An important challenge in understanding climate change is to uncover the dependency relationships between various climate observations and forcing factors. Graphical lasso, a recently proposed L 1 penalty based structure learning algorithm, has been proven successful for learning underlying dependency structures for the data drawn from a multivariate Gaussian distribution. However, climatological data often turn out to be non-Gaussian, e.g. cloud cover, precipitation, etc. In this paper, we examine nonparametric learning methods to address this challenge. In particular, we develop a methodology to learn dynamic graph structures from spatial-temporal data so that the graph structures at adjacent time or locations are similar. Experimental results demonstrate that our method not only recovers the underlying graph well but also captures the smooth variation properties on both synthetic data and climate data. An important challenge in understanding climate change is to uncover the dependency relationships between various climate observations and forcing factors. Graphical lasso, a recently proposed An important challenge in understanding climate change is to uncover the dependency relationships between various climate observations and forcing factors. Graphical lasso, a recently proposed L 1 penalty based structure learning algorithm, has been proven successful for learning underlying dependency structures for the data drawn from a multivariate Gaussian distribution. However, climatological data often turn out to be non-Gaussian, e.g. cloud cover, precipitation, etc. In this paper, we examine nonparametric learning methods to address this challenge. In particular, we develop a methodology to learn dynamic graph structures from spatial-temporal data so that the graph structures at adjacent time or locations are similar. Experimental results demonstrate that our method not only recovers the underlying graph well but also captures the smooth variation properties on both synthetic data and climate data.

The precise specification of reward functions for Markov decision processes (MDPs) is often extremely difficult, motivating research into both reward elicitation and the robust solution of MDPs with imprecisely specified reward (IRMDPs). We develop new techniques for the robust optimization of IRMDPs, using the minimax regret decision criterion, that exploit the set of nondominated policies, i.e., policies that are optimal for some instantiation of the imprecise reward function. Drawing parallels to POMDP value functions, we devise a Witness-style algorithm for identifying nondominated policies. We also examine several new algorithms for computing minimax regret using the nondominated set, and examine both practically and theoretically the impact of approximating this set. Our results suggest that a small subset of the nondominated set can greatly speed up computation, yet yield very tight approximations to minimax regret.

Model minimization in Factored Markov Decision Processes (FMDPs) is concerned with finding the most compact partition of the state space such that all states in the same block are action-equivalent. This is an important problem because it can potentially transform a large FMDP into an equivalent but much smaller one, whose solution can be readily used to solve the original model. Previous model minimization algorithms are iterative in nature, making opaque the relationship between the input model and the output partition. We demonstrate that given a set of well-defined concepts and operations on partitions, we can express the model minimization problem in an analytic fashion. The theoretical results developed can be readily applied to solving problems such as estimating the size of the minimum partition, refining existing algorithms, and so on.

Planning in large, partially observable domains is challenging, especially when a long-horizon lookahead is necessary to obtain a good policy. Traditional POMDP planners that plan a different potential action for each future observation can be prohibitively expensive when planning many steps ahead. An efficient solution for planning far into the future in fully observable domains is to use temporally-extended sequences of actions, or "macro-actions." In this paper, we present a POMDP algorithm for planning under uncertainty with macro-actions (PUMA) that automatically constructs and evaluates open-loop macro-actions within forward-search planning, where the planner branches on observations only at the end of each macro-action. Additionally, we show how to incrementally refine the plan over time, resulting in an anytime algorithm that provably converges to an epsilon-optimal policy. In experiments on several large POMDP problems which require a long horizon lookahead, PUMA outperforms existing state-of-the art solvers.

Pairwise Markov Networks (PMN) are an important class of Markov networks which, due to their simplicity, are widely used in many applications such as image analysis, bioinformatics, sensor networks, etc. However, learning of Markov networks from data is a challenging task; there are many possible structures one must consider and each of these structures comes with its own parameters making it easy to overfit the model with limited data. To deal with the problem, recent learning methods build upon the L1 regularization to express the bias towards sparse network structures. In this paper, we propose a new and more flexible framework that let us bias the structure, that can, for example, encode the preference to networks with certain local substructures which as a whole exhibit some special global structure. We experiment with and show the benefit of our framework on two types of problems: learning of modular networks and learning of traffic networks models.

