The sum-product or belief propagation (BP) algorithm is a widely-used message-passing algorithm for computing marginal distributions in graphical models with discrete variables. At the core of the BP message updates, when applied to a graphical model with pairwise interactions, lies a matrix-vector product with complexity that is quadratic in the state dimension $d$, and requires transmission of a $(d-1)$-dimensional vector of real numbers (messages) to its neighbors. Since various applications involve very large state dimensions, such computation and communication complexities can be prohibitively complex. In this paper, we propose a low-complexity variant of BP, referred to as stochastic belief propagation (SBP). As suggested by the name, it is an adaptively randomized version of the BP message updates in which each node passes randomly chosen information to each of its neighbors. The SBP message updates reduce the computational complexity (per iteration) from quadratic to linear in $d$, without assuming any particular structure of the potentials, and also reduce the communication complexity significantly, requiring only $\log{d}$ bits transmission per edge. Moreover, we establish a number of theoretical guarantees for the performance of SBP, showing that it converges almost surely to the BP fixed point for any tree-structured graph, and for graphs with cycles satisfying a contractivity condition. In addition, for these graphical models, we provide non-asymptotic upper bounds on the convergence rate, showing that the $\ell_{\infty}$ norm of the error vector decays no slower than $O(1/\sqrt{t})$ with the number of iterations $t$ on trees and the mean square error decays as $O(1/t)$ for general graphs. These analysis show that SBP can provably yield reductions in computational and communication complexities for various classes of graphical models.

We present a new algorithm for exactly solving decision making problems represented as influence diagrams. We do not require the usual assumptions of no forgetting and regularity; this allows us to solve problems with simultaneous decisions and limited information. The algorithm is empirically shown to outperform a state-of-the-art algorithm on randomly generated problems of up to 150 variables and 10^64 solutions. We show that these problems are NP-hard even if the underlying graph structure of the problem has low treewidth and the variables take on a bounded number of states, and that they admit no provably good approximation if variables can take on an arbitrary number of states.

We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as established in machine learning. The equivalence holds when energy distances are computed with semimetrics of negative type, in which case a kernel may be defined such that the RKHS distance between distributions corresponds exactly to the energy distance. We determine the class of probability distributions for which kernels induced by semimetrics are characteristic (that is, for which embeddings of the distributions to an RKHS are injective). Finally, we investigate the performance of this family of kernels in two-sample and independence tests: we show in particular that the energy distance most commonly employed in statistics is just one member of a parametric family of kernels, and that other choices from this family can yield more powerful tests.

The quality criteria of system P have been guiding qualitative uncertain reasoning now for more than two decades. Different semantical approaches have been presented to provide semantics for system P. The aim of the present paper is to investigate the semantical structures underlying system P in more detail, namely, on the level of the models. In particular, we focus on the approach via conditional objects which relies on Boolean intervals, without making any use of qualitative or quantitative information. Indeed, our studies confirm the singular position of conditional objects, but we are also able to establish semantical relationships via novel variants of model theories.

Several authors analyzed propositional attitudes ( wish , fear , regret , glad ) by integrating their epistemic and deontic components. This paper extends previous work done by the author and presents a logical calculus inspired by Possibility Theory, a non-compositional version of fuzzy logic.

Analyzing international political behavior based on similar precedent circumstances is one of the basic techniques that policymakers use to monitor and assess current situations. Our goal is to investigate how to analyze geopolitical conflicts as sequences of events and to determine what probabilistic models are suitable to perform these analyses. In this paper, we evaluate the performance of N-grams models on the problem of forecasting political conflicts from sequences of events. For the current phase of the project, we focused on event data collected from the Balkans war in the 1990's. Our experimental results indicate that N-gram models have impressive results when applied to this data set, with accuracies above 90\% for most configurations.

The current paradigm in student modeling has continued to show the power of its simplifying assumption of knowledge as a binary and monotonically increasing construct, the value of which directly causes the outcome of student answers to questions. Recent efforts have focused on optimizing the prediction accuracy of responses to questions using student models. Incorporating individual student parameter interactions has been an interpretable and principled approach which has improved the performance of this task, as demonstrated by its application in the 2010 KDD Cup challenge on Educational Data. Performance prediction, however, can have limited practical utility. The greatest utility of such student models can be their ability to model the tutor and the attributes of the tutor which are causing learning. Harnessing the same simplifying assumption of learning used in student modeling, we can turn this model on its head to effectively tease out the tutor attributes causing learning and begin to optimize the tutor model to benefit the student model.

A possible approach to extend classical logics to probabilistic logics is to consider a probability distribution over the classical interpretations that satisfies some constraints and maximizes entropy. Over the past years miscellaneous languages and semantics have been considered often based on similar ideas. In this paper a hierarchy of general probabilistic semantics is developed. It incorporates some interesting specific semantics and a family of standard semantics that can be used to extend arbitrary languages with finite interpretation sets to probabilistic languages. We use the hierarchy to generalize an approach reducing the complexity of the whole entailment process and sketch the importance for further theoretical and practical applications.

We evaluated an affect-sensitive version of AutoTutor, a dialogue based ITS that simulates human tutors. While the original AutoTutor is sensitive to students’ cognitive states, the affect-sensitive tutor (Supportive tutor) also responds to students’ affective states (boredom, confusion, and frustration) with empathetic, encouraging, and motivational dialogue moves that are accompanied by appropriate emotional expressions. We conducted an experiment that compared the Supportive and Regular (non-affective) tutors over two 30-minute learning sessions with respect to perceived effectiveness, fidelity of cognitive and emotional feedback, engagement, and enjoyment. The results indicated that, irrespective of tutor, students’ ratings of engagement, enjoyment, and perceived learning decreased across sessions, but these ratings were not correlated with actual learning gains. In contrast, students’ perceptions of how closely the computer tutors resembled human tutors increased across learning sessions, was related to the quality of tutor feedback, the increase was greater for the Supportive tutor, and was a powerful predictor of learning. Implications of our findings for the design of affect-sensitive ITSs are discussed.

Decision making has proposed multiple methods to help the decision maker in his analysis, by suggesting ways of formalization of the preferences as well as the assessment of the uncertainties. Although these techniques are established and proven to be mathematically sound, experience has shown that in certain situations we tend to avoid the formal approach by acting intuitively. Especially, when the decision involves a large number of attributes and outcomes, and where we need to use pragmatic and heuristic simplifications such as considering only the most important attributes and omitting the others. In this paper, we provide a model for decision making in situations subject to a large predictive uncertainty with a small learning sample. The high predictive uncertainty is concretized by a countably infinite number of prospects, making the preferences assessment more difficult. Our main result is an extension of the Maximum Entropy utility (MEU) principle into an asymptotic maximum entropy utility principle for preferences elicitation. This will allow us to overcome the limits of the existing MEU method to the extend that we focus on utility assessment when the set of the available discrete prospects is countably infinite. Furthermore, our proposed model can be used to analyze situations of high-cognitive load as well as to understand how humans handle these problems under Ceteris Paribus assumption.