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.

Dependency networks are a compelling alternative to Bayesian networks for learning joint probability distributions from data and using them to compute probabilities. A dependency network consists of a set of conditional probability distributions, each representing the probability of a single variable given its Markov blanket. Running Gibbs sampling with these conditional distributions produces a joint distribution that can be used to answer queries, but suffers from the traditional slowness of sampling-based inference. In this paper, we observe that the mean field update equation can be applied to dependency networks, even though the conditional probability distributions may be inconsistent with each other. In experiments with learning and inference on 12 datasets, we demonstrate that mean field inference in dependency networks offers similar accuracy to Gibbs sampling but with orders of magnitude improvements in speed. Compared to Bayesian networks learned on the same data, dependency networks offer higher accuracy at greater amounts of evidence. Furthermore, mean field inference is consistently more accurate in dependency networks than in Bayesian networks learned on the same data.

The automated processing of multiple seismic signals to detect and localize seismic events is a central tool in both geophysics and nuclear treaty verification. This paper reports on a project, begun in 2009, to reformulate this problem in a Bayesian framework. A Bayesian seismic monitoring system, NET-VISA, has been built comprising a spatial event prior and generative models of event transmission and detection, as well as an inference algorithm. Applied in the context of the International Monitoring System (IMS), a global sensor network developed for the Comprehensive Nuclear-Test-Ban Treaty (CTBT), NET-VISA achieves a reduction of around 50% in the number of missed events compared to the currently deployed system. It also finds events that are missed even by the human analysts who post-process the IMS output.

We consider a learning setting of importance to large scale machine learning: potentially unlimited data arrives sequentially, but only a small fraction of it is labeled. The learner cannot store the data; it should learn from both labeled and unlabeled data, and it may also request labels for some of the unlabeled items. This setting is frequently encountered in real-world applications and has the characteristics of online, semi-supervised, and active learning. Yet previous learning models fail to consider these characteristics jointly. We present OASIS, a Bayesian model for this learning setting. The main contributions of the model include the novel integration of a semi-supervised likelihood function, a sequential Monte Carlo scheme for efficient online Bayesian updating, and a posterior-reduction criterion for active learning. Encouraging results on both synthetic and real-world optical character recognition data demonstrate the synergy of these characteristics in OASIS.

We address the problem of building a continuous occupancy representation of the environment with ranging sensors. Observations from such sensors provide two types of information: a line segment or a beam indicating no returns along them (free-space); a point or return at the end of the segment representing an occupied surface. To model these two types of observations in a principled statistical manner, we propose a novel methodology based on integral kernels. We show that integral kernels can be directly incorporated into a Gaussian process classification (GPC) framework to provide a continuous non-parametric Bayesian estimation of occupancy. Directly handling line segment and point observations avoids the need to discretise segments into points, reducing the computational cost of GPC inference and learning. We present experiments on 2D and 3D datasets demonstrating the benefits of the approach.

We study iterative randomized greedy algorithms for generating (elimination) orderings with small induced width and state space size — two parameters known to bound the complexity of inference in graphical models. We propose and implement the Iterative Greedy Variable Ordering (IGVO) algorithm, a new variant within this algorithm class. An empirical evaluation using different ranking functions and conditions of randomness, demonstrates that IGVO finds significantly better orderings than standard greedy ordering implementations when evaluated within an anytime framework. Additional order of magnitude improvements are demonstrated on a multi-core system, thus further expanding the set of solvable graphical models. The experiments also confirm the superiority of the MinFill heuristic within the iterative scheme.

Categories are often organized into hierarchical taxonomies, that is, tree structures where each node represents a labeled category, and a node's parent and children are, respectively, the category's supertype and subtypes. A natural question is whether it is possible to reconstruct category taxonomies in cases where we are not given explicit information about how categories are related to each other, but only a sample of observations of the members of each category. In this paper, we introduce a nonparametric Bayesian model of multi-level category learning, an extension of the hierarchical Dirichlet process (HDP) that we call the tree-HDP. We demonstrate the ability of the tree-HDP to reconstruct simulated datasets of artificial taxonomies, and show that it produces similar performance to human learners on a taxonomy inference task.

This paper studies how automated agents can persuade humans to behave in certain ways. The motivation behind such agent's behavior resides in the utility function that the agent's designer wants to maximize and which may be different from the user's utility function. Specifically, in the strategic settings studied, the agent provides correct yet partial information about a state of the world that is unknown to the user but relevant to his decision. Persuasion games were designed to study interactions between automated players where one player sends state information to the other to persuade it to behave in a certain way. We show that this game theory based model is not sufficient to model human-agent interactions, since people tend to deviate from the rational choice. We use machine learning to model such deviation in people from this game theory based model. The agent generates a probabilistic description of the world state that maximizes its benefit and presents it to the users. The proposed model was evaluated in an extensive empirical study involving road selection tasks that differ in length, costs and congestion. Results showed that people's behavior indeed deviated significantly from the behavior predicted by the game theory based model. Moreover, the agent developed in our model performed better than an agent that followed the behavior dictated by the game-theoretical models.

We propose a novel probabilistic model for collaborative filtering (CF), called SRMCoFi, which seamlessly integrates both linear and bilinear random effects into a principled framework. The formulation of SRMCoFi is supported by both social psychological experiments and statistical theories. Not only can many existing CF methods be seen as special cases of SRMCoFi, but it also integrates their advantages while simultaneously overcoming their disadvantages. The solid theoretical foundation of SRMCoFi is further supported by promising empirical results obtained in extensive experiments using real CF data sets on movie ratings.

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.