but not clearly associated with a specific member), and the default ranking
function chose any of them, we consider the case a “Confusing” one and then
manually mark other possible hosts. If any possible host is beyond the search
radius and is therefore not cross-matched into a group, we set a “host beyond
radius” flag and then mark the galaxy (RA, Dec offsets) in the image when
possible.

If the ranking function missed the most likely host, or rarely, all possible
hosts when there are multiple, we consider this a “Failed” case and then
manually mark the most likely host(s). This also includes the situation in
which the ranking function chose some substructure of the most likely host
rather than the main component. However, if the most likely host lies beyond
the search radius, or if it is marginally visible but not cataloged and cross-
matched, we group the case into “Other” instead of “Failed,” because this is a
failure in the source accessing and cross-matching process, rather than the
ranking function itself.

When there is no cross-matched group for the ranking function to choose from,
a possible situation for high-redshift transients such as GRBs, we mark the
case with “No Group.” If the sensitivity of the background image is fairly
good (DESI LS image, or PS1 image without stacking artifacts) and there is no
possible host near the transient position, we further flag the case as
“hostless.”

For any reason, if the most likely host is not clearly visible in the image,
we consider the case as “Unclear.” This includes, but is not limited to the
following situations as we flagged: 1) the transient is likely hostless
(“hostless”) in images of fairly good sensitivity (see also 3.7); 2) the field
is overly crowded (“crowded,” e.g., low-galactic latitude regions), hindering
the visual identification of the host; 3) there are multiple faint sources,
likely background galaxies, in the vicinity (“multiple faint sources”), in
which no one appears to be a better host than others, yet possible association
with the transient cannot be fully excluded; 4) low-resolution, low-
sensitivity, or corrupted images (“image quality issue”). When possible, we
also comment with the detailed reason if the case does not fit in these
typical reasons.

###  J.3 Empirical accuracy from visual inspection

We summarize the results of visual inspection in Table 10, Figure 7 and Figure
22.

We use empirical accuracy (Section 3.6.2 to evaluate the performance of
ranking functions in new hosts. The empirical accuracy here refers to the
fraction of clearly visible and unambiguous hosts that the ranking function
has successfully recovered. Assuming that the best host is inside the search
radius, our default ranking functions achieve $97.4\%$ when redshift-dependent
parameters are used for ranking, and $96.8\%$ when only redshift-independent
parameters are used (Table 10).

There are a considerable fraction of indecisive cases (“Unclear,” “Confusing”)
in which the best host is unidentifiable, ambiguous, or even absent. The
empirical accuracy must take this potential source of uncertainty into
account. We quote the range of empirical accuracy by making assumptions about
the performance of ranking functions in these indecisive cases. Assuming that
these indecisive cases are all successfully identified, we may estimate an
optimistic upper limit of accuracy; on the other hand, in the improbable worst
situation where all their hosts are misidentified, we can estimate a
pessimistic lower limit of accuracy. The upper and lower limits of accuracy
are also listed in Table 10. Considering the uncertainty due to these
indecisive cases, the accuracy of the redshift-dependent default ranking
function ranges from an optimistic case of $97.5\%$ to an unlikely pessimistic
case of $92.5\%$. For the redshift-independent default ranking function, the
limits are $97.0\%$ and $88.9\%$, respectively. These indecisive cases are
more relevant to high-redshift events (Figure 7, Figure 22) and are less of a
concern for mid and low-redshift transients.

We checked the accuracy of the default ranking functions, while the accuracy
of other ranking functions can be derived once the visually-identified most
likely host is known in each field. We noticed that the inclusion of detailed
source properties in PS1 or DESI LS catalogs could clearly improve the
results, as we pointed out earlier in Section I.3. The improved accuracy has
similar dependence on key transient and host parameters as the default ranking
functions due to the overlap in their input parameters or training sets. Any
percent-level improvement of accuracy in this range implies a significant
reduction of misassociation rates compared to the default ranking functions.
However, the improvement comes with the cost that the algorithm could ignore
some true hosts if they do not have the required parameters measured. For
example, PS1/PS1_z feature sets, which rely on source properties in PS1
catalog, have close to $99\%$ accuracy. However, the sensitivity of the PS1
catalog may not detect some fainter hosts, which leads to a decreased feature
availability towards higher redshift. Higher redshift transients will likely
not benefit from the improved accuracy here.

