |  |  | Mg ii | 2799.9 | 7011.2 | $1.504\pm 0.001$ |  S *
IVS B0301$-$721 | 03 01 38.4456 |  $-$71 56 34.399 | GS | Mg ii | 2799.9 | 5105.8 |  |
|  |  |  | [O ii] | 3726.8 | 6795.7 |  |
|  |  |  | [Ne iii] | 3868.7 | 7051.2 | $0.8232\pm 0.0003$ |
IVS B0318$-$388 | 03 20 46.4048 |  $-$38 37 28.503 | NTT | C iii] | 1908.7 | 4191.0 |  |
|  |  |  | Mg ii | 2799.9 | 6151.3 | $1.1964\pm 0.0006$ |
IVS B0319$-$056 | 03 21 59.8703 |  $-$05 26 12.429 | NTT | Mg ii | 2799.9 | 4417.8 |  |
|  |  |  | H $\gamma$ | 4340.5 | 6843.3 |  |
|  |  |  | H $\beta$ | 4861.3 | 7686.5 | $0.5785\pm 0.0014$ |
IVS B0319$-$315 | 03 21 28.7402 |  $-$31 22 56.336 | NTT | Si iv | 1398.3 | [3900.0] |  |
|  |  |  | C iv | 1549.5 | 4316.8 |  |
|  |  |  | C iii] | 1908.7 | 5312.2 |  |
|  |  |  | Mg ii | 2799.9 | [7783.9] | $1.7845\pm 0.0014$ |
IVS B0340$-$600 | 03 41 21.6148 |  $-$59 54 08.907 | GS | C iv | 1549.5 | 4746.4 |  |
|  |  |  | He ii | 1640.4 | 5026.6 |  |
|  |  |  | C iii] | 1908.7 | 5847.5 | $2.0637\pm 0.0004$ |
IVS B0341$+$158 | 03 44 23.1721 |  $+$15 59 43.369 | GS/NOT | Ly $\alpha$ | 1215.7 | 3993.3 |  |
|  |  |  | C iv | 1549.5 | 5071.8 |  |
|  |  |  | C iii] | 1908.7 | 6240.7 | $2.276\pm 0.005$ |
IVS B0343$+$485 | 03 47 11.6133 |  $+$48 42 37.473 | GN | C iii] | 1908.7 | [5798.6] |  |
|  |  |  | Mg ii | 2799.9 | 8519.1 | $2.043\pm 0.002$ |  S
IVS B0346$+$514 | 03 50 25.0515 |  $+$51 38 38.734 | GN | Mg ii | 2799.9 | 6823.8 | $1.437\pm 0.001$ |  S
IVS B0355$-$669 | 03 55 47.8834 |  $-$66 45 33.817 | GS | Mg ii | 2799.9 | 4970.3 |  |
|  |  |  | [Ne v] | 3425.5 | 6081.2 |  |
|  |  |  | [O ii] | 3726.8 | 6619.3 |  |
|  |  |  | [Ne iii] | 3868.7 | 6866.0 |  |
|  |  |  | [Ne iii] | 3969.8 | [7052.8] |  |
|  |  |  | H $\delta$ | 4101.7 | [7285.6] | $0.7753\pm 0.0003$ |
IVS B0410$-$519 | 04 11 37.1499 |  $-$51 49 23.350 | GS/NTT | C iii] | 1908.7 | 4306.7 |  |
|  |  |  | Mg ii | 2799.9 | 6319.2 | $1.2566\pm 0.0003$ |
IVS B0412$-$779 | 04 10 42.3092 |  $-$77 50 43.293 | GS | Si iv | 1398.3 | [4820.2] |  |
|  |  |  | C iv | 1549.5 | 5343.9 |  |
|  |  |  | He ii | 1640.4 | [5656.4] |  |
|  |  |  | C iii] | 1908.7 | 6583.0 | $2.4489\pm 0.0002$ |
IVS B0416$-$216 | 04 19 00.4182 |  $-$21 32 35.675 | NTT | C iv | 1549.5 | 4103.8 |  |
|  |  |  | C iii] | 1908.7 | 5044.8 |  |
|  |  |  | Mg ii | 2799.9 | [7428.9] | $1.6458\pm 0.0027$ |
IVS B0417$-$302 | 04 19 47.2054 |  $-$30 10 23.835 | GS | Mg ii | 2799.9 | 5609.2 | $1.003\pm 0.002$ |  S *
IVS B0418$-$151 | 04 20 18.3933 |  $-$15 01 26.576 | NTT | C iii] | 1908.7 | 4160.1 |  |
|  |  |  | Mg ii | 2799.9 | 6102.3 | $1.1795\pm 0.0002$ |
IVS B0428$-$042 | 04 31 28.0885 |  $-$04 06 27.319 | GS | Mg ii | 2799.9 | 4556.9 |  |
|  |  |  | [O ii] | 3726.8 | 6065.9 |  |
|  |  |  | [Ne iii] | 3868.7 | 6298.0 |  |
|  |  |  | H $\gamma$ | 4340.5 | [7072.0] |  |
|  |  |  | [O iii] | 4363.2 | [7098.9] |  |
|  |  |  | H $\beta$ | 4861.3 | [7918.0] |  |
|  |  |  | [O iii] | 4958.9 | 8072.2 |  |
|  |  |  | [O iii] | 5006.8 | 8151.6 | $0.6278\pm 0.0002$ |
IVS B0432$-$606 | 04 33 34.1084 |  $-$60 30 13.769 | GS | Mg ii | 2799.9 | 5403.6 |  |
|  |  |  | [Ne v] | 3345.4 | 6458.1 |  |
|  |  |  | [Ne v] | 3425.5 | 6612.6 |  |
|  |  |  | [O ii] | 3726.8 | 7193.1 | $0.9301\pm 0.0002$ |
IVS B0432$+$254 | 04 35 34.5829 |  $+$25 32 59.696 | GN | [Ne v] | 3425.5 | [5483.6] |  |
|  |  |  | H $\epsilon$ | 3969.8 | [6364.5] |  |
|  |  |  | H $\delta$ | 4101.7 | [6573.0] |  |
|  |  |  | H $\gamma$ | 4340.5 | [6952.7] |  |
|  |  |  | H $\beta$ | 4861.3 | 7792.2 |  |
|  |  |  | [O iii] | 4958.9 | 7942.9 |  |
|  |  |  | [O iii] | 5006.8 | 8021.0 | $0.6021\pm 0.0003$ |
IVS B0437$-$303 | 04 39 53.2015 |  $-$30 17 45.624 | GS/NTT | C iv | 1549.5 | 3793.0 |  |
|  |  |  | He ii | 1640.4 | [4016.3] |  |
|  |  |  | C iii] | 1908.7 | 4669.5 |  |
|  |  |  | Mg ii | 2799.9 | 6851.0 | $1.4466\pm 0.0002$ |
IVS B0446$-$265 | 04 48 23.9646 |  $-$26 26 14.821 | NTT | Si iv | 1398.3 | [3862.7] |  |
|  |  |  | C iv | 1549.5 | 4282.5 |  |
|  |  |  | C iii] | 1908.7 | 5276.4 |  |
|  |  |  | Mg ii | 2799.9 | [7731.9] | $1.7641\pm 0.0004$ |
IVS B0447$-$507 | 04 48 22.3029 |  $-$50 41 33.827 | GS | C iii] | 1908.7 | 4724.1 |  |
|  |  |  | Mg ii | 2799.9 | 6949.0 | $1.4785\pm 0.0034$ |  *
IVS B0448$-$482 | 04 49 39.5904 |  $-$48 09 40.709 | GS | Al iii | 1858.8 | [4683.2] |  |
|  |  |  | C iii] | 1908.7 | [4765.2] |  |
|  |  |  | Mg ii | 2799.9 | 6992.4 | $1.497\pm 0.001$ |  S *
IVS B0450$-$469 | 04 51 53.3452 |  $-$46 53 19.888 | GS | Mg ii | 2799.9 | 4485.8 |  |
|  |  |  | [Ne v] | 3425.5 | 5486.0 |  |
|  |  |  | [O ii] | 3726.8 | 5970.9 |  |
|  |  |  | [Ne iii] | 3868.7 | 6196.0 |  |
|  |  |  | [Ne iii] | 3969.8 | 6355.7 |  |
|  |  |  | H $\delta$ | 4101.7 | [6562.1] |  |
|  |  |  | H $\gamma$ | 4340.5 | 6952.9 |  |
|  |  |  | [O iii] | 4363.2 | 6986.5 | $0.6016\pm 0.0002$ |
IVS B0455$-$183 | 04 57 54.3252 |  $-$18 19 16.072 | GS | C iii] | 1908.7 | 4825.1 |  |
|  |  |  | Mg ii | 2799.9 | 7071.2 | $1.5267\pm 0.0012$ |
IVS B0503$-$608 | 05 04 01.7011 |  $-$60 49 52.539 | NTT | Mg ii | 2799.9 | 5702.0 | $1.037\pm 0.002$ |  S
IVS B0511$+$009 | 05 13 40.0325 |  $+$01 00 21.654 | NTT | Ly $\alpha$ | 1215.7 | 4479.2 |  |
|  |  |  | N v | 1240.1 | [4566.9] |  |
|  |  |  | Si iv | 1398.3 | [5156.0] |  |
|  |  |  | C iv | 1549.5 | 5698.4 |  |
|  |  |  | C iii] | 1908.7 | 7016.5 | $2.6794\pm 0.0026$ |
IVS B0514$-$156 | 05 16 57.1855 |  $-$15 37 10.367 | NTT | C iv | 1549.5 | 4029.7 |  |
|  |  |  | C iii] | 1908.7 | 4948.2 |  |
|  |  |  | Mg ii | 2799.9 | 7257.3 | $1.5950\pm 0.0028$ |
IVS B0515$-$053 | 05 17 28.1101 |  $-$05 20 40.842 | NTT | C iv | 1549.5 | [3744.3] |  |
|  |  |  | C iii] | 1908.7 | 4602.1 |  |
|  |  |  | Mg ii | 2799.9 | 6760.8 | $1.4129\pm 0.0018$ |
IVS B0519$-$176 | 05 21 23.5574 |  $-$17 37 30.184 | GS | [O ii] | 3726.8 | 5022.4 |  |
|  |  |  | [Ne iii] | 3868.7 | [5213.1] |  |
|  |  |  | H $\beta$ | 4861.3 | 6548.4 |  |
|  |  |  | [O iii] | 4958.9 | 6686.0 |  |
|  |  |  | [O iii] | 5006.8 | 6744.8 | $0.3475\pm 0.0003$ |
IVS B0520$-$165 | 05 22 44.6549 |  $-$16 27 52.405 | NTT | Si iv | 1398.3 | [4105.3] |  |
|  |  |  | C iv | 1549.5 | 4532.1 |  |
|  |  |  | C iii] | 1908.7 | 5588.8 |  |
|  |  |  | Mg ii | 2799.9 | [8220.0] | $1.9265\pm 0.0016$ |
IVS B0521$-$262 | 05 23 18.4695 |  $-$26 14 09.555 | NTT | Ly $\alpha$ | 1215.7 | [5020.9] |  |
|  |  |  | Si iv | 1398.3 | [5773.0] |  |
|  |  |  | C iv | 1549.5 | 6366.5 |  |
|  |  |  | C iii] | 1908.7 | 7842.3 | $3.1087\pm 0.0002$ |  *
IVS B0524$-$485 | 05 26 16.6713 |  $-$48 30 36.791 | NTT | C iii] | 1908.7 | 4393.6 |  |
|  |  |  | Mg ii | 2799.9 | 6457.5 | $1.3041\pm 0.0022$ |  $z=1.299$ [S]
IVS B0529$-$031 | 05 32 07.5192 |  $-$03 07 07.037 | GN | Mg ii | 2799.9 | 8063.7 | $1.880\pm 0.002$ |  S *
IVS B0548$-$527 | 05 49 43.8055 |  $-$52 46 25.962 | NTT | Mg ii | 2799.9 | 4061.2 |  |
