We present a new way of converting a reversible finite Markov chain into a nonreversible one, with a theoretical guarantee that the asymptotic variance of the MCMC estimator based on the non-reversible chain is reduced. The method is applicable to any reversible chain whose states are not connected through a tree, and can be interpreted graphically as inserting vortices into the state transition graph. Our result confirms that non-reversible chains are fundamentally better than reversible ones in terms of asymptotic performance, and suggests interesting directions for further improving MCMC.

This paper introduces a Monte-Carlo algorithm for online planning in large POMDPs. The algorithm combines a Monte-Carlo update of the agent's belief state with a Monte-Carlo tree search from the current belief state. The new algorithm, POMCP, has two important properties. First, Monte-Carlo sampling is used to break the curse of dimensionality both during belief state updates and during planning. Second, only a black box simulator of the POMDP is required, rather than explicit probability distributions. These properties enable POMCP to plan effectively in significantly larger POMDPs than has previously been possible. We demonstrate its effectiveness in three large POMDPs. We scale up a well-known benchmark problem, Rocksample, by several orders of magnitude. We also introduce two challenging new POMDPs: 10x10 Battleship and Partially Observable PacMan, with approximately 10^18 and 10^56 states respectively. Our Monte-Carlo planning algorithm achieved a high level of performance with no prior knowledge, and was also able to exploit simple domain knowledge to achieve better results with less search. POMCP is the first general purpose planner to achieve high performance in such large and unfactored POMDPs.

The reinforcement learning community has explored many approaches to obtain- ing value estimates and models to guide decision making; these approaches, how- ever, do not usually provide a measure of confidence in the estimate. Accurate estimates of an agent’s confidence are useful for many applications, such as bi- asing exploration and automatically adjusting parameters to reduce dependence on parameter-tuning. Computing confidence intervals on reinforcement learning value estimates, however, is challenging because data generated by the agent- environment interaction rarely satisfies traditional assumptions. Samples of value- estimates are dependent, likely non-normally distributed and often limited, partic- ularly in early learning when confidence estimates are pivotal. In this work, we investigate how to compute robust confidences for value estimates in continuous Markov decision processes. We illustrate how to use bootstrapping to compute confidence intervals online under a changing policy (previously not possible) and prove validity under a few reasonable assumptions. We demonstrate the applica- bility of our confidence estimation algorithms with experiments on exploration, parameter estimation and tracking.

We propose a novel Bayesian nonparametric approach to learning with probabilistic deterministic finite automata (PDFA). We define and develop and sampler for a PDFA with an infinite number of states which we call the probabilistic deterministic infinite automata (PDIA). Posterior predictive inference in this model, given a finite training sequence, can be interpreted as averaging over multiple PDFAs of varying structure, where each PDFA is biased towards having few states. We suggest that our method for averaging over PDFAs is a novel approach to predictive distribution smoothing. We test PDIA inference both on PDFA structure learning and on both natural language and DNA data prediction tasks. The results suggest that the PDIA presents an attractive compromise between the computational cost of hidden Markov models and the storage requirements of hierarchically smoothed Markov models.

We present a simple and effective approach to learning tractable conditional random fieldswith structure that depends on the evidence. Our approach retains the advantages of tractable discriminative models, namely efficient exact inference and arbitrarily accurate parameter learning in polynomial time. At the same time, our algorithm does not suffer a large expressive power penalty inherent to fixed tractable structures. On real-life relational datasets, our approach matches or exceeds stateof the art accuracy of the dense models, and at the same time provides an order of magnitude speedup.

Markov networks (MNs) can incorporate arbitrarily complex features in modeling relational data. However, this flexibility comes at a sharp price of training an exponentially complex model. To address this challenge, we propose a novel relational learning approach, which consists of a restricted class of relational MNs (RMNs) called relation tree-based RMN (treeRMN), and an efficient Hidden Variable Detection algorithm called Contrastive Variable Induction (CVI). On one hand, the restricted treeRMN only considers simple (e.g., unary and pairwise) features in relational data and thus achieves computational efficiency; and on the other hand, the CVI algorithm efficiently detects hidden variables which can capture long range dependencies. Therefore, the resultant approach is highly efficient yet does not sacrifice its expressive power. Empirical results on four real datasets show that the proposed relational learning method can achieve similar prediction quality as the state-of-the-art approaches, but is significantly more efficient in training; and the induced hidden variables are semantically meaningful and crucial to improve the training speed and prediction qualities of treeRMNs.