Table 10: Empirical Accuracy of Ranking functions

Name |  Basic(_z) |  AnyMag(_z) |  PS1(_z) |  LS(_z)
---|---|---|---|---
| With redshift-dependent parameters
Accuracy | $97.4$ | $98.0$ | $98.8$ | $98.6$
Upper Limit | $97.5$ | $98.1$ | $98.9$ | $98.7$
Lower Limit | $92.5$ | $93.5$ | $95.6$ | $95.0$
| Only redshift-independent parameters
Accuracy | $96.8$ | $97.5$ | $98.7$ | $97.9$
Upper Limit | $97.0$ | $97.6$ | $98.7$ | $98.0$
Lower Limit | $88.9$ | $90.7$ | $93.9$ | $93.2$

Note. — The empirical accuracy is estimated for the default ranking functions
(Appendix I). We use the fraction of clearly visible and unambiguous hosts
that have been successfully recovered as the accuracy here. The upper and
lower limits of accuracy due to indecisive cases are also quoted.

Figure 21: The decision tree of visual inspection for transients with known
and properly cross-matched hosts (Appendix J.1) and transients with newly
identified hosts (Appendix J.2). For transients with known hosts, we assign
“OK” or “Failed” based on the results of cross-matching. If there is clearly a
better host than the reported one, we also flag the case and mark the
“alternative host” in the image. If we cannot determine if the indicated host
is successfully cross-matched and if any better host exists, we consider this
an “Unclear” case and set flags for the detailed reasons. For events with new
hosts, if the algorithm chose the unique best host in the images, we consider
the case “OK.” If the algorithm chose one likely host while there are other
equally possible hosts, we consider this a “Confusing” case. If the algorithm
missed the best host in the radius, we consider the case a “Failed” one and
then manually reassign the host if we can. However, if the best host is
outside the radius, we group the case under “Other.” If no group has been
cross-matched near the event, the case falls into “No Group.” Finally, similar
to the case of known hosts, if we cannot determine the best host from the
image, we consider the case “Unclear” with appropriate flags indicating the
detailed reason.

Figure 22:  The empirical accuracy of new hosts from visual inspection. Here
the accuracy is the fraction of correctly identified hosts in cases where the
host, either correctly identified or not, is clearly visible and unambiguous.
We show the dependence of accuracy on transient redshift, transient-host
angular distance, transient type, and host optical-NIR magnitude in four
separate panels. Except for the panel of transient type, we divide the sample
into bins of equal sample size over the axis of interest and plot the per-bin
accuracy and mean value there. Each colored accuracy curve represents the
performance of an input feature set using the default Logistic Regression
classifier. Redshift-dependent and redshift-independent feature sets are
grouped into two sub-panels for clarity. We calculate the accuracy for feature
sets using detailed source properties with the subset of events whose best
hosts (either correctly identified or not) have the catalogs cross-matched.
Since these properties are not universally available, we further plot the
fraction of best hosts with the required features available in the bottom sub-
panels to indicate the possible loss of accuracy. Furthermore, as transient
type and redshift are independent of the best host, we also estimated the
uncertainty of accuracy contributed by indecisive cases (“Unclear” and
“Confusing” cases). The optimistic and pessimistic limits of accuracy are
indicated as “error bars” of these points. Similar as Figure 7, for events
without redshift, we plot their accuracy in the rightmost gray shaded area of
the redshift panel.

##  Appendix K Confidence Scores of Host Candidates

To evaluate the reliability of individual newly identified hosts, besides
visual inspection, we also derived a separate set of numeric metrics for each
cross-matched group, which we refer to as the “confidence score.”

The confidence score is a metric for outliers or anomalies, which distinguish
likely host galaxies from the bulk of nearby non-host objects by comparing
their ranking scores. We create a reference sample of nearby non-host objects
by generating 16384 mock transients with randomized positions (i.e., without
association with any galaxies). Galaxies and stars near these mock transients
are always nearby non-host objects rather than their “true hosts.” The
highest-ranking “host candidates” of these mock transients then outline the
possible range of ranking scores, represented as a baseline distribution, that
a nearby non-host object may reach by chance under the best cases. For a true
transient, if the ranking score of a host candidate is at the higher value
tail of the baseline distribution, then this candidate is likely an outlier
among nearby non-host objects, and we can be more confident about this new
candidate. Conversely, if the ranking score of this host candidate is inside
or even below the range of the baseline distribution, then this candidate
could be a nearby non-host object that ranked high in the field simply by
chance. When no host candidate in a field achieves an outstanding ranking
score compared to the baseline distribution, the transient itself could be a
hostless one.