Recent research has shown that surprisingly rich models of human behavior can be learned from GPS (positional) data. However, most research to date has concentrated on modeling single individuals or aggregate statistical properties of groups of people. Given noisy real-world GPS data, we---in contrast---consider the problem of modeling and recognizing activities that involve multiple related individuals playing a variety of roles. Our test domain is the game of capture the flag---an outdoor game that involves many distinct cooperative and competitive joint activities. We model the domain using Markov logic, a statistical relational language, and learn a theory that jointly denoises the data and infers occurrences of high-level activities, such as capturing a player. Our model combines constraints imposed by the geometry of the game area, the motion model of the players, and by the rules and dynamics of the game in a probabilistically and logically sound fashion. We show that while it may be impossible to directly detect a multi-agent activity due to sensor noise or malfunction, the occurrence of the activity can still be inferred by considering both its impact on the future behaviors of the people involved as well as the events that could have preceded it. We compare our unified approach with three alternatives (both probabilistic and nonprobabilistic) where either the denoising of the GPS data and the detection of the high-level activities are strictly separated, or the states of the players are not considered, or both. We show that the unified approach with the time window spanning the entire game, although more computationally costly, is significantly more accurate.

As we see later, the mathematical derivations are more elaborate A Bayesian network is a probabilistic graphical model that than those recently introduced for BIC and AIC criteria relies on a structured dependency among random variables (de Campos, Zeng, and Ji 2009), and the reduction in the to represent a joint probability distribution in a compact and search space and cache size are less effective when priors efficient manner. It is composed by a directed acyclic graph are strong, but still relevant. This is expected, as the BIC (DAG) where nodes are associated to random variables and score is known to penalize complex graphs more than BD conditional probability distributions are defined for variables scores do. We show that the search space can be reduced given their parents in the graph. Learning the graph (or without losing the global optimality guarantee and that the structure) of these networks from data is one of the most memory requirements are small in many practical cases.

This paper introduces a principled approach for the design of a scalable general reinforcement learning agent. This approach is based on a direct approximation of AIXI, a Bayesian optimality notion for general reinforcement learning agents. Previously, it has been unclear whether the theory of AIXI could motivate the design of practical algorithms. We answer this hitherto open question in the affirmative, by providing the first computationally feasible approximation to the AIXI agent. To develop our approximation, we introduce a Monte Carlo Tree Search algorithm along with an agent-specific extension of the Context Tree Weighting algorithm. Empirically, we present a set of encouraging results on a number of stochastic, unknown, and partially observable domains.

In an interlinked corpus of documents, the context in which a citation appears provides extra information about the cited document. However, associating terms in the context to the cited document remains an open problem. We propose a novel document generation approach that statistically incorporates the context in which a document links to another document. We quantitatively show that the proposed generation scheme explains the linking phenomenon better than previous approaches. The context information along with the actual content of the document provides significant improvements over the previous approaches for various real world evaluation tasks such as link prediction and log-likelihood estimation on unseen content. The proposed method is more scalable to large collection of documents compared to the previous approaches.

Many problems require repeated inference on probabilistic graphical models, with different values for evidence variables or other changes. Examples of such problems include utility maximization, MAP inference, online and interactive inference, parameter and structure learning, and dynamic inference. Since small changes to the evidence typically only affect a small region of the network, repeatedly performing inference from scratch can be massively redundant. In this paper, we propose expanding frontier belief propagation (EFBP), an efficient approximate algorithm for probabilistic inference with incremental changes to the evidence (or model). EFBP is an extension of loopy belief propagation (BP) where each run of inference reuses results from the previous ones, instead of starting from scratch with the new evidence; messages are only propagated in regions of the network affected by the changes. We provide theoretical guarantees bounding the difference in beliefs generated by EFBP and standard BP, and apply EFBP to the problem of expected utility maximization in influence diagrams. Experiments on viral marketing and combinatorial auction problems show that EFBP can converge much faster than BP without significantly affecting the quality of the solutions.