16,917 research outputs found
Hierarchical Models for Relational Event Sequences
Interaction within small groups can often be represented as a sequence of
events, where each event involves a sender and a recipient. Recent methods for
modeling network data in continuous time model the rate at which individuals
interact conditioned on the previous history of events as well as actor
covariates. We present a hierarchical extension for modeling multiple such
sequences, facilitating inferences about event-level dynamics and their
variation across sequences. The hierarchical approach allows one to share
information across sequences in a principled manner---we illustrate the
efficacy of such sharing through a set of prediction experiments. After
discussing methods for adequacy checking and model selection for this class of
models, the method is illustrated with an analysis of high school classroom
dynamics
Transforming Graph Representations for Statistical Relational Learning
Relational data representations have become an increasingly important topic
due to the recent proliferation of network datasets (e.g., social, biological,
information networks) and a corresponding increase in the application of
statistical relational learning (SRL) algorithms to these domains. In this
article, we examine a range of representation issues for graph-based relational
data. Since the choice of relational data representation for the nodes, links,
and features can dramatically affect the capabilities of SRL algorithms, we
survey approaches and opportunities for relational representation
transformation designed to improve the performance of these algorithms. This
leads us to introduce an intuitive taxonomy for data representation
transformations in relational domains that incorporates link transformation and
node transformation as symmetric representation tasks. In particular, the
transformation tasks for both nodes and links include (i) predicting their
existence, (ii) predicting their label or type, (iii) estimating their weight
or importance, and (iv) systematically constructing their relevant features. We
motivate our taxonomy through detailed examples and use it to survey and
compare competing approaches for each of these tasks. We also discuss general
conditions for transforming links, nodes, and features. Finally, we highlight
challenges that remain to be addressed
From Relational Data to Graphs: Inferring Significant Links using Generalized Hypergeometric Ensembles
The inference of network topologies from relational data is an important
problem in data analysis. Exemplary applications include the reconstruction of
social ties from data on human interactions, the inference of gene
co-expression networks from DNA microarray data, or the learning of semantic
relationships based on co-occurrences of words in documents. Solving these
problems requires techniques to infer significant links in noisy relational
data. In this short paper, we propose a new statistical modeling framework to
address this challenge. It builds on generalized hypergeometric ensembles, a
class of generative stochastic models that give rise to analytically tractable
probability spaces of directed, multi-edge graphs. We show how this framework
can be used to assess the significance of links in noisy relational data. We
illustrate our method in two data sets capturing spatio-temporal proximity
relations between actors in a social system. The results show that our
analytical framework provides a new approach to infer significant links from
relational data, with interesting perspectives for the mining of data on social
systems.Comment: 10 pages, 8 figures, accepted at SocInfo201
Locally Adaptive Dynamic Networks
Our focus is on realistically modeling and forecasting dynamic networks of
face-to-face contacts among individuals. Important aspects of such data that
lead to problems with current methods include the tendency of the contacts to
move between periods of slow and rapid changes, and the dynamic heterogeneity
in the actors' connectivity behaviors. Motivated by this application, we
develop a novel method for Locally Adaptive DYnamic (LADY) network inference.
The proposed model relies on a dynamic latent space representation in which
each actor's position evolves in time via stochastic differential equations.
Using a state space representation for these stochastic processes and
P\'olya-gamma data augmentation, we develop an efficient MCMC algorithm for
posterior inference along with tractable procedures for online updating and
forecasting of future networks. We evaluate performance in simulation studies,
and consider an application to face-to-face contacts among individuals in a
primary school
The Block Point Process Model for Continuous-Time Event-Based Dynamic Networks
We consider the problem of analyzing timestamped relational events between a
set of entities, such as messages between users of an on-line social network.
Such data are often analyzed using static or discrete-time network models,
which discard a significant amount of information by aggregating events over
time to form network snapshots. In this paper, we introduce a block point
process model (BPPM) for continuous-time event-based dynamic networks. The BPPM
is inspired by the well-known stochastic block model (SBM) for static networks.
We show that networks generated by the BPPM follow an SBM in the limit of a
growing number of nodes. We use this property to develop principled and
efficient local search and variational inference procedures initialized by
regularized spectral clustering. We fit BPPMs with exponential Hawkes processes
to analyze several real network data sets, including a Facebook wall post
network with over 3,500 nodes and 130,000 events.Comment: To appear at The Web Conference 201
Ranking relations using analogies in biological and information networks
Analogical reasoning depends fundamentally on the ability to learn and
generalize about relations between objects. We develop an approach to
relational learning which, given a set of pairs of objects
,
measures how well other pairs A:B fit in with the set . Our work
addresses the following question: is the relation between objects A and B
analogous to those relations found in ? Such questions are
particularly relevant in information retrieval, where an investigator might
want to search for analogous pairs of objects that match the query set of
interest. There are many ways in which objects can be related, making the task
of measuring analogies very challenging. Our approach combines a similarity
measure on function spaces with Bayesian analysis to produce a ranking. It
requires data containing features of the objects of interest and a link matrix
specifying which relationships exist; no further attributes of such
relationships are necessary. We illustrate the potential of our method on text
analysis and information networks. An application on discovering functional
interactions between pairs of proteins is discussed in detail, where we show
that our approach can work in practice even if a small set of protein pairs is
provided.Comment: Published in at http://dx.doi.org/10.1214/09-AOAS321 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A survey of statistical network models
Networks are ubiquitous in science and have become a focal point for
discussion in everyday life. Formal statistical models for the analysis of
network data have emerged as a major topic of interest in diverse areas of
study, and most of these involve a form of graphical representation.
Probability models on graphs date back to 1959. Along with empirical studies in
social psychology and sociology from the 1960s, these early works generated an
active network community and a substantial literature in the 1970s. This effort
moved into the statistical literature in the late 1970s and 1980s, and the past
decade has seen a burgeoning network literature in statistical physics and
computer science. The growth of the World Wide Web and the emergence of online
networking communities such as Facebook, MySpace, and LinkedIn, and a host of
more specialized professional network communities has intensified interest in
the study of networks and network data. Our goal in this review is to provide
the reader with an entry point to this burgeoning literature. We begin with an
overview of the historical development of statistical network modeling and then
we introduce a number of examples that have been studied in the network
literature. Our subsequent discussion focuses on a number of prominent static
and dynamic network models and their interconnections. We emphasize formal
model descriptions, and pay special attention to the interpretation of
parameters and their estimation. We end with a description of some open
problems and challenges for machine learning and statistics.Comment: 96 pages, 14 figures, 333 reference
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