|  |  |  | [Ne v] | 3425.5 | 4956.9 |  |
|  |  |  | [O ii] | 3726.8 | 5392.3 |  |
|  |  |  | [Ne iii] | 3868.7 | [5603.7] |  |
|  |  |  | [Ne iii] | 3967.8 | [5743.2] |  |
|  |  |  | H $\delta$ | 4101.7 | [5931.7] |  |
|  |  |  | H $\gamma$ | 4340.5 | [6303.7] |  |
|  |  |  | [O iii] | 4363.2 | [6314.3] |  |
|  |  |  | H $\beta$ | 4861.3 | 7053.1 |  |
|  |  |  | [O iii] | 4958.9 | 7171.7 |  |
|  |  |  | [O iii] | 5006.8 | 7242.2 | $0.4467\pm 0.0002$ |  *
IVS B0554$+$242 | 05 57 04.7135 |  $+$24 13 55.298 | NOT | Ly $\alpha$ | 1215.7 | 5148.3 |  |
|  |  |  | C iv | 1549.5 | 6541.6 | $3.228\pm 0.007$ |  *
IVS B0558$+$234 | 06 01 47.3569 |  $+$23 24 53.484 | GN | H $\beta$ | 4861.3 | 6205.1 |  |
|  |  |  | [O iii] | 4958.9 | 6311.4 |  |
|  |  |  | [O iii] | 5006.8 | 6373.6 |  |
|  |  |  | He i | 5875.6 | [7494.5] |  |
|  |  |  | H $\alpha$ | 6562.8 | 8356.7 |  |
|  |  |  | [N ii] | 6583.5 | 8381.7 | $0.2737\pm 0.0007$ |
IVS B0559$-$276 | 06 01 48.7208 |  $-$27 36 22.011 | NTT | C iv | 1549.5 | 4125.9 |  |
|  |  |  | C iii] | 1908.7 | 5083.6 |  |
|  |  |  | Mg ii | 2799.9 | 7461.8 | $1.6637\pm 0.0007$ |
IVS B0559$-$200 | 06 01 52.8263 |  $-$20 04 45.212 | NTT | C iii] | 1908.7 | 4244.2 |  |
|  |  |  | Mg ii | 2799.9 | 6226.8 | $1.2238\pm 0.0002$ |  * $z=1.216$ [S12]
IVS B0601$+$245 | 06 04 55.1213 |  $+$24 29 55.036 | NOT | C iii] | 1908.7 | [4068.2] |  |
|  |  |  | Mg ii | 2799.9 | 5972.3 | $1.133\pm 0.002$ |  S
IVS B0608$-$230 | 06 10 38.7873 |  $-$23 01 45.836 | NTT | Ly $\beta$ | 1025.7 | [3978.2] |  |
|  |  |  | Ly $\alpha$ | 1215.7 | 4688.8 |  |
|  |  |  | N v | 1240.1 | [4766.8] |  |
|  |  |  | Si iv | 1398.3 | [5390.8] |  |
|  |  |  | C iv | 1549.5 | 5957.8 |  |
|  |  |  | C iii] | 1908.7 | 7367.8 | $2.854\pm 0.005$ |  *
IVS B0620$-$194 | 06 22 28.5370 |  $-$19 27 18.178 | NTT | Ly $\alpha$ | 1215.7 | [3900.0] |  |
|  |  |  | N v | 1240.1 | [3963.9] |  |
|  |  |  | Si iv | 1398.3 | [4481.8] |  |
|  |  |  | C iv | 1549.5 | 4941.1 |  |
|  |  |  | C iii] | 1908.7 | 6089.2 | $2.1895\pm 0.0007$ |
IVS B0633$-$26B | 06 35 19.4162 |  $-$26 20 55.717 | NTT | Mg ii | 2799.9 | 7467.0 | $1.67:$ |  S *
IVS B0642$-$617 | 06 42 46.9991 |  $-$61 50 08.674 | NTT | C iii] | 1908.7 | 4243.5 |  |
|  |  |  | Mg ii | 2799.9 | 6224.4 | $1.2232\pm 0.0001$ |
IVS B0657$-$586 | 06 58 13.7788 |  $-$58 40 27.567 | NTT | Mg ii | 2799.9 | [3985.7] |  |
|  |  |  | [O ii] | 3726.8 | 5299.9 |  |
|  |  |  | [O iii] | 4958.9 | 7045.9 |  |
|  |  |  | [O iii] | 5006.8 | 7114.8 | $0.4213\pm 0.0004$ |
IVS B0718$-$622 | 07 19 04.4740 |  $-$62 18 02.444 | NTT | C iii] | 1908.7 | 4288.3 |  |
|  |  |  | Mg ii | 2799.9 | 6289.4 |  |
|  |  |  | [O ii] | 3726.0 | [8376.6] | $1.2465\pm 0.0003$ |
IVS B0726$-$132 | 07 29 17.8177 |  $-$13 20 02.271 | NTT | H $\beta$ | 4861.3 | [6512.0] |  |
|  |  |  | [O iii] | 4958.9 | 6659.1 |  |
|  |  |  | [O iii] | 5006.8 | 6729.8 | $0.3435\pm 0.0006$ |
IVS B0728$-$320 | 07 30 38.2983 |  $-$32 08 20.176 | NTT | Mg ii | 2799.9 | 4249.5 |  |
|  |  |  | [O ii] | 3726.8 | 5652.6 |  |
|  |  |  | H $\gamma$ | 4340.5 | [6576.3] |  |
|  |  |  | [O iii] | 4363.2 | 6613.2 |  |
|  |  |  | H $\beta$ | 4861.3 | [7355.1] |  |
|  |  |  | [O iii] | 4958.9 | 7510.5 |  |
|  |  |  | [O iii] | 5006.8 | 7584.2 | $0.5159\pm 0.0006$ |
IVS B0748$-$006 | 07 51 10.2050 |  $-$00 46 51.055 | NTT | Ly $\alpha$ | 1215.7 | 3779.5 |  |
|  |  |  | Si iv | 1398.3 | [4342.6] |  |
|  |  |  | C iv | 1549.5 | 4804.4 |  |
|  |  |  | C iii] | 1908.7 | 5903.0 | $2.101\pm 0.005$ |
IVS B0754$-$155 | 07 56 50.6989 |  $-$15 42 05.436 | GS | C iii] | 1908.7 | 4618.2 |  |
|  |  |  | C ii] | 2326.9 | [5631.8] |  |
|  |  |  | Mg ii | 2799.9 | 6778.3 | $1.4202\pm 0.0007$ |
IVS B0802$-$170 | 08 04 33.7013 |  $-$17 12 04.200 | NTT | C iii] | 1908.7 | 3893.6 |  |
|  |  |  | Mg ii | 2799.9 | 5727.0 | $1.0427\pm 0.0028$ |
IVS B0810$-$180 | 08 12 28.5159 |  $-$18 10 42.813 | GS | Ly $\alpha$ | 1215.7 | 4830.5 |  |
|  |  |  | N v | 1240.1 | [4927.3] |  |
|  |  |  | C iv | 1549.5 | 6154.3 | $2.9726\pm 0.0009$ |  *
IVS B0828$-$064 | 08 30 49.7439 |  $-$06 36 19.988 | NTT | C iv | 1549.5 | 4236.8 |  |
|  |  |  | C iii] | 1908.7 | 5200.9 | $1.730\pm 0.005$ |  *
IVS B0828$-$222 | 08 31 09.1490 |  $-$22 28 26.804 | NTT | C iv | 1549.5 | 4031.3 |  |
|  |  |  | C iii] | 1908.7 | 4958.6 |  |
|  |  |  | Mg ii | 2799.9 | 7274.2 | $1.5992\pm 0.0012$ |
IVS B0834$-$729 | 08 33 43.1410 |  $-$73 05 26.204 | NTT | Si iv | 1398.3 | [4188.8] |  |
|  |  |  | C iv | 1549.5 | 4630.8 |  |
|  |  |  | C iii] | 1908.7 | 5707.0 |  |
|  |  |  | Mg ii | 2799.9 | [8389.8] | $1.9893\pm 0.0007$ |
IVS B0844$-$557 | 08 45 49.6795 |  $-$55 55 26.744 | NTT | Mg ii | 2799.9 | 4026.5 |  |
|  |  |  | H $\gamma$ | 4340.5 | [6246.6] |  |
|  |  |  | [O iii] | 4363.2 | [6253.8] |  |
|  |  |  | H $\beta$ | 4861.3 | 6986.6 |  |
|  |  |  | [O iii] | 4958.9 | 7105.9 |  |
|  |  |  | [O iii] | 5006.8 | 7174.3 | $0.4329\pm 0.0001$ |  *
IVS B0859$-$068 | 09 01 44.2393 |  $-$07 02 16.067 | NTT | Si iv | 1398.3 | [3852.0] |  |
|  |  |  | C iv | 1549.5 | 4244.5 |  |
|  |  |  | C iii] | 1908.7 | 5224.3 |  |
|  |  |  | Mg ii | 2799.9 | [7705.7] | $1.7382\pm 0.0011$ |
IVS B0909$-$745 | 09 09 20.9450 |  $-$74 45 08.148 | NTT | C iii] | 1908.7 | 4268.1 |  |
|  |  |  | Mg ii | 2799.9 | 6268.9 | $1.2376\pm 0.0014$ |
IVS B0924$-$819 | 09 21 42.6981 |  $-$82 09 36.219 | NTT | C iii] | 1908.7 | [4363.4] |  |
|  |  |  | Mg ii | 2799.9 | 6413.4 | $1.291\pm 0.002$ |  S
IVS B0930$-$200 | 09 32 19.5864 |  $-$20 16 37.206 | NTT | C iii] | 1908.7 | 4268.4 |  |
|  |  |  | Mg ii | 2799.9 | 6260.1 | $1.2361\pm 0.0003$ |
IVS B0948$-$860 | 09 41 55.6159 |  $-$86 15 01.817 | GS | Ly $\alpha$ | 1215.7 | 5708.5 |  |
|  |  |  | C iv | 1549.5 | 7281.2 | $3.6974\pm 0.0017$ |  *
IVS B0950$-$246 | 09 52 31.6543 |  $-$24 53 50.885 | NTT | Ly $\alpha$ | 1215.7 | 4410.0 |  |
|  |  |  | Si iv | 1398.3 | [5084.7] |  |
|  |  |  | C iv | 1549.5 | 5612.3 |  |
|  |  |  | C iii] | 1908.7 | [6959.4] | $2.6248\pm 0.0028$ |
IVS B0951$+$488 | 09 55 05.0011 |  $+$48 38 19.042 | GN | [O ii] | 3726.8 | 5718.2 |  |
|  |  |  | H $\beta$ | 4861.3 | 7455.6 |  |
|  |  |  | [O iii] | 5006.8 | 7684.5 | $0.5343\pm 0.0003$ |
IVS B0952$-$185 | 09 55 14.6807 |  $-$18 45 31.866 | NTT | Ly $\alpha$ | 1215.7 | [4779.7] |  |
|  |  |  | N v | 1240.1 | [4904.7] |  |
|  |  |  | Si iv | 1398.3 | 5484.0 |  |
|  |  |  | C iv | 1549.5 | 6056.2 |  |
|  |  |  | C iii] | 1908.7 | 7464.1 | $2.9137\pm 0.0042$ |  *
IVS B0956$-$409 | 09 58 38.2960 |  $-$41 10 33.176 | NTT | Ly $\alpha$ | 1215.7 | [4827.6] |  |
|  |  |  | N v | 1240.1 | [4902.2] |  |
|  |  |  | Si iv | 1398.3 | [5544.5] |  |
|  |  |  | C iv | 1549.5 | 6096.4 |  |
|  |  |  | C iii] | 1908.7 | [7548.6] | $2.934\pm 0.002$ |  S *
