56,965 research outputs found
Stochastic Block Transition Models for Dynamic Networks
There has been great interest in recent years on statistical models for
dynamic networks. In this paper, I propose a stochastic block transition model
(SBTM) for dynamic networks that is inspired by the well-known stochastic block
model (SBM) for static networks and previous dynamic extensions of the SBM.
Unlike most existing dynamic network models, it does not make a hidden Markov
assumption on the edge-level dynamics, allowing the presence or absence of
edges to directly influence future edge probabilities while retaining the
interpretability of the SBM. I derive an approximate inference procedure for
the SBTM and demonstrate that it is significantly better at reproducing
durations of edges in real social network data.Comment: To appear in proceedings of AISTATS 201
Random graph models for dynamic networks
We propose generalizations of a number of standard network models, including
the classic random graph, the configuration model, and the stochastic block
model, to the case of time-varying networks. We assume that the presence and
absence of edges are governed by continuous-time Markov processes with rate
parameters that can depend on properties of the nodes. In addition to computing
equilibrium properties of these models, we demonstrate their use in data
analysis and statistical inference, giving efficient algorithms for fitting
them to observed network data. This allows us, for instance, to estimate the
time constants of network evolution or infer community structure from temporal
network data using cues embedded both in the probabilities over time that node
pairs are connected by edges and in the characteristic dynamics of edge
appearance and disappearance. We illustrate our methods with a selection of
applications, both to computer-generated test networks and real-world examples.Comment: 15 pages, four figure
Seasonality in Dynamic Stochastic Block Models
Sociotechnological and geospatial processes exhibit time varying structure
that make insight discovery challenging. This paper proposes a new statistical
model for such systems, modeled as dynamic networks, to address this challenge.
It assumes that vertices fall into one of k types and that the probability of
edge formation at a particular time depends on the types of the incident nodes
and the current time. The time dependencies are driven by unique seasonal
processes, which many systems exhibit (e.g., predictable spikes in geospatial
or web traffic each day). The paper defines the model as a generative process
and an inference procedure to recover the seasonal processes from data when
they are unknown. Evaluation with synthetic dynamic networks show the recovery
of the latent seasonal processes that drive its formation.Comment: 4 page worksho
Detectability thresholds and optimal algorithms for community structure in dynamic networks
We study the fundamental limits on learning latent community structure in
dynamic networks. Specifically, we study dynamic stochastic block models where
nodes change their community membership over time, but where edges are
generated independently at each time step. In this setting (which is a special
case of several existing models), we are able to derive the detectability
threshold exactly, as a function of the rate of change and the strength of the
communities. Below this threshold, we claim that no algorithm can identify the
communities better than chance. We then give two algorithms that are optimal in
the sense that they succeed all the way down to this limit. The first uses
belief propagation (BP), which gives asymptotically optimal accuracy, and the
second is a fast spectral clustering algorithm, based on linearizing the BP
equations. We verify our analytic and algorithmic results via numerical
simulation, and close with a brief discussion of extensions and open questions.Comment: 9 pages, 3 figure
- …