# Interactions in Information Spread

Gaël Poux-Médard
Under the supervision of Julien Velcin and Sabine Loudcher gael.poux-
<EMAIL_ADDRESS>Université de Lyon, Lyon 2, ERIC UR 30835 avenue Pierre
Mendès FranceBronFrance69676

(2022)

###### Abstract.

Large quantities of data flow on the internet. When a user decides to help the
spread of a piece of information (by retweeting, liking, posting content),
most research works assumes she does so according to information’s content,
publication date, the user’s position in the network, the platform used, etc.
However, there is another aspect that has received little attention in the
literature: the information interaction. The idea is that a user’s choice is
partly conditioned by the previous pieces of information she has been exposed
to. In this document, we review the works done on interaction modeling and
underline several aspects of interactions that complicate their study. Then,
we present an approach seemingly fit to answer those challenges and detail a
dedicated interaction model based on it. We show our approach fits the problem
better than existing methods, and present leads for future works. Throughout
the text, we show that taking interactions into account improves our
comprehension of information interaction processes in real-world datasets, and
argue that this aspect of information spread is should not be neglected when
modeling spreading processes.

Information, Interaction, Diffusion, MMSBM, Dirichlet-Hawkes Process

††journalyear: 2022††copyright: acmcopyright††conference: Companion
Proceedings of the Web Conference 2022; April 25–29, 2022; Virtual Event,
Lyon, France††booktitle: Companion Proceedings of the Web Conference 2022 (WWW
’22 Companion), April 25–29, 2022, Virtual Event, Lyon, France††price:
15.00††doi: 10.1145/3487553.3524190††isbn: 978-1-4503-9130-6/22/04††ccs:
General and reference Surveys and overviews††ccs: Information systems
Clustering††ccs: Information systems Social recommendation Figure 1. State of
the art results on information interaction — (top) Interactions take place
between very specific pairs of clusters; interactions are sparse (Poux-Médard
et al., 2021a). (bottom) Interactions between specific pairs of entities tend
to follow an exponential decay in time; interactions do not last (Poux-Medard
et al., 2021)

##  1\. Motivation

As of today, every minute, approximately 400h of Youtube content, 350.000
tweets and 500.000 Facebook comments are uploaded to the internet. Such
amounts of data do not appear randomly. They are generated by users given a
context: publication platform, user interests, date of publication, position
of the user in a communication network, etc. Many of these aspects have been
widely explored in the literature; it has been shown that users interests can
be efficiently modeled (Mavroforakis et al., 2017; Du et al., 2013), dynamics
of publication can be inferred in efficient ways (Du et al., 2015), and
methods have been proposed to model the underlying diffusion networks of
information diffusion (Gomez-Rodriguez et al., 2011; Rodriguez et al., 2013).
However, an open problem has been independently raised on several occasions,
and received little interest over the last decade: how to efficiently model
interactions between the spreading entities?

Intuitively, we say there is an interaction anytime the combination of
entities yields more than their independent sum. Imagine answering a simple
question, whose interacting entities are unique words: to the question
”Capital France?”, the answer is obvious. However, to the bit ”Capital?”,
answers can be very broad; same for the bit ”France?”. The interaction between
those words narrowed the field of possible answers; they are interacting. This
idea can easily be generalized to retweets (does a user retweet A only because
of A, or also because of tweet B she has seen before?), online buying (does
the user buy A because she likes it, or because she also bought B before?),
and in general to online publication of documents (what are the bits of
information making a user publish this post in particular on this particular
platform?).

The understanding of interactions in information spread should provide a more
exhaustive description of the publication process on the internet, as well as
provide leads on how users react in a given context. At a time where three
quarters of the world population has an online
identity111https://en.wikipedia.org/wiki/Global_Internet_usage, the
understanding of these mechanisms could find applications anytime an internet
user has to make a choice: click, buy, like, comment, etc. One could think of
nudging users towards healthier internet behaviours on forum or better
consumption habits on online retail websites for instance.

The goal of this document is to briefly review the challenges that arise when
it comes to modeling interactions in information spread –interactions are
sparse and short. We then present a candidate methodology to deal with them,
based on both Bayesian clustering and temporal point-processes. We show this
method has flaws and propose a way to correct them. Our method allows to get
better results on several datasets. Finally, we present leads to extend the
existing framework and discuss research perspectives on interactions modeling.