IVS B1004$-$125 | 10 07 15.2277 |  $-$12 47 45.995 | GS | Si iv | 1398.3 | 4369.8 |  |
|  |  |  | C iv | 1549.5 | 4833.0 |  |
|  |  |  | C iii] | 1908.7 | 5964.4 | $2.1230\pm 0.0020$ |  * $z=0.24$ [S]
IVS B1005$-$739 | 10 06 04.1454 |  $-$74 09 44.087 | NTT | Ly $\alpha$ | 1215.7 | 3959.0 |  |
|  |  |  | Si iv | 1398.3 | 4533.3 |  |
|  |  |  | C iv | 1549.5 | 5028.5 |  |
|  |  |  | C iii] | 1908.7 | 6153.4 | $2.242\pm 0.007$ |
IVS B1010$-$374 | 10 12 24.0748 |  $-$37 40 05.899 | NTT | Mg ii | 2799.9 | 4196.4 |  |
|  |  |  | [O ii] | 3726.8 | [5562.4] |  |
|  |  |  | [Ne III] | 3869.1 | 5793.8 |  |
|  |  |  | H $\gamma$ | 4340.5 | 6503.4 |  |
|  |  |  | [O iii] | 4363.2 | 6539.5 |  |
|  |  |  | H $\beta$ | 4861.3 | 7292.8 |  |
|  |  |  | [O iii] | 4958.9 | [7420.3] |  |
|  |  |  | [O iii] | 5006.8 | 7506.9 | $0.4991\pm 0.0003$ |
IVS B1013$-$196 | 10 15 52.2525 |  $-$19 52 26.567 | GS | Mg ii | 2799.9 | 5827.5 |  |
|  |  |  | [Ne v] | 3425.5 | [7127.5] | $1.081\pm 0.001$ |  S $z=1.0865$ [6dF]
IVS B1020$+$270 | 10 20 11.1028 |  $+$26 49 41.724 | NOT | Si iv | 1398.3 | 5294.9 |  |
|  |  |  | C iv | 1549.5 | 5876.7 | $2.7900\pm 0.0030$ |
IVS B1023$-$049 | 10 25 45.4229 |  $-$05 09 54.132 | NTT | C iii] | 1908.7 | 4050.3 |  |
|  |  |  | Mg ii | 2799.9 | 5961.1 | $1.1255\pm 0.0035$ |
IVS B1034$-$058 | 10 36 47.5730 |  $-$06 05 41.184 | NTT | C iii] | 1908.7 | 3915.8 |  |
|  |  |  | Mg ii | 2799.9 | 5736.7 | $1.0502\pm 0.0013$ |
IVS B1035$+$046 | 10 37 39.3395 |  $+$04 24 01.745 | NOT | C iv | 1549.5 | 5154.0 |  |
|  |  |  | C iii] | 1908.7 | 6316.8 | $2.318\pm 0.008$ |
IVS B1039$-$474 | 10 41 44.6497 |  $-$47 40 00.064 | GS | Ly $\alpha$ | 1215.7 | 4324.1 |  |
|  |  |  | N v | 1240.1 | [4421.6] |  |
|  |  |  | Si iv | 1398.3 | 4981.2 |  |
|  |  |  | C iv | 1549.5 | 5507.2 |  |
|  |  |  | C iii] | 1908.7 | 6792.5 | $2.5580\pm 0.0017$ |  *
IVS B1055$-$028 | 10 58 11.0106 |  $-$03 09 27.254 | GN | [O ii] | 3726.8 | 6367.3 |  |
|  |  |  | H $\gamma$ | 4340.5 | [7419.4] |  |
|  |  |  | [O iii] | 4363.2 | [7451.9] |  |
|  |  |  | H $\beta$ | 4861.3 | [8306.2] |  |
|  |  |  | [O iii] | 4958.9 | 8468.6 |  |
|  |  |  | [O iii] | 5006.8 | 8553.0 | $0.7082\pm 0.0002$ |
IVS B1102$-$392 | 11 05 11.0815 |  $-$39 28 42.138 | NTT | C iv | 1549.5 | 4042.6 |  |
|  |  |  | C iii] | 1908.7 | 4981.9 |  |
|  |  |  | Mg ii | 2799.9 | 7320.5 | $1.6112\pm 0.0017$ |
IVS B1104$+$525 | 11 07 25.8277 |  $+$52 19 31.636 | NOT | Mg ii | 2799.9 | 5443.8 | $0.944\pm 0.002$ |  S
IVS B1115$-$306 | 11 18 20.6102 |  $-$30 54 58.520 | GS | Si iv | 1398.3 | [4701.3] |  |
|  |  |  | C iv | 1549.5 | 5194.6 |  |
|  |  |  | C iii] | 1908.7 | 6400.0 | $2.3528\pm 0.0004$ |
IVS B1119$-$044 | 11 21 43.1144 |  $-$04 42 36.149 | NTT | C iv | 1549.5 | 4230.9 |  |
|  |  |  | C iii] | 1908.7 | 5211.4 |  |
|  |  |  | Mg ii | 2799.9 | [7660.0] | $1.7304\pm 0.0002$ |
IVS B1121$-$147 | 11 24 02.5656 |  $-$15 01 58.948 | NTT | Ly $\alpha$ | 1215.7 | [4345.9] |  |
|  |  |  | N v | 1240.1 | [4422.3] |  |
|  |  |  | Si iv | 1398.3 | [4990.1] |  |
|  |  |  | C iv | 1549.5 | 5517.5 |  |
|  |  |  | C iii] | 1908.7 | 6796.0 | $2.5607\pm 0.0003$ |
IVS B1121$+$661 | 11 24 24.6667 |  $+$65 55 01.380 | GN | [O ii] | 3726.8 | 5731.3 |  |
|  |  |  | [O iii] | 5006.8 | 7699.9 | $0.5379\pm 0.0001$ |
IVS B1127$-$443 | 11 29 31.7220 |  $-$44 35 49.937 | GS | [O ii] | 3726.8 | 4906.7 | $0.317\pm 0.001$ |  S *
IVS B1129$-$161 | 11 31 36.7478 |  $-$16 28 33.439 | NTT | Mg ii | 2799.9 | 4999.7 | $0.786:$ |  S
IVS B1131$-$088 | 11 33 35.9928 |  $-$09 05 23.401 | NTT | C iii] | 1908.7 | 3804.5 |  |
|  |  |  | Mg ii | 2799.9 | 5574.2 | $0.9920\pm 0.0012$ |
IVS B1143$-$696 | 11 45 53.6241 |  $-$69 54 01.797 | GS | H $\epsilon$ | 3970.1 | 4939.2 |  |
|  |  |  | H $\delta$ | 4101.7 | 5102.7 |  |
|  |  |  | H $\gamma$ | 4340.5 | 5399.8 |  |
|  |  |  | H $\beta$ | 4861.3 | 6043.9 |  |
|  |  |  | [O iii] | 4958.9 | 6160.7 |  |
|  |  |  | [O iii] | 5006.8 | 6222.2 | $0.2434\pm 0.0003$ |  *
IVS B1152$+$462 | 11 55 11.0092 |  $+$45 55 39.624 | GN | [O ii] | 3726.8 | 6387.0 |  |
|  |  |  | [Ne iii] | 3868.7 | [6626.9] |  |
|  |  |  | [O iii] | 4958.9 | 8500.2 |  |
|  |  |  | [O iii] | 5006.8 | 8583.2 | $0.7141\pm 0.0002$ |
IVS B1223$+$452 | 12 25 54.619 |  $+$44 56 23.01 | NOT | [O ii] | 3726.8 | 6230.0 |  |
|  |  |  | [Ne iii] | 3868.7 | 6467.2 | $0.6716\pm 0.0001$ |
IVS B1241$+$410 | 12 43 55.7815 |  $+$40 43 58.451 | NOT | C iii] | 1908.7 | 4806.4 |  |
|  |  |  | Mg ii | 2799.9 | 7050.3 | $1.5181\pm 0.0002$ |
IVS B1338$+$362 | 13 40 36.0099 |  $+$36 00 26.737 | NOT | [O ii] | 3726.8 | 6564.5 |  |
|  |  |  | Ca K | 3937.8 | 6956.1 |  |
|  |  |  | Ca H | 3969.6 | 6993.5 | $0.7632\pm 0.0016$ |
IVS B1446$-$111 | 14 48 51.1600 |  $-$11 22 15.737 | GS | Ly $\alpha$ | 1215.7 | 4416.3 |  |
|  |  |  | N v | 1240.1 | [4506.0] |  |
|  |  |  | Si iv | 1398.3 | [5080.7] |  |
|  |  |  | C iv | 1549.5 | 5628.4 |  |
|  |  |  | He ii | 1640.4 | 5960.1 |  |
|  |  |  | C iii] | 1908.7 | 6932.0 | $2.6326\pm 0.0004$ |
IVS B1533$+$200 | 15 35 16.560 |  $+$19 54 51.30 | NOT | Ly $\alpha$ | 1215.7 | 5582.7 |  |
|  |  |  | N v | 1240.1 | [5692.8] |  |
|  |  |  | C iv | 1549.5 | 7108.4 | $3.5899\pm 0.0023$ |
IVS B1607$+$563 | 16 08 20.7501 |  $+$56 13 56.375 | NOT | Si iv | 1398.3 | [5723.5] |  |
|  |  |  | C iv | 1549.5 | 6329.8 |  |
|  |  |  | He ii | 1640.4 | 6697.8 | $3.0840\pm 0.0010$ |
IVS B1630$+$505 | 16 31 31.6980 |  $+$50 28 22.493 | NOT | C iv | 1549.5 | 5179.4 |  |
|  |  |  | He ii | 1640.4 | [5497.3] |  |
|  |  |  | C iii] | 1908.7 | 6400.0 | $2.348\pm 0.005$ |
IVS B1641$-$179 | 16 44 35.7468 |  $-$18 04 32.459 | GS | Mg ii | 2799.9 | 5619.4 | $1.007\pm 0.001$ |  S
IVS B1722$+$562 | 17 22 58.0084 |  $+$56 11 22.320 | NOT | Ly $\alpha$ | 1215.7 | 3976.2 |  |
|  |  |  | C iv | 1549.5 | 5077.9 |  |
|  |  |  | C iii] | 1908.7 | 6222.9 | $2.269\pm 0.005$ |  *
IVS B1744$-$629 | 17 49 25.7102 |  $-$62 58 18.950 | GS | C iii] | 1908.7 | [4228.8] |  |
|  |  |  | Mg ii | 2799.9 | 6202.1 | $1.215\pm 0.001$ |  S
IVS B2107$-$016 | 21 10 22.6190 |  $-$01 26 58.242 | GN | Mg ii | 2799.9 | 5331.3 |  |
|  |  |  | [Ne v] | 3425.5 | 6525.0 |  |
|  |  |  | [O ii] | 3726.8 | 7095.6 |  |
|  |  |  | [Ne iii] | 3868.7 | 7366.9 |  |
|  |  |  | H $\gamma$ | 4340.5 | [8263.8] |  |
|  |  |  | [O iii] | 4363.2 | [8308.3] | $0.9043\pm 0.0002$ |
IVS B2112$-$556 | 21 16 29.8161 |  $-$55 27 20.444 | GS | C iv | 1549.5 | 4215.5 |  |
|  |  |  | C iii] | 1908.7 | 5196.8 | $1.7216\pm 0.0011$ |
IVS B2142$-$765 | 21 47 53.1505 |  $-$76 21 29.221 | GS | C iv | 1549.5 | 4464.5 |  |
|  |  |  | C iii] | 1908.7 | 5510.3 | $1.8841\pm 0.0029$ |
IVS B2144$-$065 | 21 47 21.8896 |  $-$06 20 25.342 | GN/BTA | Mg ii | 2799.9 | 5056.1 |  |
|  |  |  | [Ne v] | 3425.5 | 6186.8 |  |
|  |  |  | [O ii] | 3726.8 | 6729.5 |  |
|  |  |  | [Ne iii] | 3868.7 | 6986.2 |  |
