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.

A common challenge for Bayesian models of perception is the fact that the two fundamental Bayesian components, the prior distribution and the likelihood function, areformally unconstrained. Here we argue that a neural system that emulates Bayesian inference is naturally constrained by the way it represents sensory information inpopulations of neurons. More specifically, we show that an efficient coding principle creates a direct link between prior and likelihood based on the underlying stimulus distribution. The resulting Bayesian estimates can show biases awayfrom the peaks of the prior distribution, a behavior seemingly at odds with the traditional view of Bayesian estimation, yet one that has been reported in human perception. We demonstrate that our framework correctly accounts for the repulsive biases previously reported for the perception of visual orientation, and show that the predicted tuning characteristics of the model neurons match the reported orientation tuning properties of neurons in primary visual cortex. Our results suggest that efficient coding is a promising hypothesis in constraining Bayesianmodels of perceptual inference.

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.

Approaches to audio classification and retrieval tasks largely rely on detectionbased discriminativemodels. We submit that such models make a simplistic assumption inmapping acoustics directly to semantics, whereas the actual process is likely more complex. We present a generative model that maps acoustics in a hierarchical manner to increasingly higher-level semantics. Our model has two layers with the first layer modeling generalized sound units with no clear semantic associations, while the second layer models local patterns over these sound units. We evaluate our model on a large-scale retrieval task from TRECVID 2011, and report significant improvements over standard baselines.

We present a multi-task learning approach to jointly estimate the means of multiple independent data sets. The proposed multi-task averaging (MTA) algorithm results in a convex combination of the single-task averages. We derive the optimal amount of regularization, and show that it can be effectively estimated. Simulations and real data experiments demonstrate that MTA both maximum likelihood and James-Stein estimators, and that our approach to estimating the amount of regularization rivals cross-validation in performance but is more computationally efficient.

We consider the problem of learning control policies via trajectory preference queries to an expert. In particular, the learning agent can present an expert with short runs of a pair of policies originating from the same state and the expert then indicates the preferred trajectory. The agent's goal is to elicit a latent target policy from the expert with as few queries as possible. To tackle this problem we propose a novel Bayesian model of the querying process and introduce two methods that exploit this model to actively select expert queries. Experimental results on four benchmark problems indicate that our model can effectively learn policies from trajectory preference queries and that active query selection can be substantially more efficient than random selection.

We present a new learning strategy based on an efficient blocked Gibbs sampler for sparse overcomplete linear models. Particular emphasis is placed on statistical image modeling, where overcomplete models have played an important role in discovering sparse representations. Our Gibbs sampler is faster than general purpose sampling schemes while also requiring no tuning as it is free of parameters. Using the Gibbs sampler and a persistent variant of expectation maximization, we are able to extract highly sparse distributions over latent sources from data. When applied to natural images, our algorithm learns source distributions which resemble spike-and-slab distributions. We evaluate the likelihood and quantitatively compare the performance of the overcomplete linear model to its complete counterpart as well as a product of experts model, which represents another overcomplete generalization of the complete linear model. In contrast to previous claims, we find that overcomplete representations lead to significant improvements, but that the overcomplete linear model still underperforms other models.

In this work, we consider the problem of modeling the dynamic structure of human activities in the attributes space. A video sequence is first represented in a semantic feature space, where each feature encodes the probability of occurrence of an activity attribute at a given time. A generative model, denoted the binary dynamic system (BDS), is proposed to learn both the distribution and dynamics of different activities in this space. The BDS is a non-linear dynamic system, which extends both the binary principal component analysis (PCA) and classical linear dynamic systems (LDS), by combining binary observation variables with a hidden Gauss-Markov state process. In this way, it integrates the representation power of semantic modeling with the ability of dynamic systems to capture the temporal structure of time-varying processes. An algorithm for learning BDS parameters, inspired by a popular LDS learning method from dynamic textures, is proposed. A similarity measure between BDSs, which generalizes the Binet-Cauchy kernel for LDS, is then introduced and used to design activity classifiers. The proposed method is shown to outperform similar classifiers derived from the kernel dynamic system (KDS) and state-of-the-art approaches for dynamics-based or attribute-based action recognition.