##  2\. Problem

###  2.1. Interactions are sparse

In a first attempt to explicitly model interactions in a real-world dataset,
the authors in (Myers and Leskovec, 2012) proposed to apply a classical block
model to Twitter data. The goal is to predict the probability that a link will
be retweeted, given a history of links that appeared before it. The method
makes a central assumption: the interaction between tweets is a small
modulation of a base retweet probability, which is precomputed as the total
frequency of this tweet being retweeted. On this basis, the authors show that
interaction modeling indeed helps to improve the predictive performances of
the model. The analysis of the inferred interaction terms has led them to the
following conclusions: most interactions are small, and interactions are
slightly negative overall (meaning the lower the base probability of a
retweet). By running their model for different sizes of prior exposures (or
history), they also conclude that users rely mostly on a short-term memory,
which correlates previous findings on users modeling (Gutiérres-Roig et al.,
2016; Poux-Médard et al., 2021).

However, more recent works proved the core-hypothesis of this modeling false
(Poux-Médard et al., 2021a). By precomputing the base probability of a retweet
as the total number of times a tweet has been retweeted divided by the number
of times it appeared, the authors in (Myers and Leskovec, 2012) already
account for interactions. Imagine that interactions lead to a shift of $\Delta
p$ on the true base probability of a retweet $p$, and that this interaction
happens in a fraction $f$ of all observations of a given tweet being
retweeted. The base probability as defined in (Myers and Leskovec, 2012) then
equals $p(1-f)+(p+\Delta p)f=p+f\Delta p$, which is likely not to equal the
actual probability of a retweet in the absence of interaction $p$. Therefore,
defining interaction according to $p$ is wrong. The base probability for a
retweet needs to be inferred by the model at the same time as the contribution
of interactions to be properly defined.

The authors in (Poux-Médard et al., 2021a) then propose a mixed membership
stochastic block model (MMSBM) in order to jointly infer the base probability
of an entity spreading, as well as the interaction terms that modulate it. The
idea is to group entities into clusters according to the way those clusters
interact together. The authors in (Poux-Médard et al., 2021a) study the
importance of interactions in 4 different datasets. The conclusions are as
follow: modeling interactions improve predictive results, most interactions
are small, and significant interactions are sparse, meaning that they take
place only between rare specific pairs of clusters. This result for the
Twitter dataset is reported on Fig. 1-top.

###  2.2. Interactions are short

An important aspect of interactions that (Poux-Médard et al., 2021a) does not
consider is time. The position of entities in the considered history is not
considered. In (Myers and Leskovec, 2012), the order of appearance is taken
into account, but each temporal slice is modeled as independent from the
others.

In (Poux-Medard et al., 2021), the authors propose to study the evolution of
the interaction term in continuous time, using a convex model based on
survival theory. This framework allows to infer both a time-independent
probability of a retweet and a linear combination of time-dependent kernel
functions that account for temporal evolution of the interaction terms. The
data considered is similar as in (Myers and Leskovec, 2012; Poux-Médard et
al., 2021a) as it consists of pairs of entities (typically tweets) associated
to a given action (typically retweet), separated by a time $\Delta t$ in a
user’s history. Note that this model does not have any clustering component;
the interaction is studied only between the most interacting pairs of entities
for every of the 3 considered datasets.

The results of (Poux-Medard et al., 2021) are as follow: interactions
magnitudes follow an exponential decay in time, and therefore do not last in
time. Besides, the model recovers previous findings on interactions:
interactions are sparse, and their maximum magnitude is small. This result is
reported Fig. 1-bottom.

##  3\. State of the art

###  3.1. Historical approach to dynamic clustering

We reviewed the main challenges associated with interactions modeling. First,
interactions take place between specific pairs of clusters, and even more
specific pairs of entities; to be able to spot them using non-convex models
requires a clustering aspect. Second, interactions quickly fade in time,
meaning that the information clusters must also take into account a temporal
aspect.