Accurate short-term wind forecasts (STWFs), with time horizons from 0.5 to 6 hours, are essential for efficient integration of wind power to the electrical power grid. Physical models based on numerical weather predictions are currently not competitive, and research on machine learning approaches is ongoing. Two major challenges confronting these efforts are missing observations and weather-regime induced dependency shifts among wind variables at geographically distributed sites. In this paper we introduce approaches that address both of these challenges. We describe a new regime-aware approach to STWF that use auto-regressive hidden Markov models (AR-HMM), a subclass of conditional linear Gaussian (CLG) models. Although AR-HMMs are a natural representation for weather regimes, as with CLG models in general, exact inference is NP-hard when observations are missing (Lerner and Parr, 2001). Because of this high cost, we introduce a simple approximate inference method for AR-HMMs, which we believe has applications to other sequential and temporal problem domains that involve continuous variables. In an empirical evaluation on publicly available wind data from two geographically distinct regions, our approach makes significantly more accurate predictions than baseline models, and uncovers meteorologically relevant regimes.

Since the discovery of sophisticated fully polynomial randomized algorithms for a range of #P problems (Karzanov et al., 1991; Jerrum et al., 2001; Wilson, 2004), theoretical work on approximate inference in combinatorial spaces has focused on Markov chain Monte Carlo methods. Despite their strong theoretical guarantees, the slow running time of many of these randomized algorithms and the restrictive assumptions on the potentials have hindered the applicability of these algorithms to machine learning. Because of this, in applications to combinatorial spaces simple exact models are often preferred to more complex models that require approximate inference (Siepel et al., 2004). Variational inference would appear to provide an appealing alternative, given the success of variational methods for graphical models (Wainwright et al., 2008); unfortunately, however, it is not obvious how to develop variational approximations for combinatorial objects such as matchings, partial orders, plane partitions and sequence alignments. We propose a new framework that extends variational inference to a wide range of combinatorial spaces. Our method is based on a simple assumption: the existence of a tractable measure factorization, which we show holds in many examples. Simulations on a range of matching models show that the algorithm is more general and empirically faster than a popular fully polynomial randomized algorithm. We also apply the framework to the problem of multiple alignment of protein sequences, obtaining state-of-the-art results on the BAliBASE dataset (Thompson et al., 1999).

We propose a new approach to value function approximation which combines linear temporal difference reinforcement learning with subspace identification. In practical applications, reinforcement learning (RL) is complicated by the fact that state is either high-dimensional or partially observable. Therefore, RL methods are designed to work with features of state rather than state itself, and the success or failure of learning is often determined by the suitability of the selected features. By comparison, subspace identification (SSID) methods are designed to select a feature set which preserves as much information as possible about state. In this paper we connect the two approaches, looking at the problem of reinforcement learning with a large set of features, each of which may only be marginally useful for value function approximation. We introduce a new algorithm for this situation, called Predictive State Temporal Difference (PSTD) learning. As in SSID for predictive state representations, PSTD finds a linear compression operator that projects a large set of features down to a small set that preserves the maximum amount of predictive information. As in RL, PSTD then uses a Bellman recursion to estimate a value function. We discuss the connection between PSTD and prior approaches in RL and SSID. We prove that PSTD is statistically consistent, perform several experiments that illustrate its properties, and demonstrate its potential on a difficult optimal stopping problem.

We propose a new probabilistic model for analyzing dynamic evolutions of relational data, such as additions, deletions and split & merge, of relation clusters like communities in social networks. Our proposed model abstracts observed time-varying object-object relationships into relationships between object clusters. We extend the infinite Hidden Markov model to follow dynamic and time-sensitive changes in the structure of the relational data and to estimate a number of clusters simultaneously. We show the usefulness of the model through experiments with synthetic and real-world data sets.