|  |  |  | [Ne iii] | 3967.8 | 7166.1 |  |
|  |  |  | H $\delta$ | 4101.7 | 7406.9 |  |
|  |  |  | H $\gamma$ | 4340.5 | 7836.8 |  |
|  |  |  | [O iii] | 4363.2 | 7878.0 | $0.8058\pm 0.0001$ |
IVS B2201$-$778 | 22 06 44.4595 |  $-$77 35 23.761 | GS | Mg ii | 2799.9 | 5544.1 | $0.980\pm 0.001$ |  S
IVS B2202$+$716 | 22 03 30.4676 |  $+$71 51 08.530 | GN | Mg ii | 2799.9 | 7097.4 | $1.535\pm 0.001$ |  S
IVS B2235$-$556 | 22 39 06.0344 |  $-$55 25 59.410 | GS | C iv | 1549.5 | [4591.7] |  |
|  |  |  | C iii] | 1908.7 | 5678.2 | $1.975\pm 0.001$ |  S *
IVS B2251$-$597 | 22 54 56.8282 |  $-$59 26 00.683 | GS | C iv | 1549.5 | 4523.4 |  |
|  |  |  | C iii] | 1908.7 | 5569.5 | $1.9186\pm 0.0007$ |
IVS B2253$+$227 | 22 56 10.6750 |  $+$23 01 45.175 | GN | C iii] | 1908.7 | 5404.3 |  |
|  |  |  | Mg ii | 2799.9 | 7925.2 | $1.8310\pm 0.0005$ |
IVS B2253$-$658 | 22 56 24.8717 |  $-$65 33 25.648 | GS | [Ne iii] | 3868.7 | 4826.9 |  |
|  |  |  | H $\epsilon$ | 3970.1 | [4953.2] |  |
|  |  |  | H $\delta$ | 4101.7 | [5125.5] |  |
|  |  |  | H $\gamma$ | 4340.5 | [5415.1] |  |
|  |  |  | [O iii] | 4363.2 | [5442.1] |  |
|  |  |  | H $\beta$ | 4861.3 | 6066.5 |  |
|  |  |  | [O iii] | 4958.9 | 6186.7 |  |
|  |  |  | [O iii] | 5006.8 | 6246.9 | $0.2477\pm 0.0001$ |
IVS B2300$-$307 | 23 03 05.8207 |  $-$30 30 11.473 | NTT | C iii] | 1908.7 | 3887.4 |  |
|  |  |  | Mg ii | 2799.9 | 5714.3 | $1.0388\pm 0.0021$ |
IVS B2303$+$083 | 23 06 01.2714 |  $+$08 37 15.391 | GN | Mg ii | 2799.9 | 6456.8 |  |
|  |  |  | [Ne v] | 3425.5 | 7890.3 |  |
|  |  |  | [O ii] | 3726.8 | 8598.7 | $1.3056\pm 0.0011$ |
IVS B2309$-$663 | 23 12 58.8400 |  $-$66 07 31.735 | GS | He ii | 1640.4 | [4326.3] |  |
|  |  |  | C iii] | 1908.7 | 5035.1 |  |
|  |  |  | [Ne iv] | 2423.8 | [6393.6] | $1.638\pm 0.001$ |  S
IVS B2325$-$408 | 23 28 19.2648 |  $-$40 35 09.846 | GS | C iv | 1549.5 | 4598.8 |  |
|  |  |  | C iii] | 1908.7 | 5680.3 | $1.972\pm 0.004$ |
IVS B2334$-$525 | 23 37 23.1667 |  $-$52 16 20.103 | GS | C ii] | 2326.9 | [5016.6] |  |
|  |  |  | Mg ii | 2799.9 | 6080.1 | $1.172\pm 0.002$ |  S *
IVS B2341$+$295 | 23 44 22.5524 |  $+$29 52 20.700 | GN | Mg ii | 2799.9 | 5454.4 |  |
|  |  |  | [Ne v] | 3425.5 | [6657.1] |  |
|  |  |  | [O ii] | 3726.8 | 7264.1 |  |
|  |  |  | [Ne iii] | 3868.7 | 7538.5 | $0.9486\pm 0.0003$ |  *
IVS B2355$+$042 | 23 58 28.8469 |  $+$04 30 24.835 | GN | C iv | 1549.5 | 5109.4 |  |
|  |  |  | C iii] | 1908.7 | 6285.7 | $2.2953\pm 0.0021$ |  $z=2.294$ [A09]
Table 2: Probable BL Lac objects Source | RA (J2000)aaICRF2 radio position | Dec (J2000)aaICRF2 radio position | Telescope
---|---|---|---
IVS B0026$-$710 | 00 28 41.5626 |  $-$70 45 15.926 | GS
IVS B0313$-$171 | 03 15 27.6783 |  $-$16 56 29.711 | NTT
IVS B0608$-$187 | 06 10 17.8861 |  $-$18 47 40.090 | GS
IVS B0633$-$263 | 06 35 20.9090 |  $-$26 20 39.866 | NTT
IVS B0700$-$661 | 07 00 31.2531 |  $-$66 10 45.232 | NTT
IVS B0729$-$826 | 07 23 39.4063 |  $-$82 47 41.089 | NTT
IVS B0744$-$158 | 07 46 18.2360 |  $-$15 55 34.745 | NTT
IVS B0752$-$116 | 07 54 26.4564 |  $-$11 47 16.948 | GS
IVS B0804$-$055 | 08 07 09.6175 |  $-$05 41 13.914 | NTT
IVS B0815$-$094 | 08 17 49.7495 |  $-$09 33 30.528 | GS
IVS B1123$-$356 | 11 25 31.4818 |  $-$35 57 03.352 | NTT
IVS B1424$-$328 | 14 27 41.3610 |  $-$33 05 31.505 | GS
IVS B1922$-$224 | 19 25 39.7901 |  $-$22 19 35.112 | GS
IVS B1942$-$313 | 19 45 59.3693 |  $-$31 11 38.356 | GS
IVS B1951$-$115 | 19 54 41.1557 |  $-$11 23 22.641 | GS
IVS B2022$-$289 | 20 25 53.6128 |  $-$28 45 48.697 | GS
IVS B2036$-$109 | 20 39 00.7104 |  $-$10 46 41.863 | GS
IVS B2104$-$668 | 21 08 51.8207 |  $-$66 37 22.744 | GS
IVS B2240$-$064 | 22 43 08.7606 |  $-$06 09 02.567 | GN
Table 3: Objects with low signal-to-noise spectra Source | RA (J2000)aaICRF2 radio position | Dec (J2000)aaICRF2 radio position | Telescope
---|---|---|---
IVS B0205$-$242 | 02 07 33.3992 |  $-$24 02 02.210 | NTT
IVS B0227$-$542 | 02 29 12.7856 |  $-$54 03 24.036 | NTT
IVS B0244$-$050 | 02 46 49.1315 |  $-$04 51 10.933 | NTT
IVS B0253$-$754 | 02 53 10.8816 |  $-$75 13 16.686 | GS
IVS B0334$-$546 | 03 35 53.9248 |  $-$54 30 25.114 | NTT
IVS B0458+138 | 05 01 45.2708 | +13 56 07.220 | NTT
IVS B0516$-$621 | 05 16 44.9261 |  $-$62 07 05.389 | NTT
IVS B0600+219 | 06 03 51.5570 | +21 59 37.698 | GN
IVS B0628$-$627 | 06 28 57.4877 |  $-$62 48 44.744 | NTT
IVS B0705$-$649 | 07 05 26.0526 |  $-$65 00 43.484 | NTT
IVS B0718$-$523 | 07 19 14.2919 |  $-$52 28 32.506 | NTT
IVS B0821$-$094 | 08 23 52.0233 |  $-$09 39 25.907 | NTT
IVS B0905$-$202 | 09 07 54.0404 |  $-$20 26 49.475 | GS
IVS B0939$-$077 | 09 42 21.4614 |  $-$07 59 53.204 | GS
IVS B1118+073 | 11 20 38.4438 | +07 04 47.174 | NTT
IVS B1134$-$739 | 11 36 09.6597 |  $-$74 15 45.274 | NTT
IVS B1821$-$525 | 18 25 13.8097 |  $-$52 30 58.281 | GS
IVS B2020$-$015 | 20 23 32.8163 |  $-$01 23 42.153 | GS
Table 4: SDSS magnitudes and redshifts for five color-selected NVSS radio sources  Source | RA (J2000)aaNVSS radio position | Dec (J2000)aaNVSS radio position | $g$ | $r$ | TelescopebbNordic Optical Telescope | Line | Rest $\lambda$ | Obs $\lambda$ccSquare brackets indicate the line was not used for redshift determination | zddColon indicates approximate redshift based on Ly $\alpha$ alone
---|---|---|---|---|---|---|---|---|---
NVSS J101335+281118 | 10 13 35.49 | +28 11 18.3 | 25.76 | 22.03 | NOT | Ly $\alpha$ | 1215.7 | 6990 |
|  |  |  |  |  | Ly $\beta$ | 1025.7 | 5897 | 4.75:
NVSS J125944+240707 | 12 59 44.59 | +24 07 07.9 | 22.94 | 21.82 | NOT | Mg ii | 2799.9 | 5895.5 | $1.138\pm 0.001$
NVSS J145459+110928 | 14 54 59.36 | +11 09 28.5 | 26.09 | 22.67 | NOT | Ly $\alpha$ | 1215.7 | 7208 | 4.93:
NVSS J162830+115403 | 16 28 30.55 | +11 54 03.5 | 25.27 | 22.25 | NOT | Ly $\alpha$ | 1215.7 | 6650 | 4.47:
NVSS J163400+640821 | 16 34 00.47 | +64 08 21.6 | 24.67eeMagnitudes are $u$ and $g$, respectively, for this object | 19.57eeMagnitudes are $u$ and $g$, respectively, for this object | NOT | Ly $\alpha$ | 1215.7 | [5628.4] |
|  |  |  |  |  | O i/Si ii | 1303.3 | [6039.0] |
|  |  |  |  |  | Si iv | 1398.3 | [6458.1] |
|  |  |  |  |  | C iv | 1549.5 | 7157.7 | $3.619\pm 0.001$
Figure 1: Optical spectra for 120 emission-line IVS targets. Dashed lines
(blue) indicate emission lines used for redshift determination; dot-dashed
lines (red) indicate lines detected at a lower signal-to-noise ratio or
blended. Figure 1 (continued):  Figure 1 (continued):  Figure 1 (continued):
Figure 1 (continued):  Figure 1 (continued):  Figure 1 (continued):  Figure 1
(continued):  Figure 1 (continued):  Figure 1 (continued):  Figure 2: Spectra
of 19 probable BL Lac objects from our observations, classified on the basis
of their featureless spectra; see Table 2 for ICRF2 positions.  Figure 2
(continued):