The use of temporal dimension in documents clustering has been studied several
occasions; a notable spike of interest happened in 2006. Many authors tackled
the problem of inferring time-dependent clusters using models based on LDA
(Blei and Lafferty, 2006; Wang and McCallum, 2006). The idea is to sample the
data provided to each model with a temporal function; the data can be selected
using a temporal sliding window, or a temporal data sampling function. Time is
not explicitly modeled. Most of these models are parametric, meaning the
number of clusters is fixed at the beginning of the algorithm. In 2008, A.
Ahmed & al proposed the Recurrent Chinese Restaurant Process (RCRP) as an
answer to this problem (Ahmed and Xing, 2008). Instead of considering a fixed-
size dataset, this model can handle a stream of documents arriving in
chronological order, and the number of clusters is automatically updated. In
this model, time is still not modeled explicitly (data is split into episodes
to capture the temporal aspect of cluster formation). A later version of the
model from 2010, the Distance-Dependent Chinese Restaurant Process (DD-CRP),
tries to alleviate this approximation by replacing fixed-time episodes with a
continuous-time sampling function (Blei and Frazier, 2010). However, the model
is still not designed to explicitly model temporal information in a
continuous-time setting. The slicing of the considered data introduces a
consequent bias in the modeling.

###  3.2. Dirichlet-Hawkes process (DHP)

In 2015, N. Du & al (Du et al., 2015) answered this problem by developing the
Dirichlet-Hawkes Bayesian prior, that can be used to model the appearance of
events in a continuous-time setting. The key idea is to replace the counts in
a Dirichlet process prior by the intensity function of a Hawkes process.

Explicitly, given a standard Bayesian textual clustering model:

(1) $\underbrace{P(\text{cluster}|\text{text, time})}_{\text{Posterior
probability}}\propto\underbrace{P(\text{text}|\text{cluster})}_{\text{Textual
likelihood}}\times\underbrace{P(\text{cluster}|\text{time})}_{\text{Temporal
prior}}$

the authors propose the following form for the temporal prior:

(2)
$P(C_{i}=c|t_{i},\lambda_{0},\mathcal{H}_{<t_{i},c})=\begin{cases}\frac{\lambda_{c}(t_{i})}{\lambda_{0}+\sum_{c^{\prime}}\lambda_{c^{\prime}}(t_{i})}\text{
if c$\leq$C}\\\
\frac{\lambda_{0}}{\lambda_{0}+\sum_{c^{\prime}}\lambda_{c^{\prime}}(t_{i})}\text{
if c=C+1}\end{cases}$

where $C_{i}$ is the cluster allocation among $C$ clusters of the $i^{th}$
document appearing at time $t_{i}$, $c$ a random variable,
$\mathcal{H}_{<t_{i},c}$ the date of all documents within cluster $c$
published before $t_{i}$, $\lambda_{c}(t)$ the intensity of cluster $c$ at
time $t$, and $\lambda_{0}$ a parameter.

The functions $\lambda_{c}(t)$ need to be inferred as the intensities of a
Hawkes process (Rizoiu et al., 2018), and represent the instantaneous
probability that a document appears at time $t$. Note that in Eq.2, the prior
probability that a new document belongs to a given cluster depends on the
intensity of this cluster at a time $t$: clusters are self-stimulated. In the
problematic of information interaction, it means that pieces of information
can only interact with other pieces of information from the same cluster. An
example of a situation where a new observation gets allocated to any of the
existing clusters is illustrated Fig. 2.

The resulting Dirichlet-Hawkes process (DHP) is then used as a prior for
clustering documents appearing in a continuous-time stream. The inference is
realized with a Sequential Monte-Carlo (SCM) algorithm. Following DHP, two
articles have been published extending the idea: the Hierarchical Dirichlet
Hawkes process (HDHP) (Mavroforakis et al., 2017) in 2016 and Indian Buffet
Hawkes process in 2018 (Tan et al., 2018). Recently, (Kapoor et al., 2018)
underlined that this formulation suffers from a vanishing prior problem
($\lambda_{c}(t)$ can go to 0), and proposes a small procedure in order to
avoid it, without modifying the core idea of the prior.

Figure 2. Illustration of the Dirichlet-Hawkes prior — Each cluster is
associated to a temporal intensity function. The prior probability (Eq.2) of a
new observation belonging to a cluster is linearly proportional to this
cluster’s intensity.