We use the same source searching and cross-matching workflow for these mock
transients under a constant search radius of $45^{\prime\prime}$, where the
ranking scores are calculated using the same trained ranking functions as we
used for those true transients. For each feature set and classifier
combination, we construct the baseline distribution using the highest-ranking
score of each mock transient. The confidence score is defined as the
percentile rank of a new ranking score in the baseline distribution of the
same feature set and classifier. A value closer to $100\%$ indicates a more
outstanding and possibly more reliable candidate. Clearly, if the ranking
scores depend on transient redshift and catalog coverage, then the baseline
distributions should also be adjusted for these factors. To compensate the
redshift dependence of some feature sets (with “_z” suffix), we generate a
series of baseline distributions by setting these mock transients at some
fixed redshifts on a pre-defined axis so that we can choose the nearest
baseline distribution on the axis later. To ensure similar catalog coverage of
mock transients as our existing true transients, we generate mock transients
following the density of true transients on the celestial sphere, represented
in a healpix grid smoothed by a Gaussian kernel of FWHM$\sim$1 degree.
Furthermore, we also calculate local confidence scores using only the nearest
1024 mock transients, rather than the entire sample of 16384 mock transients,
for baseline distributions. Despite being noisy due to smaller sample sizes,
this localized version of confidence scores may better offset the dependence
of baseline distributions on the coverage of external catalogs.

Figure 23: Examples of estimating confidence scores from baseline
distributions. We compare the ranking scores of new host candidates (orange)
to a baseline distribution (blue), i.e., the highest-ranking scores that
nearby non-host objects can achieve by chance in a randomized mock transient
sample. We use the cumulative percentage curve of the baseline distribution
(red) to quote the ranking scores of new host candidates. True hosts, ideally,
should have ranking scores at the positive tail of the baseline distribution.
Their confidence scores are closer to $100\%$. Here we show the case for the
redshift-independent default ranking function (top panel) and the redshift-
dependent default ranking function in several redshift intervals (centered at
$z$, with bin width $\Delta z$).

In Figure 23, we show examples of baseline distributions, ranking scores of
newly identified hosts, and their derived confidence scores with our default
ranking functions. For the redshift-dependent ranking function, we also show
the results in several redshift bins. The baseline distributions are clearly
redshift-dependent. Towards higher redshift, although angular distance-related
parameters may still distinguish true hosts from other objects, other
properties of hosts become similar to those ubiquitous galaxies in the field.
However, the ranking scores of true hosts remain well above the ranges of
baseline distributions, and the behavior of confidence scores remains stable.
In Figure 24, we show the cumulative distributions of confidence scores for a
few kinds of host candidates identified during our visual inspection.
Successfully identified new hosts (“OK”), as expected, have confidence scores
close to $100\%$. Misidentified hosts (“Failed: Identified”), as a comparison,
have lower confidence scores than successful cases. Higher confidence scores
usually, but not always, mean better candidates. The manually reassigned hosts
(“Failed: Manual Fix”) of “Failed” cases have lower confidence scores than
galaxies misidentified in the same field (“Failed: Identified”). Similarly, in
“Confusing” cases, the equally-possible hosts (“Confusing: Lowest”) have lower
confidence scores than ones chosen by the ranking functions in the same field
(“Confusing: Highest”). There are “Unclear” cases with multiple faint sources
in the vicinity of transient coordinates, in which no one appears to be a
clearly visible and unambiguous host, while any transient-host association
cannot be fully excluded. Their highest-ranking “hosts” (“Multiple Faint”)
have much lower confidence scores, although the distribution overlaps with
manually reassigned hosts (“Failed: Manual Fix”). Finally, the primary
candidates of possible hostless transients (“Hostless”) have very low
confidence scores, following the baseline distributions.

