Applications such as robot control and wireless communication require planning under uncertainty. Partially observable Markov decision processes (POMDPs) plan policies for single agents under uncertainty and their decentralized versions (DEC-POMDPs) find a policy for multiple agents. The policy in infinite-horizon POMDP and DEC-POMDP problems has been represented as finite state controllers (FSCs). We introduce a novel class of periodic FSCs, composed of layers connected only to the previous and next layer. Our periodic FSC method finds a deterministic finite-horizon policy and converts it to an initial periodic infinite-horizon policy.

The expected return is a widely used objective in decision making under uncer- tainty. Many algorithms, such as value iteration, have been proposed to optimize it. In risk-aware settings, however, the expected return is often not an appropriate objective to optimize. We propose a new optimization objective for risk-aware planning and show that it has desirable theoretical properties. We also draw con- nections to previously proposed objectives for risk-aware planing: minmax, ex- ponential utility, percentile and mean minus variance.

We uncover relations between robust MDPs and risk-sensitive MDPs. The objective of a robust MDP is to minimize a function, such as the expectation of cumulative cost, for the worst case when the parameters have uncertainties. The objective of a risk-sensitive MDP is to minimize a risk measure of the cumulative cost when the parameters are known. We show that a risk-sensitive MDP of minimizing the expected exponential utility is equivalent to a robust MDP of minimizing the worst-case expectation with a penalty for the deviation of the uncertain parameters from their nominal values, which is measured with the Kullback-Leibler divergence. We also show that a risk-sensitive MDP of minimizing an iterated risk measure that is composed of certain coherent risk measures is equivalent to a robust MDP of minimizing the worst-case expectation when the possible deviations of uncertain parameters from their nominal values are characterized with a concave function.

Markov logic is a widely used tool in statistical relational learning, which uses a weighted first-order logic knowledge base to specify a Markov random field (MRF) or a conditional random field (CRF). In many applications, a Markov logic network (MLN) is trained in one domain, but used in a different one. This paper focuses on dynamic Markov logic networks, where the domain of time points typically varies between training and testing. It has been previously pointed out that the marginal probabilities of truth assignments to ground atoms can change if one extends or reduces the domains of predicates in an MLN. We show that in addition to this problem, the standard way of unrolling a Markov logic theory into a MRF may result in time-inhomogeneity of the underlying Markov chain.

Probabilistic graphical models are powerful tools for analyzing constrained, continuous domains. However, finding most-probable explanations (MPEs) in these models can be computationally expensive. In this paper, we improve the scalability of MPE inference in a class of graphical models with piecewise-linear and piecewise-quadratic dependencies and linear constraints over continuous domains. We derive algorithms based on a consensus-optimization framework and demonstrate their superior performance over state of the art. We show empirically that in a large-scale voter-preference modeling problem our algorithms scale linearly in the number of dependencies and constraints.

Applications of Bayesian nonparametric methods require learning and inference algorithms which efficiently explore models of unbounded complexity. We develop new Markov chain Monte Carlo methods for the beta process hidden Markov model (BP-HMM), enabling discovery of shared activity patterns in large video and motion capture databases. By introducing split-merge moves based on sequential allocation, we allow large global changes in the shared feature structure. We also develop data-driven reversible jump moves which more reliably discover rare or unique behaviors. Our proposals apply to any choice of conjugate likelihood for observed data, and we show success with multinomial, Gaussian, and autoregressive emission models.

Conditional Markov Chains (also known as Linear-Chain Conditional Random Fields in the literature) are a versatile class of discriminative models for the distribution of a sequence of hidden states conditional on a sequence of observable variables. Large-sample properties of Conditional Markov Chains have been first studied by Sinn and Poupart [1]. The paper extends this work in two directions: first, mixing properties of models with unbounded feature functions are being established; second, necessary conditions for model identifiability and the uniqueness of maximum likelihood estimates are being given.

We propose a Deep Boltzmann Machine for learning a generative model of multimodal data. We show how to use the model to extract a meaningful representation of multimodal data. We find that the learned representation is useful for classification and information retreival tasks, and hence conforms to some notion of semantic similarity. The model defines a probability density over the space of multimodal inputs. By sampling from the conditional distributions over each data modality, it possible to create the representation even when some data modalities are missing.

The Restricted Boltzmann Machine (RBM) is a popular density model that is also good for extracting features. A main source of tractability in RBM models is the model's assumption that given an input, hidden units activate independently from one another. Sparsity and competition in the hidden representation is believed to be beneficial, and while an RBM with competition among its hidden units would acquire some of the attractive properties of sparse coding, such constraints are not added due to the widespread belief that the resulting model would become intractable. In this work, we show how a dynamic programming algorithm developed in 1981 can be used to implement exact sparsity in the RBM's hidden units. We then expand on this and show how to pass derivatives through a layer of exact sparsity, which makes it possible to fine-tune a deep belief network (DBN) consisting of RBMs with sparse hidden layers.

Hierarchical Hidden Markov Models (HHMMs) are sophisticated stochastic models that enable us to capture a hierarchical context characterization of sequence data. However, existing HHMM parameter estimation methods require large computations of time complexity O(TN {2D}) at least for model inference, where D is the depth of the hierarchy, N is the number of states in each level, and T is the sequence length. In this paper, we propose a new inference method of HHMMs for which the time complexity is O(TN {D 1}). A key idea of our algorithm is application of the forward-backward algorithm to ''state activation probabilities''. The notion of a state activation, which offers a simple formalization of the hierarchical transition behavior of HHMMs, enables us to conduct model inference efficiently. We present some experiments to demonstrate that our proposed method works more efficiently to estimate HHMM parameters than do some existing methods such as the flattening method and Gibbs sampling method.