##  4\. Proposed approach

###  4.1. Improvements over DHP

A common feature of all the models we mentioned built on DHP is that they use
a non-parametric Dirichlet process (DP) prior or variations built on it, such
as DHP and HDHP. Yet, on several occasions, it has been pointed out that there
are no specific reasons to use this process in particular and that alternative
forms might work better depending on the dataset (Welling, 2006; Wallach et
al., 2010). In (Welling, 2006), the author relaxes several properties
associated with DP and shows that alternative priors are an equally valid
choice in Bayesian modeling. In (Wallach et al., 2010), the authors derive the
Uniform process (UP) and show that it performs better on a document clustering
task. In (Poux-Médard et al., 2021b), the authors generalize UP and DP within
a more general framework, the Powered Dirichlet process (PDP), and show it
performs better than DP on several datasets.

Moreover, it has recently been highlighted that DHP does not work well when
the textual information within documents conveys little information, that is
when the text is short (Yin et al., 2018) or when vocabularies overlap
significantly. To answer this problem, the authors develop an approach based
on Dirichlet process mixtures, which is not designed for continuous-time
document streams – the temporal aspect comes from a sampling function as in
(Ahmed and Xing, 2008; Blei and Frazier, 2010). There are other limiting cases
for DHP, for instance when temporal information is conveys little information
(few observations, entangled dynamics) or when documents within textual
clusters do not follow a unique temporal dynamic. To overcome those
limitations, we develop the Powered Dirichlet-Hawkes process in the next
section.

###  4.2. The model

Taking back Eq.2, we note that the linear dependence of the prior on
$\lambda_{c}(t)$ is justified only by analogy with the standard Dirichlet
process. At this stage, we believe that a small modification of Eq.2 can lead
to great variations in the comprehension of a dataset. In particular, making
the prior more or less dependent on the temporal dimension (in the same way
that (Wallach et al., 2010; Poux-Médard et al., 2021c) makes the DP more or
less dependent on the “rich-get-richer” hypothesis) could lead to clusters
that are more text or time orientated. By replacing the standard Dirichlet
process in (Du et al., 2015) by the Powered Dirichlet process from (Poux-
Médard et al., 2021b), we derive the Powered Dirichlet-Hawkes process(Poux-
Médard et al., 2021c):

(3)
$P(C_{i}=c|r,t_{i},\lambda_{0},\mathcal{H}_{<t_{i},c})=\begin{cases}\frac{\lambda_{c}^{r}(t_{i})}{\lambda_{0}+\sum_{c^{\prime}}\lambda_{c^{\prime}}^{r}(t_{i})}\text{
if c$\leq$C}\\\
\frac{\lambda_{0}}{\lambda_{0}+\sum_{c^{\prime}}\lambda_{c^{\prime}}^{r}(t_{i})}\text{
if c=C+1}\end{cases}$

We show in Fig. 3 what this change implies for a standard Bayesian textual
clustering model. The value of $r$ tunes how much we rely on either the
textual or the temporal information every time the algorithm chooses a cluster
for a new document.

The algorithm used for inference is a sequential Monte-Carlo; it is the same
as described in (Du et al., 2015; Mavroforakis et al., 2017; Poux-Médard et
al., 2021c). It is especially fit for modeling data streams, as it considers
data sequentially. The underlying idea is that for each new observation, a
number of particles $N_{part}$ will make a cluster allocation hypothesis
according to Eq.1, update the cluster’s intensity function $\lambda_{c}(t)$,
and pass on to the next document. When the likelihood of a particle $L_{p}$
goes under a given threshold $\omega$, the particle is discarded and replaced
by a more likely one. In our case, we consider 8 particles and a threshold of
$\omega=\frac{\sum_{p}L_{p}}{2N_{part}}$

Figure 3. Effect of the parameter $r$ in PDHP on the posterior probability
(Eq.1 using the prior in Eq.3) for a new observation to belong to each
cluster.