As a summary, the confidence score here serves as a quantitative metric for
the reliability of host candidates, which clearly differentiates robust hosts
from those less reliable ones. However, the confidence score is based on the
same training framework as our ranking algorithm, which does not directly
indicate the correctness of individual host identifications. Cross-checking
with visual inspection is encouraged.

Figure 24:  The cumulative distribution of confidence scores for some host
candidates identified during our visual inspection of new hosts (Appendix J).
Successfully identified hosts (“OK”) usually have very high confidence scores.
However, higher confidence scores do not guarantee more reliable hosts;
misidentified hosts (“Failed: Identified”) still have higher confidence scores
than the manually reassigned hosts in the same field (“Failed: Manual Fix”).
When there are multiple possible hosts, the other equally-possible host
(“Confusing: Lowest”) also has high confidence scores, although not as high as
the “best” host selected by the algorithm in the same field (“Confusing:
Highest”). We see much lower confidence scores for the selected “host” when
the vicinity contains multiple faint sources, yet no one stands out to be a
clear and unambiguous host (“Multiple Faint”). Finally, the “best candidate”
of possible hostless transients (“Hostless”) have much lower confidence scores
than other candidates. They basically follow the baseline distribution.
Results here are global confidence scores using the default ranking function
in each field.

##  Appendix L Database Schema

Here we show the schema of host collection using an example with comments. The
output is abbreviated for clarity.

⬇

# transient info

"event_name": "SN2011fe", # preferred name

"event_alias": ["SN2011fe", "PTF11kly", ...], # other alternative names

"event_ra": 210.7737, # RA of event (degree)

"event_dec": 54.2736, # Dec of event (degree)

"event_z": 0.0008, # reported transient or host redshift

"event_dxy": [-59.8553, -270.9878], # event position in the field center
(arcsec)

"revised_type": ["_SN", "Ia", ...], # curated type labels

# as-reported host info

"reported_host": {

"name": ["M101", "NGC 5457"], # reported host name(s)

"ra": 210.8042, # reported host RA (degree)

"dec": 54.3492, # reported host Dec (degree)

},

# summary of host name resolving,

"resolved_host_coord" : {

"valid_names" : ["M101", "NGC 5457"], # list of valid host names

"resolved_names" : { # resolved host coord. of valid names

# ** key: input host name; value: results of name resolving

"M101" : {

# selected coord. for this name

"vac" : "NED", # selected reference for host coord

"ra" : "14:03:12.5448", # resolved RA

"dec" : "+54:20:56.22", # resolved Dec

"ra_deg" : 210.8022, # resolved RA (degree)

"dec_deg" : 54.3489 # resolved Dec (degree)

"src" : "MESSIER 101/PREC:1.20e-01,1.20e-01", # resolved name and coord.
precision

"SIMBAD" : { # results from SIMBAD

"src" : "M 101/QUAL:C", "ra" : "14:03:12.583", "dec" : "+54:20:55.50",

"ra_deg" : 210.8024, "dec_deg" : 54.3487, "raw_rec" : [...] # raw results in
SIMBAD

},

"NED" : {...}, # results from NED

},

"NGC 5457": {...},

...

}

# consistency check of name-resolved coord.

"resolved_coord_inconsistent" : False, # flag for any inconsistent pairs

"inconsistent_pairs" : [...], # list of inconsistent pairs, if any

# ** list of tuple: (name, the other host name, distance in arcsecond)

# best name-resolved coord., same structure as values under "resolved_names"

"resolved_coord_best" : {

"vac" : "...", "ra" : "14:03:12.5448", "dec" : "+54:20:56.22",

"ra_deg" : 210.8022, "dec_deg" : 54.3489, "src" : "MESSIER
101/PREC:1.20e-01,1.20e-01",

"SIMBAD" : {...}, "NED" : {...},

}

}

# flags for input host coord.

"host_coord_known" : True, # host coord known or not

"host_coord_matched" : True, # host coord cross-matched or not

"host_coord_type" : "name_resolved", # type of host coord

# "name_resolved" or "reported_host_coord"

# queried coordinates and projection

"field_coord": {

"ra": 210.8022, # field center RA (degree)

"dec": 54.3489, # field center Dec (degree)