Distributed Gaussian process (DGP) is a popular approach to scale GP to big data which divides the training data into some subsets, performs local inference for each partition, and aggregates the results to acquire global prediction. To combine the local predictions, the conditional independence assumption is used which basically means there is a perfect diversity between the subsets. Although it keeps the aggregation tractable, it is often violated in practice and generally yields poor results. In this paper, we propose a novel approach for aggregating the Gaussian experts' predictions by Gaussian graphical model (GGM) where the target aggregation is defined as an unobserved latent variable and the local predictions are the observed variables. We first estimate the joint distribution of latent and observed variables using the Expectation-Maximization (EM) algorithm. The interaction between experts can be encoded by the precision matrix of the joint distribution and the aggregated predictions are obtained based on the property of conditional Gaussian distribution. Using both synthetic and real datasets, our experimental evaluations illustrate that our new method outperforms other state-of-the-art DGP approaches.

§ INTRODUCTION

Gaussian processes (GPs) are powerful non-parametric statistical methods based on Bayes' theorem. Without the need for restrictive assumptions, they are capable to estimate complex models with a low amount of uncertainty. They have been widely used in practice, e.g. optimization [Shahriari et al., 2016], data visualization [Lawrence, 2005], reinforcement learning [Deisenroth et al., 2013], multitask learning [Alvarez et al., 2012], online streaming models [Le et al., 2017], and time series analysis [Tobar et al., 2015]. Despite many advantages, GPs suffer from their computational costs where they poorly scale with the size of the dataset.
The prominent distributed Gaussian processes (also called local approximation GPs) are based on the divide-and-conquer approach. It means the training data is divided into some partitions (called experts), the local inference is done for each partition separately, and at the end, these local estimations are combined using an ensemble method. All experts share the same hyper-parameters, which leads to automatic regularisation and the model tends to prevent the overfitting of individual experts [Deisenroth and Ng, 2015].

In a DGP, the conditional independence assumption (CI) between partitions allows factorizing the global posterior distribution as a product of local distributions. Although this assumption reduces the computational cost, it is often violated in practice. However, solutions that deal with the dependency problem (e.g. NPAE method [Rullière et al., 2018]) suffer from extra computational costs and therefore, are impractical for large data sets.

The key contribution of our work lies in aggregating the local experts' predictions considering their dependencies. Unlike conventional DGPs, here the CI assumption is violated to improve the prediction quality. The conditional dependency is inferred as the interactions between nodes in a continuous form of a Markov random field (MRF). We consider the local and latent experts as nodes of an undirected graph. Then, the Gaussian graphical model (GGM) is used to construct the undirected graph between Gaussian experts and their interactions. Since the latent expert is unobserved, we use the latent variable Gaussian graphical model (LVGGM) to estimate the joint distribution of observed and latent experts. The final predictions are the mean of the conditional distribution of the latent expert given observed experts. Relative to the available baselines, our approach substantially provides competitive prediction performance than other state-of-the-art (SOTA) approaches, which use the CI assumption.
The structure of the paper is as follows. Section <ref> introduces the problem formulation and related works. In Section <ref> the proposed model and the inference process are presented. Section <ref> shows the experimental results and we conclude in Section <ref>.

