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.

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 [1] 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.

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.

Kernel-based stochastic factorization (KBSF) is an algorithm for solving reinforcement learningtasks with continuous state spaces which builds a Markov decision process (MDP) based on a set of sample transitions. What sets KBSF apart from other kernel-based approaches is the fact that the size of its MDP is independent ofthe number of transitions, which makes it possible to control the tradeoff between the quality of the resulting approximation and the associated computational cost.However, KBSF's memory usage grows linearly with the number of transitions, precluding its application in scenarios where a large amount of data must be processed. In this paper we show that it is possible to construct KBSF's MDP in a fully incremental way, thus freeing the space complexity of this algorithm fromits dependence on the number of sample transitions. The incremental version of KBSF is able to process an arbitrary amount of data, which results in a model-based reinforcement learning algorithm that can be used to solve continuous MDPsin both off-line and online regimes. We present theoretical results showing that KBSF can approximate the value function that would be computed by conventional kernel-based learning with arbitrary precision. We empirically demonstrate the effectiveness of the proposed algorithm in the challenging threepole balancingtask, in which the ability to process a large number of transitions is crucial for success.

Partially-observable Markov decision processes (POMDPs) provide a powerful model for real-world sequential decision-making problems. In recent years, point- based value iteration methods have proven to be extremely effective techniques for finding (approximately) optimal dynamic programming solutions to POMDPs when an initial set of belief states is known. However, no point-based work has provided exact point-based backups for both continuous state and observation spaces, which we tackle in this paper. Our key insight is that while there may be an infinite number of possible observations, there are only a finite number of observation partitionings that are relevant for optimal decision-making when a finite, fixed set of reachable belief states is known. To this end, we make two important contributions: (1) we show how previous exact symbolic dynamic pro- gramming solutions for continuous state MDPs can be generalized to continu- ous state POMDPs with discrete observations, and (2) we show how this solution can be further extended via recently developed symbolic methods to continuous state and observations to derive the minimal relevant observation partitioning for potentially correlated, multivariate observation spaces. We demonstrate proof-of- concept results on uni- and multi-variate state and observation steam plant control.

Undirected graphical models, or Markov networks, such as Gaussian graphical models and Ising models enjoy popularity in a variety of applications. In many settings, however, data may not follow a Gaussian or binomial distribution assumed by these models. We introduce a new class of graphical models based on generalized linear models (GLM) by assuming that node-wise conditional distributions arise from exponential families. Our models allow one to estimate networks for a wide class of exponential distributions, such as the Poisson, negative binomial, and exponential, by fitting penalized GLMs to select the neighborhood for each node. A major contribution of this paper is the rigorous statistical analysis showing that with high probability, the neighborhood of our graphical models can be recovered exactly. We provide examples of high-throughput genomic networks learned via our GLM graphical models for multinomial and Poisson distributed data.

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. Together, these innovations allow tractable analysis of hundreds of time series, where previous inference required clever initialization and at least ten thousand burn-in iterations for just six sequences.

How does the brain combine prior knowledge with sensory evidence when making decisions under uncertainty? Two competing descriptive models have been proposed based on experimental data. The first posits an additive offset to a decision variable, implying a static effect of the prior. However, this model is inconsistent with recent data from a motion discrimination task involving temporal integration of uncertain sensory evidence. To explain this data, a second model has been proposed which assumes a time-varying influence of the prior. Here we present a normative model of decision making that incorporates prior knowledge in a principled way. We show that the additive offset model and the time-varying prior model emerge naturally when decision making is viewed within the framework of partially observable Markov decision processes (POMDPs). Decision making in the model reduces to (1) computing beliefs given observations and prior information in a Bayesian manner, and (2) selecting actions based on these beliefs to maximize the expected sum of future rewards. We show that the model can explain both data previously explained using the additive offset model as well as more recent data on the time-varying influence of prior knowledge on decision making.

In a large visual multi-class detection framework, the timeliness of results can be crucial. Our method for timely multi-class detection aims to give the best possible performance at any single point after a start time; it is terminated at a deadline time. Toward this goal, we formulate a dynamic, closed-loop policy that infers the contents of the image in order to decide which detector to deploy next. In contrast to previous work, our method significantly diverges from the predominant greedy strategies, and is able to learn to take actions with deferred values. We evaluate our method with a novel timeliness measure, computed as the area under an Average Precision vs. Time curve. Experiments are conducted on the eminent PASCAL VOC object detection dataset. If execution is stopped when only half the detectors have been run, our method obtains $66\%$ better AP than a random ordering, and $14\%$ better performance than an intelligent baseline. On the timeliness measure, our method obtains at least $11\%$ better performance. Our code, to be made available upon publication, is easily extensible as it treats detectors and classifiers as black boxes and learns from execution traces using reinforcement learning.

We propose a simple and novel framework for MCMC inference in continuous-time discrete-state systems with pure jump trajectories. We construct an exact MCMC sampler for such systems by alternately sampling a random discretization of time given a trajectory of the system, and then a new trajectory given the discretization. The first step can be performed efficiently using properties of the Poisson process, while the second step can avail of discrete-time MCMC techniques based on the forward-backward algorithm. We compare our approach to particle MCMC and a uniformization-based sampler, and show its advantages.