# field centers at the queried coordinate (host or transient).

"coord_src": "name_resolved", # source of queried coordinate

# "name_resolved", "reported_host_coord", "event_coord"

"coord_comm" : ["NED", "MESSIER 101", ...], # flags for provided coordinates

"radius": 15.0, # search radius (arcsec

"radius_src" : "name_resolved_default", # source of search radius

# "name_resolved_default", "reported_host_coord_default",

# "redshift", "grb_err_circle", "event_coord_default"

# unit vectors in Cartesian frame

"cvec": [-0.5006, -0.2984, 0.8125], # queried coordinate, or field center

"vn_ra": [ 0.5120, -0.8589, 0.0000], # unit vector in RA direction

"vn_dec": [ 0.6979, 0.4161, 0.5828], # unit vector in Dec direction

},

# cross-matched groups.

"N_groups": 2, # Number of cross-matched groups

"groups": [

# ** list of dictionaries, one for each cross-matched group

# confirmed host or primary candidate comes the first, followed by other
groups

{

# ** key: catalog name or ancillary info (begin with underscore)

"TwoMASSXSC": { # sources matched in 2MASS XSC catalog (example)

"srcs": [

# ** list of dictionaries, one for each source

# the representative comes the first, followed by others, if any

{

# ** key: name of source property; value: measured value

"2MASX": "14031258+5420555"

"J.ext": 6.517,

"H.ext": 5.805,

...

},

...

],

"_confusion": False # flag for confusion in this catalog

},

"MPAJHU": { # sources matched in MPA-JHU catalog (example)

"srcs": [{...}, ...], # detailed source properties

"_confusion": False,

},

... # other catalogs, and cross-matched sources

"_xid_flag": "confirmed", # type of cross-matched group

# "confirmed", "primary", "secondary", "event", "other"

# summary of cross-matched sources

"_group_uid" : "2ebb53f01d24345f...", # unique group id from cross-mateched
sources

"_includes_queried_coord" : True, # queried coord cross-matched this group or
not

"_group_srcid" : {

# ** key: catalog; value: list of source names

"HyperLEDA" : ["NGC5457"],

"TwoMASSXSC" : ["14031258+5420555"],

...

}

"_confusion": True, # flag for confusion in this group

"_confusion_cats": ["LS8pz", "Gaia2"], # list of catalogs with confusion

# source positions

"_avr_radec": [210.8023, 54.3489], # mean RA/Dec of sources (degree)

"_avr_dxy": [0.1064, -0.0938], # mean offsets w.r.t. the field center (arcsec)

"_std_dxy": [0.3033, 0.3943], # std. dev. of offsets (arcsec)

"_cov_dxy": [[0.0991, 0.0429], [0.0429, 0.1674]], # covariance of offsets
(arcsec^2)

# quality metrics for cross-matching

"_shape_r": 0.3332, # Pearson’s r

"_shape_q": 0.6455, # q = sigma_b / sigma_a

"_shape_p": 0.2154, # p = (1 - q) / (1 + q)

"_shape_e": 0.7637, # "eccentricity"

"_avr_dist": 0.4288, # "average distance" or "mean offset" (arcsec)

"_N_max_conn": 87.0, # maximal possible number of connections

"_N_conn": 82.0, # actual number of connections

"_F_conn": 0.9318, # degree of connectivity

# star-galaxy separation

"_is_stellar": False, # flag, any representative source is a star

"_stellar_srcs": [ # stellar sources

# ** list of (catalog, index) pairs; index in the "srcs" list of each catalog.

["LS8n", 2], ...

],

"_stellar_frac_all" : 0.0, # fraction of sources marked as stars

"_stellar_frac_repr" : 0.0, # fraction of representative sources marked as
stars

# denominator does not include sources in catalogs without star-galaxy
separation metrics

# summary of host candidate ranking

"_rank_score" : { # ranking scores

# ** key: feature set or ancillar info.

"Basic8Z" : {

# ** key: classifier; value: results

"Logistic_v3" : {

"score" : -0.6959, # raw ranking score

"rank" : 0, # rank in the field

"cs_global" : 98.3947, # global confidence score

"cs_local" : 98.3398, # local confidence score

},

"LSVM_v3": {...}, "RF_v3": {...}, # other classifiers and results

"_X" : [...], # raw input parameters

}

"LSZ" : {...}, "PS1Z": {...}, ... # other feature sets and results

"_default" : { # results from default ranking function

"score" : -0.6959, # raw ranking score

"rank" : 0, # rank in the field

"features" : "Basic8Z", # feature set used

"ranker" : "Logistic_v3", # classifier used

"cs_global" : 98.3947, # global confidence score

"cs_local" : 98.3398, # local confidence score

},

"_cscore_local" : { # ancillary info. for local confidence score

"avr_dist" : 11.5686, # average distance to mock transients (degrees)