§ BACKGROUND AND PROBLEM SET-UP

§.§ Background

Let us consider the regression problem $y=f(x)+\epsilon$, where $x\in R^d$ and $\epsilon \sim \mathcal{N}(0,\sigma^2)$, and the Gaussian likelihood is $p(y|f)=\mathcal{N}(f, \sigma^2 I)$. The objective is to learn the latent function f from a training set $\mathcal{D}=\{X,y\}$ of size $n$. The Gaussian process regression is a collection of random variables of which any finite subset has a joint Gaussian distribution. The GP then describes a prior distribution over the latent functions as $f \sim GP\left(0,k(x,x') \right)$, where $k(x,x')$ is the covariancee function (kernel) with hyperparameters $\psi$. To train the GP, the hyperparameters $\theta=\{\sigma^2, \psi\}$ should be determined such that they maximise the log-marginal likelihood,

\begin{equation} \label{eq:1}
\log p(y|X)=-\frac{1}{2}y^T\mathcal{C}^{-1}y - \frac{1}{2} \log|\mathcal{C}|- \frac{n}{2} \log2\pi,
\end{equation}

where $\mathcal{C}=K+\sigma^2I$ and $K=k(X,X)$. According to (<ref>), the training step scales as $\mathcal{O}(n^3)$ because it is affected by the inversion and determinant of the $n \times n$ matrix $\mathcal{C}$. Therefore, for large data sets, GP training is a time-consuming task and imposes limitations on the scalability of GPs.

§.§ Distributed Gaussian Process

The term distributed Gaussian process was proposed by [Deisenroth and Ng, 2015] uses the fact that the computations of the standard GP can be distributed among individual computing units. To do that, one divides the full training data set $\mathcal{D}$ into $M$ partitions (called experts) and trains standard GPs on these partitions. Let  $\mathcal{D}^{'}= \{\mathcal{D}_1,\ldots,\mathcal{D}_M\}$ be the partitions, and $X_i$ and $y_i$ be the input and output of partition $\mathcal{D}_i$. All GP experts are trained jointly and share a single set of hyper-parameters $\theta=\{\sigma^2,\psi\}$. For a test set $X^*$ of size $n_t$, the local prediction of the $i$-th GP expert $\mathcal{M}_i$ is:

\begin{align}
\mu_i^* &= k_{i*}^T(K_i+\sigma^2I)^{-1}y_i,\label{eq:2}
\end{align}

where $K_i=k(X_i,X_i)$, and $k_{i*}=k(X_i,X^*)$.

Aggregating the experts in DGP is based on the assumption that they are conditionally independent. For a test input $x^*$, the posterior distribution of DGP is given as the product of multiple local densities, i.e. $p(y^*|\mathcal{D},x^*) \propto \prod_{i=1}^M p_i(y^*|\mathcal{D}_i,x^*)$.
The most popular aggregations are generalised product of experts (GPoE) [Cao and Fleet, 2014], robust Bayesian committee machine (RBCM) [Deisenroth and Ng, 2015] and generalized robust Bayesian committee machine (GRBCM) [Liu et al., 2018], see Appendix <ref>.

§.§ Dependency

The CI assumption is used widely in ensemble methods for both regression and classification problems [Mendes-Moreira et al., 2012, Parisi et al., 2014]. The DGPs use CI to reduce the computational costs of the training and prediction processes. However, their predictions are not accurate enough and CI-based aggregation generally returns sub-optimal solution [Jaffe et al., 2016, Jalali and Kasneci, 2020]. In local approximation GPs, the dependency between experts has been discussed in few works. For instance, the nested pointwise aggregation of experts (NPAE) method [Rullière et al., 2018] uses the internal correlation between local experts and the dependency between local experts and target variable $y^*$. However, this pointwise aggregation suffers from high time complexity which cubically depends on the number of experts at each test point, i.e. $\mathcal{O}(n_t M^3)$, and therefore, it is not an efficient solution for large datasets. Figure <ref> in Appendix <ref> shows the computational graphs of CI-based and dependency-based aggregation strategies.

§ AGGREGATING CONDITIONALLY DEPENDENT EXPERTS WITH AN UNDIRECTED GRAPH

At the heart of our work is the following ingredient. First, we assume that $y_i$ in (<ref>) has not yet been observed, see [Rullière et al., 2018]. Then the experts' predictions $\mu^*_i$ can be considered as a random variable. This allows us to leverage correlations between experts. Then, we exert the Gaussian graphical model, where the nodes of the graph are the experts (local and latent) and the edges are the interactions between them.

§.§ Aggregating Dependent Experts' Predictions

Assume the Gaussian experts $\mathcal{M}=\{\mathcal{M}_1,\ldots,\mathcal{M}_M\}$ have been trained on separated subsets and let $\mu^*=[\mu_1^*,\ldots,\mu_M^*]^T$ be a $ n_t \times M$ matrix that contains their centered predictions at $n_t$ test points. As a consequence of the choice of the prior, the joint distribution of the local experts $\mu^*$ and target expert $y^*$ is multivariate Gaussian distribution because any vector of linear combinations of observation is itself a Gaussian vector. Let $\Sigma_{y^*\mu^*}$ encodes the correlation between latent expert $y^*$ and local experts $\mu^*$, and $\Sigma_{\mu^* \mu^*}$ depicts the correlation between local experts. Employing the properties of conditional Gaussian distributions for the centered random vector allows for the following aggregation:

\begin{equation} \label{aggregated_estimator}
\begin{split}
y_A^* =\Sigma_{y^*\mu^*}^T \Sigma_{\mu^* \mu^*}^{-1}\mu^*.
\end{split}
\end{equation}

which is the mean of conditional distribution of $y^*$ given $\mu^*$, i.e. $p(y^*|\mu^*)$.

$y_A^*$ is the best linear unbiased predictor of $y^*$, i.e. for linear estimators of the form $\beta \mu^* = \sum_{i=1}^M \beta_i \mu_i^*$, the mean square error $(y^*- \beta \mu^*)^2$ is minimized when $\beta=\Sigma_{y^*\mu^*}^T \Sigma_{\mu^*\mu^*}^{-1}$.

The proof of Proposition <ref> can be found in Appendix <ref>. In the next subsection, we show how the GGM can be adapted to the local approximation problem with a latent target variable and suggest a new method to compute the aggregated estimator $y^*_A$.

§.§ Gaussian Graphical Models for Dependent Gaussian Experts

Gaussian graphical models [Rue and Held, 2005, Uhler, 2017, Drton and Maathuis, 2017] are continuous forms of pairwise MRFs which assume the variables in the network follow a multivariate Gaussian distribution. The distribution for a GGM is

\begin{equation} \label{GGM_variance}
\begin{aligned}
p(\mu^*|\xi, \Omega) \propto \exp\left\{-\frac{1}{2}(\mu^*-\xi)^T\Omega (\mu^*-\xi) \right\},
\end{aligned}
\end{equation}

where $\mu^*=\{\mu^*_1,\ldots,\mu^*_M\}$ are the experts,  and $\xi$ and $\Omega$ are the mean and precision, respectively. The matrix $\Omega$ is also known as the potential or information matrix. In a GGM, if $\Omega_{ij}=0$, then $\mu^*_i$ ard $\mu^*_j$ are conditionally independent given all other variables, i.e. there is no edge between $\mu^*_i$ ard $\mu^*_j$ in the graph. GGMs use the common sparsity assumption, that is, there are only few edges
in the network and thus the precision matrix is sparse. To this end, the graphical Lasso (GLasso) regression [Friedman et al., 2008] is used to perform neighborhood selection for the network. It maximizes the log-likelihood subject to an element-wise $\mathcal{L}_1$ norm penalty on $\Omega$. Precisely, for sample covariance S and Gaussian log-likelihood $ \mathcal{L}(\Omega; S)=\log |\Omega| - trace(S \; \Omega)$, the objective function is

\begin{equation}  \label{GLasso}
\widehat{\Omega}_{\lambda}= \arg\min_{\Omega} \; \left( -\mathcal{L}(\Omega; S) + \lambda \left\Vert \Omega \right\Vert_1 \right).
\end{equation}

The precision matrix $\Omega$ has been used before to find clusters of strongly dependent experts [Jalali and Kasneci, 2020] and selecting most important experts in local approximation [Jalali et al., 2021].

§.§ GGM-Based Aggregation using EM Algorithm

The main input of the GLasso method is the sample covariance of our observations. Since the targeted expert $y^*$ is unobserved, one row (column) in S, related to $y^*$ is unknown. Let $S_{\mu^* \mu^*}$ is a known $M \times M$ matrix of the sample covariance of the observed variables $\mu^*$, $S_{y^*\mu^*}$ is an unknown $1 \times M$ vector that shows the sample covariance between latent and observed expert, and $S_{y^* y^*}$ is the internal potential of a latent expert. To use the GLasso, it is needed to estimate unknown partitions of $S$, i.e. $S_{y^*\mu^*}$ and $S_{y^* y^*}$. Here, we explain how the expected-maximization algorithm can help us.