##  5\. Methodology and results

###  5.1. Data generation

We simulate cases where only two clusters are considered. Each cluster has its
own vocabulary distribution over 1 000 words and its associated intensity
function $\lambda_{c}(t)$. We first simulate one independent Hawkes process
per cluster using the Tick Python library (Bacry et al., 2017). The processes
are stopped at time $t=1500$, which makes a rough average of 7 000 events per
run. Then we associate each simulated observation with a sample of 20 words
drawn from the corresponding cluster’s word distribution.

We evaluate our results according to the Normalized Mutual Information score
(NMI), which is a standard metric to compare the results of different
clustering algorithms when the number of clusters can vary.

Figure 4. Results of PDHP when textual and temporal information are not fully
reliable (a,b) and when textual content is decorrelated from temporal dynamics
(c,d).

###  5.2. Intra-cluster interactions…

####  5.2.1. …with unreliable information

A first lead to explore how information interact in time is to consider the
case where clusters are self-stimulated. However, (Yin et al., 2018) showed
that the approach in (Du et al., 2015) is not fit for cases where textual
information is weak or unreliable (e.g. Twitter) or when temporal dynamics are
highly entangled or when textual information is sufficient (e.g. long
documents or real-world process at large scales). In order to confirm that our
modeling in (Poux-Médard et al., 2021c) answers those limitations, we run
experiments for various values of informativeness of either textual or
temporal content.

To do so, we will make the clusters’ vocabulary distributions and temporal
intensity functions overlap. Given two distributions $\mathcal{A}(x)$ and
$\mathcal{B}(x)$, the overlap is defined as
$\frac{\int_{x}min(\mathcal{A}(x),\mathcal{B}(x))dx}{\int_{x}\mathcal{A}(x)+\mathcal{B}(x)dx}$.

In the case of vocabulary overlap, we shift the words distribution so that
they have a certain fraction of shared words. In the case of temporal overlap,
we first simulate each cluster’s Hawkes process, and compute the intensity
function of the whole resulting dataset. Then, we shift each process
realization on the temporal axis so that the overlap reaches the desired
value. We evaluate the models according to the documents clusters allocations
compared to the true clusters from the data generation process. We report the
average improvement for every of the 20 datasets considered in each overlaps
configuration, for various values of $r$.

Our results are shown in Figs. 4a-b. PDHP allows better performances comparing
to DHP (r=1) and UP (r=0) when textual information is unreliable (high textual
overlap), up to a gain of +0.3 NMI w.r.t. DHP (Fig. 4a). In more realistic
situations (average textual and temporal overlaps), PDHP allows better results
(up to +0.2 NMI, Fig. 4b). Our method is therefore able to accurately uncover
which cluster triggered a new document, that is to which interaction chain
this document belongs, in the case of weak temporal and textual information.

####  5.2.2. … with decorrelated content and dynamics

Another limiting situation of (Du et al., 2015) is when textual documents
about a same topic do not follow similar dynamics. Picture a famous and an
infamous newspapers publishing the exact same article; these articles would
not follow the same dynamics despite an identical textual content.

In order to explore the case where identical textual contents do not follow
identical temporal dynamics, we first generate the whole dataset with null
temporal and textual overlaps. Then, we randomly select a given fraction of
the generated observations, and resample their associated vocabulary according
to a randomly selected cluster. We have two different possible clustering:
textual (how well the model recovers the vocabulary a document’s content has
been drawn) and temporal (which intensity function made this document appear
where it is). In this case, we report the difference between the textual
clustering NMI and the temporal clustering NMI: $\Delta
NMI=NMI_{text}-NMI_{time}$.

Our results are shown Figs. 4c-d. When textual content is decorrelated from
publication dynamics (which is more in line with what happens in real-world
processes), tuning $r$ allows to consistently recover one clustering or the
other. That means we can successfully recover clusters based on either textual
similarity or on the temporal interaction between documents, or a mixture of
both.