"max_dist" : 18.8843, # maximal distance to mock transients (degrees)

"N" : 1024 # number of mock transients used

}

},

"_rank_features" : { # input parameters for ranking functions

# ** key: group features; value: list of values

"object_count" : [...], "angular_distance" : [...], "ls8_size_dRe" : [...],
...

}

}, ...

],

# coordinate of confirmed host or primary candidate, after cross-
identification

"host_ra": 210.8024, # cross-matched host RA (degree)

"host_dec": 54.3487, # cross-matched host Dec (degree)

"host_dist": 84.6571, # distance to transient position (arcsec)

"host_dxy": [0.1064, -0.0938], # position w.r.t. field center (arcsec)

"host_offset": [59.8684, 270.7856], # position w.r.t. transient (arcsec)

"host_srcid" : ["NED", "object_name", "MESSIER 101"], # source id of cross-
matched host

# ** (catalog, column name, source name)

# results from visual inspection, if applicable (copied from another event for
example)

"vis_insp" : {

# flags and comments

"status" : "Other", # status: "OK", "Failed", "Confusing", "Unclear", "Other"

"flags" : ["H", ...], #

"comment" : "possible_host_beyond_radius prefer_alternative_host",

# other flags and comments besides the "status" above

# manual reassignment

"reassigned" : { # reassigned host, if within the radius

# ** key: host name ("G0", "G1", "G2", ...)

"G0": {

# ** key: index of cross-matched group

"1": [

1, # index of selected group under "groups"

[-5.4725, 9.2440], # marked position in the image, RA Dec offset in arcsec

[-6.0513, 8.9101] # ’_avr_dxy’ of selected group

], ...

},

# each host may contain multiple cross-matched groups

},

"pin_pos" : [(-38.8769, -30.1731), ...], # manually marked host(s), if outside
the radius

# ** list of (delta_RA, delta_Dec) pairs, w.r.t. field center, in arcseconds

# summary of visual inspection

"resolved_by" : "use_existing", # source of compiled host data

"case_kind" : ["known_host", "ok", ...], # automatically generated descriptive
flags

"case_code" : "D1" # automatically generated case code

}

# cross-matching threshold

"xid_thres": {

"N_cps": 3, # number of groups under optimal threshold,

"thres_axis": [...], # trial values of matching threshold,

"conn_score": [...], # number of valid pairs under each trial value

"thres": 1.0 # the optimal matching threshold

},

# coverage of catalogs.

"coverage": {

"field": ["NED", "MPAJHU", ...], # names of catalogs covering this field

"primary": ["NED", "MPAJHU", ...], # catalogs matched in the primary group

"primary_unmatched": { # catalogs not matched in the primary group

# key: catalog name, value: list, [group_id, source_id, dist]

"GALEXAIS67" : [

1, # zero-indexed id of the group including source in this catalog

0, # index of the source in that group

2.9453 # distance of primary group to that source (arcsec)

],

... # ... other unmatched catalogs

}

}

# excluded sources in the field

"excluded_sources": {

# ** key: catalog or ancillary info (begin with underscore)

"PS1v2": { # excluded sources in PS1 DR2

"N_src": 3, # N of sources in this catalog

"N_excl": 3, # N excluded

"excl_srcs": [ # info of excluded source,

# ** list of dictionaries, one for each excluded source

{

"src": {...}, # source info

"reason": "FILTER FUNC" # reason, "FILTER FUNC" or "BEYOND RADIUS"

}, ...

]

}, ...

"_N_src": 21, # Number of sources in the field

"_N_excl": 3, # N of excluded sources.

},

"last_update": "2021-03-06T02:04:36.303Z", # time stamp for last update

"vcc": { # version control code for each data source

# ** key: data source ("tde", "grb", "rare"); value: version control code

"sn": "d147bb8861a7e838..."

},

"rand_id": 0.1157, # random number within (0, 1)

"_id": "vtdrakibitozjnpg", # global unique id of this event

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