E-Step: The E-step Calculates $Q(\Omega \mid \Omega^{(t)})$, the expected value of the penalized negative log-likelihood function with respect to the conditional distribution of $y^*$ given $\mu^*$ under the current estimate $\Omega^{(t)}$ of $\Omega$:

\begin{align*}
Q(\Omega \mid \Omega^{(t)})=\operatorname {E} _{y^* \mid  {\mu^*} ,\Omega^{(t)}} &{}\left[ -\mathcal{L}(\Omega; S) + \lambda \left\Vert \Omega \right\Vert_1 \right]
= -\log |\Omega| + trace\{ E_{y^*|\mu^*,\Omega^{(t)}}(S)\Omega\} + \lambda \left\Vert \Omega \right\Vert_1 .
\end{align*}

Let $\Sigma^{(t)}=(\Omega^{(t)})^{-1}$, the conditional distribution of $y^*$ given $\mu^*$ under the current estimate $\Omega^{(t)}$ follows

\[ N\left(\Sigma^{(t)}_{y^* \mu^*} (\Sigma^{(t)}_{\mu^* \mu^*})^{-1} \mu^*, \Sigma^{(t)}_{y^*} - \Sigma^{(t)}_{y^* \mu^*} (\Sigma^{(t)}_{\mu^* \mu^*})^{-1} \Sigma^{(t)}_{\mu^* y^*} \right).\]

Therefore, unknown partitions of $\widehat{S}=E_{y^*|\mu^*,\Omega^{(t)}}(S)$ can be estimated as below:

\begin{equation} \label{eq:S_y_mu}
\widehat{S}_{\mu^*y^*}=S_{\mu^* \mu^*} (\Sigma^{(t)}_{\mu^* \mu^*})^{-1}\Sigma^{(t)}_{\mu^* y^*},
\end{equation}

\begin{multline} \label{eq:S_y_y}
\widehat{S}_{y^* y^*}=\Sigma^{(t)}_{y^* y^*} - \Sigma^{(t)}_{y^* \mu^*} (\Sigma^{(t)}_{\mu^* \mu^*})^{-1} \Sigma^{(t)}_{\mu^* y^*} + \Sigma^{(t)}_{y^* \mu^*} (\Sigma^{(t)}_{\mu^* \mu^*})^{-1} S_{\mu^* \mu^*} (\Sigma^{(t)}_{\mu^* \mu^*})^{-1} \Sigma^{(t)}_{\mu^* y^*}.
\end{multline}

M-Step:  This step returns the updated precision matrix $\displaystyle {\boldsymbol {\Omega }}^{(t+1)}$ that maximize $Q(\Omega \mid \Omega ^{(t)})$ over all $(M+1)\times(M+1)$ positive-definite matrices $\Omega$. It is a GLasso problem and is equivalent to this minimization problem:

\begin{equation}  \label{EM_maximization}
\Omega^{(t)}=\underset{\Omega }{\arg\min} \left(- \log |\Omega| + trace\{\widehat{S}\Omega\} + \lambda \left\Vert \Omega \right\Vert_1 \right).
\end{equation}

Algorithm <ref> summarizes the whole procedure of the proposed ensemble, EMGGM.

GGM-Based Experts Aggregation (EMGGM)

$\mu^*$, $\lambda$, $R$ (number of iterations)
Aggregated predictions $y_A^*$
Initialize $y^*$
Calculate sample covariance $S^{(0)}$ of $(y^*,\mu^*)$
Estimate the initial parameter $\Omega^{(0)}$ using Equation (<ref>)
$t\gets 1$
$t \leq R$
Estimate $E_{y^*|\mu^*,\Omega^{(t)}}(S_{\mu^* y^*})$ using Equation (<ref>)
Estimate $E_{y^*|\mu^*,\Omega^{(t)}}(S_{y^* y^*})$ using Equation (<ref>)
Update the sample covariance as  $S^{(t)}=E_{y^*|\mu^*,\Omega^{(t)}}(S)$
Update the precision matrix $\Omega^{(t)}$ using Equation (<ref>)
$\Sigma^{(t)} \gets (\Omega^{(t)})^{-1}$ and $t\gets t+1$

Estimate the aggregated prediction $y_A^*$ using Equation (<ref>)

§.§ Discussion and Challenges

The proposed ensemble is capable to aggregate local experts considering their dependencies and its computational and storage costs are much smaller than NPAE which uses dependent experts, see Appendix <ref>. Besides, the normality assumption for joint distribution is not a restrictive assumption and can be relaxed, see Appendix <ref>. This gives the result that the proposed strategy can aggregate non-Gaussian experts.

An EM iteration does increase the likelihood function $\mathcal{L}(\Omega; S)$. However, no guarantee exists that the sequence converges to a maximum likelihood estimator. It is only guaranteed to converge to a point with zero gradient with respect to the parameters. So it can indeed get stuck at saddle points, see [McLachlan and Krishnan, 2008]. The converges property of the EM algorithm can be improved using a variety of heuristic or meta-heuristic approaches that enable EM to escape a local maximum, e.g. hill climbing and simulated annealing.

To avoid challenges in the convergence of EM, latent variable GGM (LVGGM) can be used. Maximizing the likelihood function of an LVGGM leads to a nonlinear optimization problem which is solved by convex or non-convex optimization methods. This strategy can be studied in future works to estimate the aggregated estimator $y_A^*$ in (<ref>), see Appendix <ref>.

§ EXPERIMENTS

In this section, we evaluate the prediction quality of the aggregated estimator using the conventional mean absolute error (MAE) and the root mean squared error (RMSE).
We use the simulated data of a one-dimensional analytical function [Liu et al., 2018, Jalali and Kasneci, 2020],

\begin{equation}
f(x) = 5x^2sin(12x) + (x^3 -0.5)sin(3x-0.5)+4cos(2x) + \epsilon,  \label{f_x}
\end{equation}

where $\epsilon \sim \mathcal{N}\left(0, (0.2)^2\right)$. We generate $n=10^4$ training points in $[0,1]$, and $n_t=10^3$ test points in $[-0.2,1.2]$. The data is normalized to zero mean and unit variance. We vary the number of experts, $M=\{10,20,30,40\}$, to evaluate different partition sizes. The prediction quality of the proposed ensemble is compared with the other baselines: GPoE [Cao and Fleet, 2014], RBCM [Deisenroth and Ng, 2015], GRBCM [Liu et al., 2018], NPAE [Rullière et al., 2018], and the full GP.
We use the standard squared exponential kernel, a Gaussian likelihood and the $K$-means partitioning method.

Figure <ref> (a) and Figure <ref> (b) depict the prediction quality of different baselines. The ensemble methods that use dependency between experts, i.e. EMGGM and NPAE, outperform the CI-based baselines. However, the proposed method has slightly better predictions than NPAE. Figure <ref> (c) presents the computation time of the ensembles that use dependency between experts. Remarkably, EMGGM provides predictions in just a fraction of NPAE's running time.

Prediction quality of DGP methods with respect for different number of experts M.

§ CONCLUSION

In this work, we have proposed a novel ensemble method, EMGGM, for distributed GPs which  aggregate dependent local experts' predictions using GGMs. Our proposed approach uses undirected graphical models and EM algorithm to estimate the final predictions. Through empirical analyses, we illustrated the superiority of EMGGM over existing SOTA aggregation methods. Finally, we hope to use our insights to develop aggregations that provide the full predictive distribution.

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§ DISTRIBUTED GP MODELS

In this section we review other divide-and-conquer distributed GP approaches in more detail, focusing on how other methods perform expert weighting. There are two main families of distributed GPs: product of experts and Bayesian committee machine.

Product of Experts.
The posterior distribution of the PoE model is given by the product of multiple densities (i.e., the experts). Because of the product operation, the prediction quality of PoE suffers considerably from weak experts. To improve on this aspect, [Cao and Fleet, 2014] proposed the GPoE model, which assigns importance weight to the experts.

For independent experts $\{\mathcal{M}\}_{i=1}^M$ trained on different partitions $\mathcal{D}_i$ the predictive distribution for a test input $X^*$ is given by:

\begin{equation} \label{eq:13}
p(y^*|\mathcal{D},X^*)= \prod_{i=1}^M p_i^{\beta_i}(y^*|\mathcal{D}_i,X^*),
\end{equation}

where $\beta = \{\beta_1,\ldots,\beta_M\}$ controls the expert importance. The product distribution in (<ref>) is proportional to a Gaussian distribution with mean and precision, respectively:

\begin{equation*}
\mu_{D}^* = \Sigma_{D}^* \sum_{i=1}^M \beta_i(\Sigma_i^*)^{-1}\mu_i^*, \;\;\;
(\Sigma_{D}^*)^{-1} = \sum_{i=1}^M \beta_i (\Sigma_i^*)^{-1}.
\end{equation*}

The standard PoE can be recovered by setting $\beta_i=1 ~ \forall i$. The precision corresponding to the PoE prediction, i.e. $(\Sigma_{D}^*)^{-1}$, is a linear sum of individual precision values: hence, an increasing number of local GPs increases the precision and therefore it leads to a decrease in variance, which consequently returns overconfident predictions in areas with little data.

To choose the weights $\beta_i$ in the PoE model several heuristics have been put forward. The authors of [Cao and Fleet, 2014] suggested the difference in differential entropy between the prior and posterior distribution of each expert, i.e. $\beta_i=\frac{1}{2}(\log \Sigma^{**} - \log \Sigma_i^{*})$ where the $(\Sigma^{**})^{-1}$ is the prior precision of $p(y^*)$. This leads to more conservative predictions. To fix this issue, [Deisenroth and Ng, 2015] suggested to choose simple uniform weights $\beta_i=\frac{1}{M}$, which provides better predictions.

Bayesian Committee Machine.
The Bayesian committee machine [Tresp, 2000] uses the Gaussian process prior $p(y^*)$ for the aggregation step and assumes conditional independence between experts, i.e. $\mathcal{D}_i \perp \!\!\! \perp  \mathcal{D}_j |y^*$ for two experts $i$ and $j$.
To mitigate the effect of weak experts on aggregation, especially in regions with few data points, [Deisenroth and Ng, 2015]
proposed the robust Bayesian committee machine (RBCM), which added importance weights $\beta_i$ to the model.
The distributed predictive distribution of this family of models can be written as:

\begin{equation*} %\label{eq:16}
p(y^*|\mathcal{D},X^*)= \frac{\prod_{i=1}^M p_i^{\beta_i}(y^*|\mathcal{D}_i,X^*)}{p^{\sum_{i=1}^M \beta_i-1}(y^*)}.
\end{equation*}

Its distribution is proportional to a Gaussian distribution with mean and precision, respectively:

\begin{align*}
\mu_{D}^* = \Sigma_{D}^* \sum_{i=1}^M \beta_i(\Sigma_i^*)^{-1}\mu_i^*, \;\;\;
(\Sigma_{D}^*)^{-1} = \sum_{i=1}^M \beta_i (\Sigma_i^*)^{-1} +(1-\sum_{i=1}^M \beta_i)(\Sigma^{**})^{-1},  %\label{eq:18}
\end{align*}

where the $(\Sigma^{**})^{-1}$ is the prior precision of $p(y^*)$. The general choice of the weights is the difference in differential entropy between the prior $p(y^*|X^*)$ and the posterior $p(y^*|\mathcal{D},X^*)$, i.e. $\beta_i=\frac{1}{2}(\log \Sigma^{**} - \log \Sigma_i^{*})$.

