This paper studies a new and more general axiomatization than one presented previously for preference on likelihood gambles. Likelihood gambles describe actions in a situation where a decision maker knows multiple probabilistic models and a random sample generated from one of those models but does not know prior probability of models. This new axiom system is inspired by Jensen's axiomatization of probabilistic gambles. Our approach provides a new perspective to the role of data in decision making under ambiguity. It avoids one of the most controversial issue of Bayesian methodology namely the assumption of prior probability.

In Bayesian networks, a Most Probable Explanation (MPE) is a complete variable instantiation with a highest probability given the current evidence. In this paper, we discuss the problem of finding robustness conditions of the MPE under single parameter changes. Specifically, we ask the question: How much change in a single network parameter can we afford to apply while keeping the MPE unchanged? We will describe a procedure, which is the first of its kind, that computes this answer for each parameter in the Bayesian network variable in time O(n exp(w)), where n is the number of network variables and w is its treewidth.

We describe an expert system, MAIES, developed for analysing forensic identification problems involving DNA mixture traces using quantitative peak area information. Peak area information is represented by conditional Gaussian distributions, and inference based on exact junction tree propagation ascertains whether individuals, whose profiles have been measured, have contributed to the mixture. The system can also be used to predict DNA profiles of unknown contributors by separating the mixture into its individual components. The use of the system is illustrated with an application to a real world example. The system implements a novel MAP (maximum a posteriori) search algorithm that is described in an appendix.

Predicting the outcomes of future events is a challenging problem for which a variety of solution methods have been explored and attempted. We present an empirical comparison of a variety of online and offline adaptive algorithms for aggregating experts' predictions of the outcomes of five years of US National Football League games (1319 games) using expert probability elicitations obtained from an Internet contest called ProbabilitySports. We find that it is difficult to improve over simple averaging of the predictions in terms of prediction accuracy, but that there is room for improvement in quadratic loss. Somewhat surprisingly, a Bayesian estimation algorithm which estimates the variance of each expert's prediction exhibits the most consistent superior performance over simple averaging among our collection of algorithms.

We introduce a new dynamic model with the capability of recognizing both activities that an individual is performing as well as where that ndividual is located. Our model is novel in that it utilizes a dynamic graphical model to jointly estimate both activity and spatial context over time based on the simultaneous use of asynchronous observations consisting of GPS measurements, and measurements from a small mountable sensor board. Joint inference is quite desirable as it has the ability to improve accuracy of the model. A key goal, however, in designing our overall system is to be able to perform accurate inference decisions while minimizing the amount of hardware an individual must wear. This minimization leads to greater comfort and flexibility, decreased power requirements and therefore increased battery life, and reduced cost. We show results indicating that our joint measurement model outperforms measurements from either the sensor board or GPS alone, using two types of probabilistic inference procedures, namely particle filtering and pruned exact inference.

In recent years Bayesian networks (BNs) with a mixture of continuous and discrete variables have received an increasing level of attention. We present an architecture for exact belief update in Conditional Linear Gaussian BNs (CLG BNs). The architecture is an extension of lazy propagation using operations of Lauritzen & Jensen [6] and Cowell [2]. By decomposing clique and separator potentials into sets of factors, the proposed architecture takes advantage of independence and irrelevance properties induced by the structure of the graph and the evidence. The resulting benefits are illustrated by examples. Results of a preliminary empirical performance evaluation indicate a significant potential of the proposed architecture.

SDYNA is a general framework designed to address large stochastic reinforcement learning problems. Unlike previous model based methods in FMDPs, it incrementally learns the structure and the parameters of a RL problem using supervised learning techniques. Then, it integrates decision-theoric planning algorithms based on FMDPs to compute its policy. SPITI is an instanciation of SDYNA that exploits ITI, an incremental decision tree algorithm, to learn the reward function and the Dynamic Bayesian Networks with local structures representing the transition function of the problem. These representations are used by an incremental version of the Structured Value Iteration algorithm. In order to learn the structure, SPITI uses Chi-Square tests to detect the independence between two probability distributions. Thus, we study the relation between the threshold used in the Chi-Square test, the size of the model built and the relative error of the value function of the induced policy with respect to the optimal value. We show that, on stochastic problems, one can tune the threshold so as to generate both a compact model and an efficient policy. Then, we show that SPITI, while keeping its model compact, uses the generalization property of its learning method to perform better than a stochastic classical tabular algorithm in large RL problem with an unknown structure. We also introduce a new measure based on Chi-Square to qualify the accuracy of the model learned by SPITI. We qualitatively show that the generalization property in SPITI within the FMDP framework may prevent an exponential growth of the time required to learn the structure of large stochastic RL problems.

This paper is concerned with graphical criteria that can be used to solve the problem of identifying casual effects from nonexperimental data in a causal Bayesian network structure, i.e., a directed acyclic graph that represents causal relationships. We first review Pearl's work on this topic [Pearl, 1995], in which several useful graphical criteria are presented. Then we present a complete algorithm [Huang and Valtorta, 2006b] for the identifiability problem. By exploiting the completeness of this algorithm, we prove that the three basic do-calculus rules that Pearl presents are complete, in the sense that, if a causal effect is identifiable, there exists a sequence of applications of the rules of the do-calculus that transforms the causal effect formula into a formula that only includes observational quantities.

Traditional approaches to Bayes net structure learning typically assume little regularity in graph structure other than sparseness. However, in many cases, we expect more systematicity: variables in real-world systems often group into classes that predict the kinds of probabilistic dependencies they participate in. Here we capture this form of prior knowledge in a hierarchical Bayesian framework, and exploit it to enable structure learning and type discovery from small datasets. Specifically, we present a nonparametric generative model for directed acyclic graphs as a prior for Bayes net structure learning. Our model assumes that variables come in one or more classes and that the prior probability of an edge existing between two variables is a function only of their classes. We derive an MCMC algorithm for simultaneous inference of the number of classes, the class assignments of variables, and the Bayes net structure over variables. For several realistic, sparse datasets, we show that the bias towards systematicity of connections provided by our model yields more accurate learned networks than a traditional, uniform prior approach, and that the classes found by our model are appropriate.

The National Airspace System (NAS) is a large and complex system with thousands of interrelated components: administration, control centers, airports, airlines, aircraft, passengers, etc. The complexity of the NAS creates many difficulties in management and control. One of the most pressing problems is flight delay. Delay creates high cost to airlines, complaints from passengers, and difficulties for airport operations. As demand on the system increases, the delay problem becomes more and more prominent. For this reason, it is essential for the Federal Aviation Administration to understand the causes of delay and to find ways to reduce delay. Major contributing factors to delay are congestion at the origin airport, weather, increasing demand, and air traffic management (ATM) decisions such as the Ground Delay Programs (GDP). Delay is an inherently stochastic phenomenon. Even if all known causal factors could be accounted for, macro-level national airspace system (NAS) delays could not be predicted with certainty from micro-level aircraft information. This paper presents a stochastic model that uses Bayesian Networks (BNs) to model the relationships among different components of aircraft delay and the causal factors that affect delays. A case study on delays of departure flights from Chicago O'Hare international airport (ORD) to Hartsfield-Jackson Atlanta International Airport (ATL) reveals how local and system level environmental and human-caused factors combine to affect components of delay, and how these components contribute to the final arrival delay at the destination airport.