This paper addresses the issue of model selection for hidden Markov models (HMMs). We generalize factorized asymptotic Bayesian inference (FAB), which has been recently developed for model selection on independent hidden variables (i.e., mixture models), for time-dependent hidden variables. As with FAB in mixture models, FAB for HMMs is derived as an iterative lower bound maximization algorithm of a factorized information criterion (FIC). It inherits, from FAB for mixture models, several desirable properties for learning HMMs, such as asymptotic consistency of FIC with marginal log-likelihood, a shrinkage effect for hidden state selection, monotonic increase of the lower FIC bound through the iterative optimization. Further, it does not have a tunable hyper-parameter, and thus its model selection process can be fully automated. Experimental results shows that FAB outperforms states-of-the-art variational Bayesian HMM and non-parametric Bayesian HMM in terms of model selection accuracy and computational efficiency.

An efficient way to learn deep density models that have many layers of latent variables is to learn one layer at a time using a model that has only one layer of latent variables. After learning each layer, samples from the posterior distributions for that layer are used as training data for learning the next layer. This approach is commonly used with Restricted Boltzmann Machines, which are undirected graphical models with a single hidden layer, but it can also be used with Mixtures of Factor Analysers (MFAs) which are directed graphical models. In this paper, we present a greedy layer-wise learning algorithm for Deep Mixtures of Factor Analysers (DMFAs). Even though a DMFA can be converted to an equivalent shallow MFA by multiplying together the factor loading matrices at different levels, learning and inference are much more efficient in a DMFA and the sharing of each lower-level factor loading matrix by many different higher level MFAs prevents overfitting. We demonstrate empirically that DM-FAs learn better density models than both MFAs and two types of Restricted Boltzmann Machine on a wide variety of datasets.

We study the convergence rate of stochastic optimization of exact (NP-hard) objectives, for which only biased estimates of the gradient are available. We motivate this problem in the context of learning the structure and parameters of Ising models. We first provide a convergence-rate analysis of deterministic errors for forward-backward splitting (FBS). We then extend our analysis to biased stochastic errors, by first characterizing a family of samplers and providing a high probability bound that allows understanding not only FBS, but also proximal gradient (PG) methods. We derive some interesting conclusions: FBS requires only a logarithmically increasing number of random samples in order to converge (although at a very low rate); the required number of random samples is the same for the deterministic and the biased stochastic setting for FBS and basic PG; accelerated PG is not guaranteed to converge in the biased stochastic setting.

In this paper, we propose a simple, versatile model for learning the structure and parameters of multivariate distributions from a data set. Learning a Markov network from a given data set is not a simple problem, because Markov networks rigorously represent Markov properties, and this rigor imposes complex constraints on the design of the networks. Our proposed model removes these constraints, acquiring important aspects from the information geometry. The proposed parameter- and structure-learning algorithms are simple to execute as they are based solely on local computation at each node. Experiments demonstrate that our algorithms work appropriately.

This paper explores unsupervised learning of parsing models along two directions. First, which models are identifiable from infinite data? We use a general technique for numerically checking identifiability based on the rank of a Jacobian matrix, and apply it to several standard constituency and dependency parsing models. Second, for identifiable models, how do we estimate the parameters efficiently? EM suffers from local optima, while recent work using spectral methods cannot be directly applied since the topology of the parse tree varies across sentences. We develop a strategy, unmixing, which deals with this additional complexity for restricted classes of parsing models.

In this paper, we consider planning in stochastic shortest path (SSP) problems, a subclass of Markov Decision Problems (MDP). We focus on medium-size problems whose state space can be fully enumerated. This problem has numerous important applications, such as navigation and planning under uncertainty. We propose a new approach for constructing a multi-level hierarchy of progressively simpler abstractions of the original problem. Once computed, the hierarchy can be used to speed up planning by first finding a policy for the most abstract level and then recursively refining it into a solution to the original problem. This approach is fully automated and delivers a speed-up of two orders of magnitude over a state-of-the-art MDP solver on sample problems while returning near-optimal solutions. We also prove theoretical bounds on the loss of solution optimality resulting from the use of abstractions.

Parameter estimation in Markov random fields (MRFs) is a difficult task, in which inference over the network is run in the inner loop of a gradient descent procedure. Replacing exact inference with approximate methods such as loopy belief propagation (LBP) can suffer from poor convergence. In this paper, we provide a different approach for combining MRF learning and Bethe approximation. We consider the dual of maximum likelihood Markov network learning - maximizing entropy with moment matching constraints - and then approximate both the objective and the constraints in the resulting optimization problem. Unlike previous work along these lines (Teh & Welling, 2003), our formulation allows parameter sharing between features in a general log-linear model, parameter regularization and conditional training. We show that piecewise training (Sutton & McCallum, 2005) is a very restricted special case of this formulation. We study two optimization strategies: one based on a single convex approximation and one that uses repeated convex approximations. We show results on several real-world networks that demonstrate that these algorithms can significantly outperform learning with loopy and piecewise. Our results also provide a framework for analyzing the trade-offs of different relaxations of the entropy objective and of the constraints.

Gaussian Markov random fields (GMRFs) are useful in a broad range of applications. In this paper we tackle the problem of learning a sparse GMRF in a high-dimensional space. Our approach uses the l1-norm as a regularization on the inverse covariance matrix. We utilize a novel projected gradient method, which is faster than previous methods in practice and equal to the best performing of these in asymptotic complexity. We also extend the l1-regularized objective to the problem of sparsifying entire blocks within the inverse covariance matrix. Our methods generalize fairly easily to this case, while other methods do not. We demonstrate that our extensions give better generalization performance on two real domains--biological network analysis and a 2D-shape modeling image task.

Recent research leverages results from the continuous-armed bandit literature to create a reinforcement-learning algorithm for continuous state and action spaces. Initially proposed in a theoretical setting, we provide the first examination of the empirical properties of the algorithm. Through experimentation, we demonstrate the effectiveness of this planning method when coupled with exploration and model learning and show that, in addition to its formal guarantees, the approach is very competitive with other continuous-action reinforcement learners.

In contrast to previous competitions, where the problems were goal-based, the 2011 International Probabilistic Planning Competition (IPPC-2011) emphasized finite-horizon reward maximization problems with large branching factors. These MDPs modeled more realistic planning scenarios and presented challenges to the previous state-of-the-art planners (e.g., those from IPPC-2008), which were primarily based on domain determinization — a technique more suited to goal-oriented MDPs with small branching factors. Moreover, large branching factors render the existing implementations of RTDP- and LAO-style algorithms inefficient as well. In this paper we present GLUTTON, our planner at IPPC-2011 that performed well on these challenging MDPs. The main algorithm used by GLUTTON is LR2TDP, an LRTDP-based optimal algorithm for finite-horizon problems centered around the novel idea of reverse iterative deepening. We detail LR2TDP itself as well as a series of optimizations included in GLUTTON that help LR2TDP achieve competitive performance on difficult problems with large branching factors -- subsampling the transition function, separating out natural dynamics, caching transition function samples, and others. Experiments show that GLUTTON and PROST, the IPPC-2011 winner, have complementary strengths, with GLUTTON demonstrating superior performance on problems with few high-reward terminal states.