The most recent model in this family is the generalized robust Bayesian committee machine (GRBCM) [Liu et al., 2018]. It introduces a base (global) expert and considers the covariance between the base and other local experts. For a global expert $M_b$ and a base partition ${D}_{b}$, the predictive distribution of GRBCM is

\begin{equation}
p(y^*|\mathcal{D},X^*)= \frac{\prod_{i=2}^M p_{bi}^{\beta_i}(y^*|\mathcal{D}_{bi},X^*)}{p_b^{\sum_{i=2}^M \beta_i-1}(y^*|\mathcal{D}_b,X^*)} ,
\end{equation}

where the $p_b(y^*|\mathcal{D}_b,X^*)$ is the predictive distribution of $M_b$, and $p_{bi}(y^*|\mathcal{D}_{bi},X^*)$ is the predictive distribution of an expert trained on the data set $\mathcal{D}_{bi}=\{\mathcal{D}_{b},\mathcal{D}_{i}\}$. The base partition is randomly selected, while the remaining experts can be chosen through a random or disjoint partitioning strategy. It is noteworthy that, for $M$ experts and $m_0$ data points per expert, the GRBCM operates based on $M-1$ experts with $2m_0$ data points per expert. Therein lies the main difference between GRBCM and the other distributed GPs, which use $m_0$ data points per expert only. Since GRBCM assigns more data points to the experts, it trains experts on more informative subsets.

§ COMPUTATIONAL GRAPHS OF AGGREGATION STRATEGIES

Figure <ref> depicts the computational graphs of both strategies. Figure <ref>(a) reveals the aggregation based on conditional independence assumption between experts $\{\mu_1,\mu_2,\mu_3,\mu_4 \}$. It means two local experts $mu_i$ and $mu_j$ are connected only via the target variable $y^*$, i.e. $mu_i \indep mu_j \mid y^*$. However, this assumption is often violated in realistic conditions and the aggregation can lead to a sub-optimal solution. On the other hand, Figure <ref>(b) represents an aggregation with dependent experts where the interactions between experts show the dependencies.

[Independent Experts]
[Dependent Experts]
Computational graphs of different aggregation strategies. (a) Conditional-Independent based aggregation where there is no interaction between the local experts. (b) An aggregation based on the conditional dependency between local experts where their interactions have not been excluded.

§ PROOF OF PROPOSITION <REF>

The proof is straightforward. We need to show that
$Var(y-\beta \mu^*) -Var(y-y_A^*)$ is positive semi-definite for all linear unbiased predictors $\beta \mu^*$. To do that, we extend the $Var(y-\beta \mu^*)$:

\begin{align*}
&{}Var(y-\beta \mu^*)= Var(y-y^*_A + y^*_A -\beta \mu^*) = Var(y-y^*_A) + var(y^*_A-\beta \mu^*) + 2cov(y-y^*_A, y^*_A- \beta \mu^*).
\end{align*}

Now, we show $cov(y-y^*_A, C\mu^*)=0, \forall{C}$.

\begin{align*}
&{}cov(y-y^*_A, C\mu^*) = cov(y,C\mu^*) - cov(y^*_A, C \mu^*) = \Sigma_{y^* \mu^*} C^T - \Sigma_{y^* \mu^*} \Sigma_{\mu^*}^{-1} \Sigma_{\mu^*} C^T  = 0.
\end{align*}

Therefore, $cov(y-y^*_A,y^*_A- \beta\mu^*)=0$ where in this case, $C=\Sigma_{y^*\mu^*}^T \Sigma_{\mu^*\mu^*}^{-1} - \beta$. It means

\begin{align*}
&{}Var(y-\beta \mu^*)-Var(y-y^*_A) = var(y^*_A-\beta \mu^*)  \geq 0
\end{align*}

because $var(y^*_A-\beta \mu^*)$ is positive semi-definite variance matrix.

§ COMPUTATIONAL COST OF EMGGM AND NPAE

Both EMGGM and NPAE use  dependent experts. However, there are two major differences between them. First, NPAE needs all training and test data points during aggregation. Let $\Gamma_i =k^T_{i*}(K_i + \sigma^2 I)^{-1}$. For a test point $x^*$, the pointwise covariance between experts i and j in NPAE, $K(x^*)_{ij}$, can be extended using (<ref>) as

\begin{align*}
K(x^*)_{ij}=cov(\mu^*_i(x^*), \mu^*(x^*)_j)=Cov(\Gamma_i y_i,\Gamma_j y_j) \notag
=\Gamma_i Cov(y_i,y_j) \Gamma_j^T = \Gamma_i k(x_i,x_j) \Gamma_j^T.
\end{align*}

Therefore, all auto-covariance $k(x_i,x_i)$ and cross-covariance $k(x_i,x_j)$ matrices are required for NPAE aggregation which raises the storage costs.

Second, both aggregation methods have a $\mathcal{O}(M^3)$ calculation in each iteration, the inverse of $M \times M$ matrix in NPAE and GLasso in the proposed method. NPAE should do this costly calculation at each test point and therefore it is not efficient for large data sets. However, the proposed model can converge after a small number of iterations. When $R \ll n_t$, the proposed method is much faster than NPAE. Although the conventional GLasso for network learning is a costly method $\mathcal{O}(M^3)$, there are newer faster methods to learn a GGM that can be used instead of the GLasso, see [Wang et al., 2016, Xu et al., 2017, Zhang et al., 2020]. For instance, the FST model [Zhang et al., 2020] reduces the computational complexity of sparse Gaussian Graphical Model to a much lower order of magnitude $\left(\mathcal{O}(M^2)\right)$.

§ GAUSSIAN ASSUMPTION

The normality assumption for joint distribution is not a restrictive assumption. In practice, we can relax this assumption and consider random variables without resorting to multi-dimensional Gaussian distribution. As a semiparametric generalization for continuous variables, authors in [Liu et al., 2009, Lafferty et al., 2012] introduced the nonparanormal graphical model where it is assumed that the variables follow a Gaussian graphical model only after some unknown smooth monotone transformations on each of them. [Mulgrave and Ghosal, 2020] considered Bayesian inference in nonparanormal graphical models by putting priors on the unknown transformations through a random series based on B-splines.

On the other hand, nonparametric methods can be used for functional graphical models. Authors in [Li and Solea, 2018] and [Solea and Dette, 2021] exerted additive conditional independence and functional principal components to learn a graphical model when observations on vertices are functions. This gives the result that the proposed strategy can be considered as a general ensemble model, and not only for the local approximation GPs.

§ LATENT VARIABLE GGMS

Latent variable GGMs (LVGGMs) are used to estimate the distribution of the observed variables with respect to some latent variables. GGMs with latent variables have been widely considered over the past decade. Authors in [Chandrasekaran et al., 2012] proposed Low-Rank Plus Sparse Decomposition (LR+SD), a regularized maximum likelihood approach to estimate $\Omega$ via convex optimization. The precision matrix in LR+SD contains two terms: sparse structure $\Omega_{\mu^*}$ and the low-rank terms $L^*=\Omega_{\mu^*y^*} \Omega_{y^* y^*}^{-1} \Omega_{y^*\mu^*}$. The precision matrix in this form is $\Omega=\Omega_{\mu^* \mu^*}-  L^*$. The log-likelihood can be expressed in terms of the $S_{\mu^* \mu^*}$, $\Omega_{\mu^* \mu^*}$, and $L^*$:

\begin{equation} \label{log_lik_lvggm}
\mathcal{L}(\Omega_{\mu^* \mu^*}, L^*; S_{\mu^* \mu^*})
=  log |\left(\Omega_{\mu^* \mu^*}-  L^* \right)| - trace\left(S_{\mu^* \mu^*} \left(\Omega_{\mu^* \mu^*}-  L^* \right)\right).
\end{equation}

Essentially, it is a misspecified optimization problem because the precision matrix is the sum of two matrices. However, if $\Omega_{\mu^* \mu^*}$ is sparse and there are few latent variables, it is possible to decompose the precision matrix into its summands [Candès et al., 2011, Chandrasekaran et al., 2012].

\begin{align}
\left(\hat{\Omega}_{\mu^* \mu^*}, \hat{L}^* \right)  &=  \underset{\Omega_{\mu^* \mu^*}, L^*  \in \mathcal{R}^{M\times M}}{\arg\min}  -\mathcal{L}(\Omega_{\mu^* \mu^*}, L^*; S_{\mu^* \mu^*}) + \lambda \left(\gamma \left\Vert \Omega_{\mu^* \mu^*} \right\Vert_1 + \left\Vert L^* \right\Vert_* \right) \label{eq:lvggm}   \\
&{} \text{such that \;\;  }  \Omega_{\mu^* \mu^*}-  L^* \succ 0 ,\; L^* \succeq 0
\end{align}

such that $\Omega_{\mu^*}-  L^* \succ 0 ,\; L^* \succeq 0$. Here, $\lambda>0$ and $\gamma > 0$ are tuning parameters for sparsity and low rankness, and $\left\Vert L^* \right\Vert_*$ denotes the nuclear norm of $ L^*$ (i.e. the sum of its singular values).

To speeding up the LR+SD model, [Xu et al., 2017] proposed a non-convex optimization model and showed that it is orders of magnitude faster than the convex relaxation-based methods. Author in [Yuan, 2012] proposed a direct approach via Expectation-Maximization algorithm which converts LR+SD model to a conventional GGM. Here, we modified this approach and proposed EMGGM.

However, LR+SD model has been developed to estimate the marginal distribution of observed variables, i.e. $p(\mu^*)= \int p(\mu^*,y^*)dy^*$, while the desired predictive distribution is the conditional distribution of $y^*$ given local experts' predictions $p(y^*|\mu^*)$. Hence, further work could consider the modified form of the log-likelihood in (<ref>) and the convex optimization in (<ref>) to estimate the aggregate estimator $y^*_A$ in (<ref>) via a convex or non-convex optimization problem.