For many large undirected models that arise in real-world applications, exact maximumlikelihood training is intractable, because it requires computing marginal distributions of the model. Conditional training is even more difficult, because the partition function depends not only on the parameters, but also on the observed input, requiring repeated inference over each training example. An appealing idea for such models is to independently train a local undirected classifier over each clique, afterwards combining the learned weights into a single global model. In this paper, we show that this piecewise method can be justified as minimizing a new family of upper bounds on the log partition function. On three natural-language data sets, piecewise training is more accurate than pseudolikelihood, and often performs comparably to global training using belief propagation.

We consider the estimation of the policy gradient in partially observable Markov decision processes (POMDP) with a special class of structured policies that are finite-state controllers. We show that the gradient estimation can be done in the Actor-Critic framework, by making the critic compute a "value" function that does not depend on the states of POMDP. This function is the conditional mean of the true value function that depends on the states. We show that the critic can be implemented using temporal difference (TD) methods with linear function approximations, and the analytical results on TD and Actor-Critic can be transfered to this case. Although Actor-Critic algorithms have been used extensively in Markov decision processes (MDP), up to now they have not been proposed for POMDP as an alternative to the earlier proposal GPOMDP algorithm, an actor-only method. Furthermore, we show that the same idea applies to semi-Markov problems with a subset of finite-state controllers.

Markov Decision Processes (MDPs) are widely popular in Artificial Intelligence for modeling sequential decision-making scenarios with probabilistic dynamics. They are the framework of choice when designing an intelligent agent that needs to act for long periods of time in an environment where its actions could have uncertain outcomes. MDPs are actively researched in two related subareas of AI, probabilistic planning and reinforcement learning. Probabilistic planning assumes known models for the agent's goals and domain dynamics, and focuses on determining how the agent should behave to achieve its objectives. On the other hand, reinforcement learning additionally learns these models based on the feedback the agent gets from the environment.

We consider unsupervised estimation of mixtures of discrete graphical models, where the class variable corresponding to the mixture components is hidden and each mixture component over the observed variables can have a potentially different Markov graph structure and parameters. We propose a novel approach for estimating the mixture components, and our output is a tree-mixture model which serves as a good approximation to the underlying graphical model mixture. Our method is efficient when the union graph, which is the union of the Markov graphs of the mixture components, has sparse vertex separators between any pair of observed variables. This includes tree mixtures and mixtures of bounded degree graphs. For such models, we prove that our method correctly recovers the union graph structure and the tree structures corresponding to maximum-likelihood tree approximations of the mixture components. The sample and computational complexities of our method scale as $\poly(p, r)$, for an $r$-component mixture of $p$-variate graphical models. We further extend our results to the case when the union graph has sparse local separators between any pair of observed variables, such as mixtures of locally tree-like graphs, and the mixture components are in the regime of correlation decay.

We present a novel approach to detecting and utilizing symmetries in probabilistic graphical models with two main contributions. First, we present a scalable approach to computing generating sets of permutation groups representing the symmetries of graphical models. Second, we introduce orbital Markov chains, a novel family of Markov chains leveraging model symmetries to reduce mixing times. We establish an insightful connection between model symmetries and rapid mixing of orbital Markov chains. Thus, we present the first lifted MCMC algorithm for probabilistic graphical models. Both analytical and empirical results demonstrate the effectiveness and efficiency of the approach.

We consider the problem of learning the optimal action-value function in the discounted-reward Markov decision processes (MDPs). We prove a new PAC bound on the sample-complexity of model-based value iteration algorithm in the presence of the generative model, which indicates that for an MDP with N state-action pairs and the discount factor \gamma\in[0,1) only O(N\log(N/\delta)/((1-\gamma)^3\epsilon^2)) samples are required to find an \epsilon-optimal estimation of the action-value function with the probability 1-\delta. We also prove a matching lower bound of \Theta (N\log(N/\delta)/((1-\gamma)^3\epsilon^2)) on the sample complexity of estimating the optimal action-value function by every RL algorithm. To the best of our knowledge, this is the first matching result on the sample complexity of estimating the optimal (action-) value function in which the upper bound matches the lower bound of RL in terms of N, \epsilon, \delta and 1/(1-\gamma). Also, both our lower bound and our upper bound significantly improve on the state-of-the-art in terms of 1/(1-\gamma).

Bayesian reinforcement learning (BRL) encodes prior knowledge of the world in a model and represents uncertainty in model parameters by maintaining a probability distribution over them. This paper presents Monte Carlo BRL (MC-BRL), a simple and general approach to BRL. MC-BRL samples a priori a finite set of hypotheses for the model parameter values and forms a discrete partially observable Markov decision process (POMDP) whose state space is a cross product of the state space for the reinforcement learning task and the sampled model parameter space. The POMDP does not require conjugate distributions for belief representation, as earlier works do, and can be solved relatively easily with point-based approximation algorithms. MC-BRL naturally handles both fully and partially observable worlds. Theoretical and experimental results show that the discrete POMDP approximates the underlying BRL task well with guaranteed performance.

We examine the problem of learning a probabilistic model for melody directly from musical sequences belonging to the same genre. This is a challenging task as one needs to capture not only the rich temporal structure evident in music, but also the complex statistical dependencies among different music components. To address this problem we introduce the Variable-gram Topic Model, which couples the latent topic formalism with a systematic model for contextual information. We evaluate the model on next-step prediction. Additionally, we present a novel way of model evaluation, where we directly compare model samples with data sequences using the Maximum Mean Discrepancy of string kernels, to assess how close is the model distribution to the data distribution. We show that the model has the highest performance under both evaluation measures when compared to LDA, the Topic Bigram and related non-topic models.

In this paper we propose an algorithm that builds sparse decision DAGs (directed acyclic graphs) from a list of base classifiers provided by an external learning method such as AdaBoost. The basic idea is to cast the DAG design task as a Markov decision process. Each instance can decide to use or to skip each base classifier, based on the current state of the classifier being built. The result is a sparse decision DAG where the base classifiers are selected in a data-dependent way. The method has a single hyperparameter with a clear semantics of controlling the accuracy/speed trade-off. The algorithm is competitive with state-of-the-art cascade detectors on three object-detection benchmarks, and it clearly outperforms them when there is a small number of base classifiers. Unlike cascades, it is also readily applicable for multi-class classification. Using the multi-class setup, we show on a benchmark web page ranking data set that we can significantly improve the decision speed without harming the performance of the ranker.

We investigate the problem of modeling symbolic sequences of polyphonic music in a completely general piano-roll representation. We introduce a probabilistic model based on distribution estimators conditioned on a recurrent neural network that is able to discover temporal dependencies in high-dimensional sequences. Our approach outperforms many traditional models of polyphonic music on a variety of realistic datasets. We show how our musical language model can serve as a symbolic prior to improve the accuracy of polyphonic transcription.