###  5.3. Ongoing: Inter-cluster interactions

As for now, we presented introductory results about self-interacting clusters.
However, in order to get the full picture, we cannot only consider the case
where only one given cluster interacts with incoming documents. Instead, we
need to consider the interaction between all existing clusters. This embeds
naturally in the proposed approach (Du et al., 2015; Poux-Médard et al.,
2021c) by considering a multivariate Hawkes process instead of a uni-variate
one (Rizoiu et al., 2018). In implies redefining the numerator in Eq.3 from
$\lambda_{c}(t)$ to $\sum_{c^{\prime}}\lambda_{c^{\prime}\rightarrow c}(t)$,
where $\lambda_{c^{\prime}\rightarrow c}(t)$ is the temporal influence of
cluster $c^{\prime}$ on cluster $c$ at a time $t$. The challenge here is to
preserve the efficiency of the proposed algorithm while the model’s complexity
increases in a polynomial fashion with the number of inferred clusters.

###  5.4. Future: User-level inter-cluster interactions

As for future works, we believe it is possible to go further by combining
temporal point processes to Dirichlet processes. While (Du et al., 2015)
opened the door to this union, it only explored a small part or possible
applications. In particular, we think of the works of Gomez-Rodriguez on
underlying network inference (Gomez-Rodriguez et al., 2011; Rodriguez et al.,
2013) and extensions (Du et al., 2013; Wang et al., 2012). In (Gomez-Rodriguez
et al., 2013), he showed that all these models can be formulated in terms of a
counting temporal point process, which naturally allows to substitute any such
modeling to the Hawkes process in Eq.2 and Eq.3. In this case, we would be
able to study the interaction between pieces of information at the user-level,
providing a deeper understanding of information interaction in real-world
processes.

##  6\. Conclusions

In this document, we first motivated the need to model the interaction between
pieces of information in order to get a better understanding of real-world
spreading processes. We then highlighted the main challenges that arise in
this perspective using recent published works. We proposed to address the
problem by considering a recent approach that seems to fit to answer the
challenges of interaction modeling, despite having its own flaws. We proposed
a simple method to overcome these, and conducted systematic experiments to
demonstrate how our methodology works at doing so. Finally, we proposed leads
for further improving our understanding of real-world information interaction
modeling.

