Learning flexible representations of stochastic processes on graphs

Graph convolutional networks adapt the architecture of convolutional neural networks to learn rich representations of data supported on arbitrary graphs by replacing the convolution operations of convolutional neural networks with graph-dependent linear operations. However, these graph-dependent linear operations are developed for scalar functions supported on undirected graphs. We propose a class of linear operations for stochastic (time-varying) processes on directed (or undirected) graphs to be used in graph convolutional networks. We propose a parameterization of such linear operations using functional calculus to achieve arbitrarily low learning complexity. The proposed approach is shown to model richer behaviors and display greater flexibility in learning representations than product graph methods

STWalk: Learning Trajectory Representations in Temporal Graphs

Analyzing the temporal behavior of nodes in time-varying graphs is useful for many applications such as targeted advertising, community evolution and outlier detection. In this paper, we present a novel approach, STWalk, for learning trajectory representations of nodes in temporal graphs. The proposed framework makes use of structural properties of graphs at current and previous time-steps to learn effective node trajectory representations. STWalk performs random walks on a graph at a given time step (called space-walk) as well as on graphs from past time-steps (called time-walk) to capture the spatio-temporal behavior of nodes. We propose two variants of STWalk to learn trajectory representations. In one algorithm, we perform space-walk and time-walk as part of a single step. In the other variant, we perform space-walk and time-walk separately and combine the learned representations to get the final trajectory embedding. Extensive experiments on three real-world temporal graph datasets validate the effectiveness of the learned representations when compared to three baseline methods. We also show the goodness of the learned trajectory embeddings for change point detection, as well as demonstrate that arithmetic operations on these trajectory representations yield interesting and interpretable results.Comment: 10 pages, 5 figures, 2 table

Distributed Dictionary Learning

The paper studies distributed Dictionary Learning (DL) problems where the learning task is distributed over a multi-agent network with time-varying (nonsymmetric) connectivity. This formulation is relevant, for instance, in big-data scenarios where massive amounts of data are collected/stored in different spatial locations and it is unfeasible to aggregate and/or process all the data in a fusion center, due to resource limitations, communication overhead or privacy considerations. We develop a general distributed algorithmic framework for the (nonconvex) DL problem and establish its asymptotic convergence. The new method hinges on Successive Convex Approximation (SCA) techniques coupled with i) a gradient tracking mechanism instrumental to locally estimate the missing global information; and ii) a consensus step, as a mechanism to distribute the computations among the agents. To the best of our knowledge, this is the first distributed algorithm with provable convergence for the DL problem and, more in general, bi-convex optimization problems over (time-varying) directed graphs

Nonasymptotic Convergence Rates for Cooperative Learning Over Time-Varying Directed Graphs

We study the problem of distributed hypothesis testing with a network of agents where some agents repeatedly gain access to information about the correct hypothesis. The group objective is to globally agree on a joint hypothesis that best describes the observed data at all the nodes. We assume that the agents can interact with their neighbors in an unknown sequence of time-varying directed graphs. Following the pioneering work of Jadbabaie, Molavi, Sandroni, and Tahbaz-Salehi, we propose local learning dynamics which combine Bayesian updates at each node with a local aggregation rule of private agent signals. We show that these learning dynamics drive all agents to the set of hypotheses which best explain the data collected at all nodes as long as the sequence of interconnection graphs is uniformly strongly connected. Our main result establishes a non-asymptotic, explicit, geometric convergence rate for the learning dynamic