Stackelberg games have recently gained significant attention for resource allocation decisions in security settings. One critical assumption of traditional Stackelberg models is that all players are perfectly rational and that the followers perfectly observe the leader’s strategy. However, in real-world security settings, security agencies must deal with human adversaries who may not always follow the utility maximizing rational strategy. Accounting for these likely deviations is important since they may adversely affect the leader’s (security agency’s) utility. In fact, a number of behavioral gametheoretic models have begun to emerge for these domains. Two such models in particular are COBRA (Combined Observability and Bounded Rationality Assumption) and BRQR (Best Response to Quantal Response), which have both been shown to outperform game-theoretic optimal models against human adversaries within a security setting based on Los Angeles International Airport (LAX). Under perfect observation conditions, BRQR has been shown to be the leading contender for addressing human adversaries. In this work we explore these models under limited observation conditions. Due to human anchoring biases, BRQR’s performance may suffer under limited observation conditions. An anchoring bias is when, given no information about the occurrence of a discrete set of events, humans will tend to assign an equal weight to the occurrence of each event (a uniform distribution). This study makes three main contributions: (i) we incorporate an anchoring bias into BRQR to improve performance under limited observation; (ii) we explore finding appropriate parameter settings for BRQR under limited observation; (iii) we compare BRQR’s performance versus COBRA under limited observation conditions.

Utility elicitation is an important component of many applications, such as decision support systems and recommender systems. Such systems query users about their preferences and offer recommendations based on the system's belief about the user's utility function. We analyze the connection between the problem of generating optimal recommendation sets and the problem of generating optimal choice queries, considering both Bayesian and regret-based elicitation. Our results show that, somewhat surprisingly, under very general circumstances, the optimal recommendation set coincides with the optimal query.

We propose an intelligent tutoring system that constructs a curriculum of hints and problems in order to teach a student skills with a rich dependency structure. We provide a template for building a multi-layered Dynamic Bayes Net to model this problem and describe how to learn the parameters of the model from data. Planning with the DBN then produces a teaching policy for the given domain. We test this end-to-end curriculum design system in two human-subject studies in the areas of finite field arithmetic and artificial language and show this method performs on par with hand-tuned expert policies.

Intelligent tutoring systems (ITSs) provide students with a one-on-one tutor, allowing them to work at their own pace, and helping them to focus on their weaker areas. The RUR1–Python Learning Environment (RUR-PLE), a game-like virtual environment to help students learn to program, provides an interface for students to write their own Python code and visualize the code execution (Roberge 2005). RUR-PLE provides a fixed sequence of learning lessons for students to explore. We are extending RUR-PLE to develop the Playing to Program (PtP) ITS, which consists of three components: (1) a Bayesian student model that tracks student competence, (2) a diagnosis module that provides tailored feedback to students, and (3) a problem selection module that guides the student’s learning process. In this paper, we summarize RUR-PLE and the PtP design, and describe an ongoing user study to evaluate the predictive accuracy of our student modeling approach.

The Approximate Linear Programming (ALP) approach to value function approximation for MDPs is a parametric value function approximation method, in that it represents the value function as a linear combination of features which are chosen a priori. Choosing these features can be a difficult challenge in itself. One recent effort, Regularized Approximate Linear Programming (RALP), uses L1 regularization to address this issue by combining a large initial set of features with a regularization penalty that favors a smooth value function with few non-zero weights. Rather than using smoothness as a backhanded way of addressing the feature selection problem, this paper starts with smoothness and develops a non-parametric approach to ALP that is consistent with the smoothness assumption. We show that this new approach has some favorable practical and analytical properties in comparison to (R)ALP.

Blocking is a technique commonly used in manual statistical analysis to account for confounding variables. However, blocking is not currently used in automated learning algorithms. These algorithms rely solely on statistical conditioning as an operator to identify conditional independence. In this work, we present relational blocking as a new operator that can be used for learning the structure of causal models. We describe how blocking is enabled by relational data sets, where blocks are determined by the links in the network. By blocking on entities rather than conditioning on variables, relational blocking can account for both measured and unobserved variables. We explain the mechanism of these methods using graphical models and the semantics of d-separation. Finally, we demonstrate the effectiveness of relational blocking for use in causal discovery by showing how blocking can be used in the causal analysis of two real-world social media systems.

A key problem in statistical modeling is model selection, how to choose a model at an appropriate level of complexity. This problem appears in many settings, most prominently in choosing the number ofclusters in mixture models or the number of factors in factor analysis. In this tutorial we describe Bayesian nonparametric methods, a class of methods that side-steps this issue by allowing the data to determine the complexity of the model. This tutorial is a high-level introduction to Bayesian nonparametric methods and contains several examples of their application.

Aggregate factors (that is, those based on aggregate functions such as SUM, AVERAGE, AND etc.) in probabilistic relational models can compactly represent dependencies among a large number of relational random variables. However, propositional inference on a factor aggregating n k -valued random variables into an r -valued result random variable is O ( r k 2 n ). Lifted methods can ameliorate this to O ( r n k ) in general and O ( r k log n ) for commutative associative aggregators. In this paper, we propose (a) an exact solution constant in n when k  = 2 for certain aggregate operations such as AND, OR and SUM, and (b) a close approximation for inference with aggregate factors with time complexity constant in n . This approximate inference involves an analytical solution for some operations when k > 2. The approximation is based on the fact that the typically used aggregate functions can be represented by linear constraints in the standard ( k  –1)-simplex in R k where k is the number of possible values for random variables. This includes even aggregate functions that are commutative but not associative (e.g., the MODE operator that chooses the most frequent value). Our algorithm takes polynomial time in k (which is only 2 for binary variables) regardless of r and n, and the error decreases as n increases. Therefore, for most applications (in which a close approximation suffices) our algorithm is a much more efficient solution than existing algorithms. We present experimental results supporting these claims. We also present a (c) third contribution which further optimizes aggregations over multiple groups of random variables with distinct distributions.

Integrating the expressive power of first-order logic with the ability of probabilistic reasoning of Bayesian networks has attracted the interest of many researchers for decades. We present an approach to integration that translates logical knowledge into Bayesian networks and uses Bayesian network composition to build a uniform representation that supports both logical and probabilistic reasoning. In particular, we propose a new way of translation of logical knowledge, relation search. Through the use of the proposed framework, without learning new languages or tools, modelers are allowed to 1) specify special knowledge using the most suitable languages, while reasoning in a uniform engine; 2) make use of pre-existing logical knowledge bases for probabilistic reasoning (to complete the model or minimize potential inconsistencies).

We focus on a class of models used for representing the dynamics between a discrete set of probabilistic events in a continuous-time setting. The proposed framework offers tractable learning and inference procedures and provides compact state representations for processes which exhibit variable delays between events. The approach is applied to a heart sound labeling task that exhibits long-range dependencies on previous events, and in which explicit modeling of the rhythm timings is justifiable by cardiological principles.