Bayesian inference is an appealing approach for leveraging prior knowledge in reinforcement learning (RL). In this paper we describe an algorithm for discovering different classes of roles for agents via Bayesian inference. In particular, we develop a Bayesian policy search approach for Multi-Agent RL (MARL), which is model-free and allows for priors on policy parameters. We present a novel optimization algorithm based on hybrid MCMC, which leverages both the prior and gradient information estimated from trajectories. Our experiments in a complex real-time strategy game demonstrate the effective discovery of roles from supervised trajectories, the use of discovered roles for successful transfer to similar tasks, and the discovery of roles through reinforcement learning.

The rigorous theoretical analyses of algorithms for #SAT have been proposed in the literature. As we know, previous algorithms for solving #SAT have been analyzed only regarding the number of variables as the parameter. However, the time complexity for solving #SAT instances depends not only on the number of variables, but also on the number of clauses. Therefore, it is significant to exploit the time complexity from the other point of view, i.e. the number of clauses. In this paper, we present algorithms for solving #2-SAT and #3-SAT with rigorous complexity analyses using the number of clauses as the parameter. By analyzing the algorithms, we obtain the new worst-case upper bounds O(1.1892m) for #2-SAT and O(1.4142m) for #3-SAT, where m is the number of clauses.

We present a method for unsupervised learning of event classes from videos in which multiple actions might occur simultaneously. It is assumed that all such activities are produced from an underlying set of event class generators. The learning task is then to recover this generative process from visual data. A set of event classes is derived from the most likely decomposition of the tracks into a set of labelled events involving subsets of interacting tracks. Interactions between subsets of tracks are modelled as a relational graph structure that captures qualitative spatio-temporal relationships between these tracks. The posterior probability of candidate solutions favours decompositions in which events of the same class have a similar relational structure, together with other measures of well-formedness. A Markov Chain Monte Carlo (MCMC) procedure is used to efficiently search for the MAP solution. This search moves between possible decompositions of the tracks into sets of unlabelled events and at each move adds a close to optimal labelling (for this decomposition) using spectral clustering. Experiments on real data show that the discovered event classes are often semantically meaningful and correspond well with groundtruth event classes assigned by hand.

Constructing models of mobile agents can be difficult without domain-specific knowledge. Parametric models flexible enough to capture all mobility patterns that an expert believes are possible are often large, requiring a great deal of training data. In contrast, nonparametric models are extremely flexible and can generalize well with relatively little training data. We propose modeling the mobility patterns of moving agents as a mixture of Gaussian processes (GP) with a Dirichlet process (DP) prior over mixture weights. The GP provides a flexible representation for each individual mobility pattern, while the DP assigns observed trajectories to particular mobility patterns. Both the GPs and the DP adjust the model's complexity based on available data, implicitly avoiding issues of over-fitting or under-fitting. We apply our model to a helicopter-based tracking task, where the mobility patterns of the tracked agents — cars — are learned from real data collected from taxis in the greater Boston area.

Matrix factorization is a fundamental technique in machine learning that is applicable to collaborative filtering, information retrieval and many other areas. In collaborative filtering and many other tasks, the objective is to fill in missing elements of a sparse data matrix. One of the biggest challenges in this case is filling in a column or row of the matrix with very few observations. In this paper we introduce a Bayesian matrix factorization model that performs regression against side information known about the data in addition to the observations. The side information helps by adding observed entries to the factored matrices. We also introduce a nonparametric mixture model for the prior of the rows and columns of the factored matrices that gives a different regularization for each latent class. Besides providing a richer prior, the posterior distribution of mixture assignments reveals the latent classes. Using Gibbs sampling for inference, we apply our model to the Netflix Prize problem of predicting movie ratings given an incomplete user-movie ratings matrix. Incorporating rating information with gathered metadata information, our Bayesian approach outperforms other matrix factorization techniques even when using fewer dimensions.

Traditional information extraction systems adopt pipeline strategies, which are highly ineffective and suffer from several problems such as error propagation. Typically, pipeline models fail to produce highly-accurate final output. On the other hand, there has been growing interest in integrated or joint models which explore mutual benefits and perform multiple subtasks simultaneously to avoid problems caused by pipeline models. However, building such systems usually increases computational complexity and requires considerable engineering. This paper presents a general, strongly-coupled, and bidirectional architecture based on discriminatively trained factor graphs for information extraction. First we introduce joint factors connecting variables of relevant subtasks to capture dependencies and interactions between them. We then propose a strong bidirectional MCMC sampling inference algorithm which allows information to flow in both directions to find the approximate MAP solution for all subtasks. Extensive experiments on entity identification and relation extraction using real-world data illustrate the promise of our approach.

Lifted inference, handling whole sets of indistinguishable objects together, is critical to the effective application of probabilistic relational models to realistic real world tasks. Recently, lifted belief propagation (LBP) has been proposed as an efficient approximate solution of this inference problem. It runs a modified BP on a lifted network where nodes have been grouped together if they have — roughly speaking — identical computation trees, the tree-structured “unrolling” of the underlying graph rooted at the nodes. In many situations, this purely syntactic criterion is too pessimistic: message errors decay along paths. Intuitively, for a long chain graph with weak edge potentials, distant nodes will send and receive identical messages yet their computation trees are quite different. To overcome this, we propose iLBP, a novel, easy-to-implement, informed LBP approach that interleaves lifting and modified BP iterations. In turn, we can efficiently monitor the true BP messages sent and received in each iteration and group nodes accordingly. As our experiments show, iLBP can yield significantly faster more lifted network while not degrading performance. Above all, we show that iLBP is faster than BP when solving the problem of distributing data to a large network, an important real-world application where BP is faster than uninformed LBP.

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.

Many methods for quantitative structure-activity relationships (QSARs) deliver point estimates only, without quantifying the uncertainty inherent in the prediction. One way to quantify the uncertainy of a QSAR prediction is to predict the conditional density of the activity given the structure instead of a point estimate. If a conditional density estimate is available, it is easy to derive prediction intervals of activities. In this paper, we experimentally evaluate and compare three methods for conditional density estimation for their suitability in QSAR modeling. In contrast to traditional methods for conditional density estimation, they are based on generic machine learning schemes, more specifically, class probability estimators. Our experiments show that a kernel estimator based on class probability estimates from a random forest classifier is highly competitive with Gaussian process regression, while taking only a fraction of the time for training. Therefore, generic machine-learning based methods for conditional density estimation may be a good and fast option for quantifying uncertainty in QSAR modeling.

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.