Finding Non-overlapping Clusters for Generalized Inference Over Graphical Models

Graphical models use graphs to compactly capture stochastic dependencies amongst a collection of random variables. Inference over graphical models corresponds to finding marginal probability distributions given joint probability distributions. In general, this is computationally intractable, which has led to a quest for finding efficient approximate inference algorithms. We propose a framework for generalized inference over graphical models that can be used as a wrapper for improving the estimates of approximate inference algorithms. Instead of applying an inference algorithm to the original graph, we apply the inference algorithm to a block-graph, defined as a graph in which the nodes are non-overlapping clusters of nodes from the original graph. This results in marginal estimates of a cluster of nodes, which we further marginalize to get the marginal estimates of each node. Our proposed block-graph construction algorithm is simple, efficient, and motivated by the observation that approximate inference is more accurate on graphs with longer cycles. We present extensive numerical simulations that illustrate our block-graph framework with a variety of inference algorithms (e.g., those in the libDAI software package). These simulations show the improvements provided by our framework.Comment: Extended the previous version to include extensive numerical simulations. See http://www.ima.umn.edu/~dvats/GeneralizedInference.html for code and dat

Cooperative answers in database systems

A major concern of researchers who seek to improve human-computer communication involves how to move beyond literal interpretations of queries to a level of responsiveness that takes the user's misconceptions, expectations, desires, and interests into consideration. At Maryland, we are investigating how to better meet a user's needs within the framework of the cooperative answering system of Gal and Minker. We have been exploring how to use semantic information about the database to formulate coherent and informative answers. The work has two main thrusts: (1) the construction of a logic formula which embodies the content of a cooperative answer; and (2) the presentation of the logic formula to the user in a natural language form. The information that is available in a deductive database system for building cooperative answers includes integrity constraints, user constraints, the search tree for answers to the query, and false presuppositions that are present in the query. The basic cooperative answering theory of Gal and Minker forms the foundation of a cooperative answering system that integrates the new construction and presentation methods. This paper provides an overview of the cooperative answering strategies used in the CARMIN cooperative answering system, an ongoing research effort at Maryland. Section 2 gives some useful background definitions. Section 3 describes techniques for collecting cooperative logical formulae. Section 4 discusses which natural language generation techniques are useful for presenting the logic formula in natural language text. Section 5 presents a diagram of the system

Subjective Causality and Counterfactuals in the Social Sciences

The article explores the role that subjective evidence of causality and associated counterfactuals and counterpotentials might play in the social sciences where comparative cases are scarce. This scarcity rules out statistical inference based upon frequencies and usually invites in-depth ethnographic studies. Thus, if causality is to be preserved in such situations, a conception of ethnographic causal inference is required. Ethnographic causality inverts the standard statistical concept of causal explanation in observational studies, whereby comparison and generalization, across a sample of cases, are both necessary prerequisites for any causal inference. Ethnographic causality allows, in contrast, for causal explanation prior to any subsequent comparison or generalization

Are Individuals Fickle-Minded?

Game theory has been used to model large-scale social events — such as constitutional law, democratic stability, standard setting, gender roles, social movements, communication, markets, the selection of officials by means of elections, coalition formation, resource allocation, distribution of goods, and war — as the aggregate result of individual choices in interdependent decision-making. Game theory in this way assumes methodological individualism. The widespread observation that game theory predictions do not in general match observation has led to many attempts to repair game theory by creating behavioral game theory, which adds corrective terms to the game theoretic predictions in the hope of making predictions that better match observations. But for game theory to be useful in making predictions, we must be able to generalize from an individual’s behavior in one situation to that individual’s behavior in very closely similar situations. In other words, behavioral game theory needs individuals to be reasonably consistent in action if the theory is to have predictive power. We argue on the basis of experimental evidence that the assumption of such consistency is unwarranted. More realistic models of individual agents must be developed that acknowledge the variance in behavior for a given individual