Tasks such as record linkage and multi-target tracking, which involve reconstructing the set of objects that underlie some observed data, are particularly challenging for probabilistic inference. Recent work has achieved efficient and accurate inference on such problems using Markov chain Monte Carlo (MCMC) techniques with customized proposal distributions. Currently, implementing such a system requires coding MCMC state representations and acceptance probability calculations that are specific to a particular application. An alternative approach, which we pursue in this paper, is to use a general-purpose probabilistic modeling language (such as BLOG) and a generic Metropolis-Hastings MCMC algorithm that supports user-supplied proposal distributions. Our algorithm gains flexibility by using MCMC states that are only partial descriptions of possible worlds; we provide conditions under which MCMC over partial worlds yields correct answers to queries. We also show how to use a context-specific Bayes net to identify the factors in the acceptance probability that need to be computed for a given proposed move. Experimental results on a citation matching task show that our general-purpose MCMC engine compares favorably with an application-specific system.

A popular approach to solving large probabilistic systems relies on aggregating states based on a measure of similarity. Many approaches in the literature are heuristic. A number of recent methods rely instead on metrics based on the notion of bisimulation, or behavioral equivalence between states (Givan et al, 2001, 2003; Ferns et al, 2004). An integral component of such metrics is the Kantorovich metric between probability distributions. However, while this metric enables many satisfying theoretical properties, it is costly to compute in practice. In this paper, we use techniques from network optimization and statistical sampling to overcome this problem. We obtain in this manner a variety of distance functions for MDP state aggregation, which differ in the tradeoff between time and space complexity, as well as the quality of the aggregation. We provide an empirical evaluation of these trade-offs.

Consider a multi-agent system in a dynamic and uncertain environment. Each agent's local decision problem is modeled as a Markov decision process (MDP) and agents must coordinate on a joint action in each period, which provides a reward to each agent and causes local state transitions. A social planner knows the model of every agent's MDP and wants to implement the optimal joint policy, but agents are self-interested and have private local state. We provide an incentive-compatible mechanism for eliciting state information that achieves the optimal joint plan in a Markov perfect equilibrium of the induced stochastic game. In the special case in which local problems are Markov chains and agents compete to take a single action in each period, we leverage Gittins allocation indices to provide an efficient factored algorithm and distribute computation of the optimal policy among the agents. Distributed, optimal coordinated learning in a multi-agent variant of the multi-armed bandit problem is obtained as a special case.

In Passive POMDPs actions do not affect the world state, but still incur costs. When the agent is bounded by information-processing constraints, it can only keep an approximation of the belief. We present a variational principle for the problem of maintaining the information which is most useful for minimizing the cost, and introduce an efficient and simple algorithm for finding an optimum.

In recent years a number of methods have been developed for automatically learning the (sparse) connectivity structure of Markov Random Fields. These methods are mostly based on L1-regularized optimization which has a number of disadvantages such as the inability to assess model uncertainty and expensive cross-validation to find the optimal regularization parameter. Moreover, the model's predictive performance may degrade dramatically with a suboptimal value of the regularization parameter (which is sometimes desirable to induce sparseness). We propose a fully Bayesian approach based on a "spike and slab" prior (similar to L0 regularization) that does not suffer from these shortcomings. We develop an approximate MCMC method combining Langevin dynamics and reversible jump MCMC to conduct inference in this model. Experiments show that the proposed model learns a good combination of the structure and parameter values without the need for separate hyper-parameter tuning. Moreover, the model's predictive performance is much more robust than L1-based methods with hyper-parameter settings that induce highly sparse model structures.

In unsupervised classification, Hidden Markov Models (HMM) are used to account for a neighborhood structure between observations. The emission distributions are often supposed to belong to some parametric family. In this paper, a semiparametric modeling where the emission distributions are a mixture of parametric distributions is proposed to get a higher flexibility. We show that the classical EM algorithm can be adapted to infer the model parameters. For the initialisation step, starting from a large number of components, a hierarchical method to combine them into the hidden states is proposed. Three likelihood-based criteria to select the components to be combined are discussed. To estimate the number of hidden states, BIC-like criteria are derived. A simulation study is carried out both to determine the best combination between the merging criteria and the model selection criteria and to evaluate the accuracy of classification. The proposed method is also illustrated using a biological dataset from the model plant Arabidopsis thaliana. A R package HMMmix is freely available on the CRAN.

In this paper we propose a novel gradient algorithm to learn a policy from an expert's observed behavior assuming that the expert behaves optimally with respect to some unknown reward function of a Markovian Decision Problem. The algorithm's aim is to find a reward function such that the resulting optimal policy matches well the expert's observed behavior. The main difficulty is that the mapping from the parameters to policies is both nonsmooth and highly redundant. Resorting to subdifferentials solves the first difficulty, while the second one is over- come by computing natural gradients. We tested the proposed method in two artificial domains and found it to be more reliable and efficient than some previous methods.

Relational Markov Random Fields are a general and flexible framework for reasoning about the joint distribution over attributes of a large number of interacting entities. The main computational difficulty in learning such models is inference. Even when dealing with complete data, where one can summarize a large domain by sufficient statistics, learning requires one to compute the expectation of the sufficient statistics given different parameter choices. The typical solution to this problem is to resort to approximate inference procedures, such as loopy belief propagation. Although these procedures are quite efficient, they still require computation that is on the order of the number of interactions (or features) in the model. When learning a large relational model over a complex domain, even such approximations require unrealistic running time. In this paper we show that for a particular class of relational MRFs, which have inherent symmetry, we can perform the inference needed for learning procedures using a template-level belief propagation. This procedure's running time is proportional to the size of the relational model rather than the size of the domain. Moreover, we show that this computational procedure is equivalent to sychronous loopy belief propagation. This enables a dramatic speedup in inference and learning time. We use this procedure to learn relational MRFs for capturing the joint distribution of large protein-protein interaction networks.

Memory-Bounded Dynamic Programming (MBDP) has proved extremely effective in solving decentralized POMDPs with large horizons. We generalize the algorithm and improve its scalability by reducing the complexity with respect to the number of observations from exponential to polynomial. We derive error bounds on solution quality with respect to this new approximation and analyze the convergence behavior. To evaluate the effectiveness of the improvements, we introduce a new, larger benchmark problem. Experimental results show that despite the high complexity of decentralized POMDPs, scalable solution techniques such as MBDP perform surprisingly well.

Relational Markov Decision Processes are a useful abstraction for complex reinforcement learning problems and stochastic planning problems. Recent work developed representation schemes and algorithms for planning in such problems using the value iteration algorithm. However, exact versions of more complex algorithms, including policy iteration, have not been developed or analyzed. The paper investigates this potential and makes several contributions. First we observe two anomalies for relational representations showing that the value of some policies is not well defined or cannot be calculated for restricted representation schemes used in the literature. On the other hand, we develop a variant of policy iteration that can get around these anomalies. The algorithm includes an aspect of policy improvement in the process of policy evaluation and thus differs from the original algorithm. We show that despite this difference the algorithm converges to the optimal policy.