Learning Latent Block Structure in Weighted Networks

arXiv.org Machine Learning

Community detection is an important task in network analysis, in which we aim to learn a network partition that groups together vertices with similar community-level connectivity patterns. By finding such groups of vertices with similar structural roles, we extract a compact representation of the network's large-scale structure, which can facilitate its scientific interpretation and the prediction of unknown or future interactions. Popular approaches, including the stochastic block model, assume edges are unweighted, which limits their utility by throwing away potentially useful information. We introduce the `weighted stochastic block model' (WSBM), which generalizes the stochastic block model to networks with edge weights drawn from any exponential family distribution. This model learns from both the presence and weight of edges, allowing it to discover structure that would otherwise be hidden when weights are discarded or thresholded. We describe a Bayesian variational algorithm for efficiently approximating this model's posterior distribution over latent block structures. We then evaluate the WSBM's performance on both edge-existence and edge-weight prediction tasks for a set of real-world weighted networks. In all cases, the WSBM performs as well or better than the best alternatives on these tasks.


Sequential effects reflect parallel learning of multiple environmental regularities

Neural Information Processing Systems

Across a wide range of cognitive tasks, recent experience influences behavior. For example, when individuals repeatedly perform a simple two-alternative forced-choice task (2AFC), response latencies vary dramatically based on the immediately preceding trial sequence. These sequential effects have been interpreted as adaptation to the statistical structure of an uncertain, changing environment (e.g. Jones & Sieck, 2003; Mozer, Kinoshita, & Shettel, 2007; Yu & Cohen, 2008). The Dynamic Belief Model (DBM) (Yu & Cohen, 2008) explains sequential effects in 2AFC tasks as a rational consequence of a dynamic internal representation that tracks second-order statistics of the trial sequence (repetition rates) and predicts whether the upcoming trial will be a repetition or an alternation of the previous trial. Experimental results suggest that first-order statistics (base rates) also influence sequential effects. We propose a model that learns both first- and second-order sequence properties, each according to the basic principles of the DBM but under a unified inferential framework. This model, the Dynamic Belief Mixture Model (DBM2), obtains precise, parsimonious fits to data. Furthermore, the model predicts dissociations in behavioral (Maloney, Dal Martello, Sahm, & Spillmann, 2005) and electrophysiological studies (Jentzsch & Sommer, 2002), supporting the psychological and neurobiological reality of its two components.


CAPIR: Collaborative Action Planning with Intention Recognition

AAAI Conferences

We apply decision theoretic techniques to construct non-player characters that are able to assist a human player in collaborative games. The method is based on solving Markov decision processes, which can be difficult when the game state is described by many variables. To scale to more complex games, the method allows decomposition of a game task into subtasks, each of which can be modelled by a Markov decision process. Intention recognition is used to infer the subtask that the human is currently performing, allowing the helper to assist the human in performing the correct task. Experiments show that the method can be effective, giving near-human level performance in helping a human in a collaborative game.


Sensible Decisions: Towar Invariants eoretic Infor

AAAI Conferences

The world demands behavior that is immediate, and yet guided by the anticipated consequences of observed events. As designers of autonomous agents, we seek robustness in agent behavior in the face of uncertainty. Decision theory and game theory (Savage 1954; von Neumann & Morgenstern 1947) are normative theories of action with optimal prescriptions about rational behavior. Applying these theories is often a battle with computational complexity (Cooper 1990). The space of possible contingencies is typically large, and guaranteeing an agent's response time to external events often requires trading off the optimality of the agent's decisions. For this reason, there is great interest in theories of qualitative probability and decision theory incorporating, for example, technology from nonmonotonic reasoning (Goldszmidt 1993). We propose a new point in the spectrum of qualitative decision-making, a continuous counterpart to symbolic qualitative reasoning. Our theory attempts to shed light on the informational utility of certain classes of geometric relations and perceptual cues.


A Proposal for Statistical Outlier Detection in Relational Structures

AAAI Conferences

This paper extends unsupervised statistical outlier detection to the case of relational data. For nonrelational data, where each individual is characterized by a feature vector, a common approach starts with learning a generative statistical model for the population. The model assigns a likelihood measure for the feature vector that characterizes the individual; the lower the feature vector likelihood, the more anomalous the individual. A difference between relational and nonrelational data is that an individual is characterized not only by a list of attributes, but also by its links and by attributes of the individuals linked to it. We refer to a relational structure that specifies this information for a specific individual as the individual's database. Our proposal is to use the likelihood assigned by a generative model to the individual's database as the anomaly score for the individual; the lower the model likelihood, the more anomalous the individual. As a novel validation method, we compare the model likelihood with metrics of individual success. An empirical evaluation reveals a surprising finding in soccer and movie data: We observe in the data a strong correlation between the likelihood and success metrics.