## References

  * (1)
  * Ahmed and Xing (2008) Amr Ahmed and E. Xing. 2008\.  Dynamic Non-Parametric Mixture Models and the Recurrent Chinese Restaurant Process: with Applications to Evolutionary Clustering. In _SIAM International Conference on Data Mining_. 219–230.
  * Bacry et al. (2017) Emmanuel Bacry, Martin Bompaire, Philip Deegan, Stéphane Gaïffas, and Søren V. Poulsen. 2017\.  Tick: A Python Library for Statistical Learning, with an Emphasis on Hawkes Processes and Time-Dependent Models.  _J. Mach. Learn. Res._ 18, 1 (2017), 5 pages.
  * Blei and Frazier (2010) David M. Blei and Peter Frazier. 2010.  Distance Dependent Chinese Restaurant Processes. In _ICML’27_ _(ICML’10)_. 87–94.
  * Blei and Lafferty (2006) David M. Blei and John D. Lafferty. 2006.  Dynamic Topic Models. In _Proceedings of the 23rd International Conference on Machine Learning_ _(ICML ’06)_. 113–120.
  * Du et al. (2015) Nan Du, Mehrdad Farajtabar, Amr Ahmed, Alex Smola, and L. Song. 2015.  Dirichlet-Hawkes Processes with Applications to Clustering Continuous-Time Document Streams.  _21th ACM SIGKDD_ (2015).
  * Du et al. (2013) Nan Du, Le Song, Hyenkyun Woo, and Hongyuan Zha. 2013\.  Uncover Topic-Sensitive Information Diffusion Networks. In _AISTATS_ _(JMLR, Vol. 31)_. 229–237.
  * Gomez-Rodriguez et al. (2011) Manuel Gomez-Rodriguez, David Balduzzi, and Bernhard Schölkopf. 2011.  Uncovering the Temporal Dynamics of Diffusion Networks. In _ICML_. 561–568.
  * Gomez-Rodriguez et al. (2013) Manuel Gomez-Rodriguez, Jure Leskovec, and Bernhard Schölkopf. 2013.  Modeling Information Propagation with Survival Theory. In _ICML_ , Vol. 28. 9 pages.
  * Gutiérres-Roig et al. (2016) Mario Gutiérres-Roig, Carlota Segura, Jordi Dutch, and Josep Perello. 2016.  Market Imitation and Win-Stay Lose-Shift Strategies Emerge as Unintended Patterns in Market Direction Guesses.  _PLOS One_ (2016).
  * Kapoor et al. (2018) J. Kapoor, A. Vergari, I Valera, and M. Gomez-Rodriguez. 2018\.  Bayesian nonparametric Hawkes processes. In _Bayesian Nonparametrics workshop NIPS’32_.
  * Mavroforakis et al. (2017) Charalampos Mavroforakis, Isabel Valera, and Manuel Gomez-Rodriguez. 2017.  Modeling the Dynamics of Learning Activity on the Web. In _Proceedings of the 26th International Conference on World Wide Web_ _(WWW ’17)_. 1421–1430.
  * Myers and Leskovec (2012) Seth A. Myers and J. Leskovec. 2012.  Clash of the Contagions: Cooperation and Competition in Information Diffusion.  _2012 IEEE 12th International Conference on Data Mining_ (2012), 539–548.
  * Poux-Médard et al. (2021) Gaël Poux-Médard, Sergio Cobo-Lopez, Jordi Duch, Roger Guimerà, and Marta Sales-Pardo. 2021\.  Complex decision-making strategies in a stock market experiment explained as the combination of few simple strategies.  _EPJ Data Science_ 10 (2021).  Issue 26.
  * Poux-Medard et al. (2021) Gael Poux-Medard, Julien Velcin, and Sabine Loudcher. 2021\.  Information Interaction Profile of Choice Adoption.  _ECML-PKDD’21_ (2021).
  * Poux-Médard et al. (2021a) Gaël Poux-Médard, Julien Velcin, and Sabine Loudcher. 2021a.  Interactions in information spread: quantification and interpretation using stochastic block models.  _RecSys’21_ (2021).
  * Poux-Médard et al. (2021b) Gaël Poux-Médard, Julien Velcin, and Sabine Loudcher. 2021b.  Powered Dirichlet Process for Controlling the Importance of ”Rich-Get-Richer” Prior Assumptions in Bayesian Clustering.  _ArXiv_ (2021).  arXiv:2104.12485 [cs.LG]
  * Poux-Médard et al. (2021c) Gaël Poux-Médard, Julien Velcin, and Sabine Loudcher. 2021c.  Powered Hawkes-Dirichlet Process: Challenging Textual Clustering using a Flexible Temporal Prior.  _ICDM_ (2021).
  * Rizoiu et al. (2018) Marian-Andrei Rizoiu, Young Lee, Swapnil Mishra, and Lexing Xie. 2018.  A Tutorial on Hawkes Processes for Events in Social Media.  _FMR_ (2018), 191–218.
  * Rodriguez et al. (2013) Manuel Gomez Rodriguez, Jure Leskovec, and Bernhard Schoelkopf. 2013.  Structure and Dynamics of Information Pathways in Online Media.  _WSDM_ (2013).
  * Tan et al. (2018) X. Tan, Vinayak A. Rao, and Jennifer Neville. 2018.  The Indian Buffet Hawkes Process to Model Evolving Latent Influences. In _UAI_.
  * Wallach et al. (2010) Hanna Wallach, Shane Jensen, Lee Dicker, and Katherine Heller. 2010.  An alternative prior process for nonparametric Bayesian clustering. In _AIS’13_. 892–899.
  * Wang et al. (2012) Liaoruo Wang, Stefano Ermon, and John E. Hopcroft. 2012\.  Feature-Enhanced Probabilistic Models for Diffusion Network Inference. In _Machine Learning and Knowledge Discovery in Databases_. 499–514.
  * Wang and McCallum (2006) Xuerui Wang and Andrew McCallum. 2006.  Topics over Time: A Non-Markov Continuous-Time Model of Topical Trends.  _KDD’06_ , 424–433.
  * Welling (2006) Max Welling. 2006\.  Flexible priors for infinite mixture models. In _Workshop on learning with non-parametric Bayesian methods_.
  * Yin et al. (2018) Jianhua Yin, Daren Chao, Zhongkun Liu, Wei Zhang, Xiaohui Yu, and Jianyong Wang. 2018\.  Model-Based Clustering of Short Text Streams _(KDD ’18)_. 2634–2642.