We propose a multiresolution Gaussian process to capture long-range, non-Markovian dependencies while allowing for abrupt changes and non-stationarity. The multiresolution GP hierarchically couples a collection of smooth GPs, each defined over an element of a random nested partition. Long-range dependencies are captured by the top-level GP while the partition points define the abrupt changes. Due to the inherent conjugacy of the GPs, one can analytically marginalize the GPs and compute the marginal likelihood of the observations given the partition tree. This property allows for efficient inference of the partition itself, for which we employ graph-theoretic techniques. We apply the multiresolution GP to the analysis of magnetoencephalography (MEG) recordings of brain activity.

In many large economic markets, goods are sold through sequential auctions. Examples include eBay, online ad auctions, wireless spectrum auctions, and the Dutch flower auctions. In this paper, we combine methods from game theory and decision theory to search for approximate equilibria in sequential auction domains, in which bidders do not know their opponents' values for goods, bidders only partially observe the actions of their opponents', and bidders demand multiple goods. We restrict attention to two-phased strategies: first predict (i.e., learn); second, optimize. We use best-reply dynamics [4] for prediction (i.e., to predict other bidders' strategies), and then assuming fixed other-bidder strategies, we estimate and solve the ensuing Markov decision processes (MDP) [18] for optimization. We exploit auction properties to represent the MDP in a more compact state space, and we use Monte Carlo simulation to make estimating the MDP tractable. We show how equilibria found using our search procedure compare to known equilibria for simpler auction domains, and we approximate an equilibrium for a more complex auction domain where analytical solutions are unknown.

We develop a Bayesian nonparametric extension of the popular Plackett-Luce choice model that can handle an infinite number of choice items. Our framework is based on the theory of random atomic measures, with the prior specified by a gamma process. We derive a posterior characterization and a simple and effective Gibbs sampler for posterior simulation. We develop a time-varying extension of our model, and apply it to the New York Times lists of weekly bestselling books.

We describe how the pretraining algorithm for Deep Boltzmann Machines (DBMs) is related to the pretraining algorithm for Deep Belief Networks and we show that under certain conditions, the pretraining procedure improves the variational lower bound of a two-hidden-layer DBM. Based on this analysis, we develop a different method of pretraining DBMs that distributes the modelling work more evenly over the hidden layers. Our results on the MNIST and NORB datasets demonstrate that the new pretraining algorithm allows us to learn better generative models.

While human listeners excel at selectively attending to a conversation in a cocktail party, machine performance is still far inferior by comparison. We show that the cocktail party problem, or the speech separation problem, can be effectively approached via structured prediction. To account for temporal dynamics in speech, we employ conditional random fields(CRFs) to classify speech dominance within each time-frequency unit for a sound mixture. To capture complex, nonlinear relationship between input and output, both state and transition feature functions in CRFs are learned by deep neural networks. The formulation of the problem as classification allows us to directly optimize a measure that is well correlated with human speech intelligibility. The proposed system substantially outperforms existing ones in a variety of noises.

The Shape Boltzmann Machine (SBM) [1] has recently been introduced as a stateof-the-art model of foreground/background object shape. We extend the SBM to account for the foreground object's parts. Our new model, the Multinomial SBM (MSBM), can capture both local and global statistics of part shapes accurately. We combine the MSBM with an appearance model to form a fully generative model of images of objects. Parts-based object segmentations are obtained simply by performing probabilistic inference in the model. We apply the model to two challenging datasets which exhibit significant shape and appearance variability, and find that it obtains results that are comparable to the state-of-the-art. There has been significant focus in computer vision on object recognition and detection e.g.

We propose a simple and novel framework for MCMC inference in continuoustime 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 show the advantage of our approach compared to particle MCMC and a uniformization-based sampler.

In this paper, we consider Bayesian reinforcement learning (BRL) where actions incur costs in addition to rewards, and thus exploration has to be constrained in terms of the expected total cost while learning to maximize the expected longterm total reward. In order to formalize cost-sensitive exploration, we use the constrained Markov decision process (CMDP) as the model of the environment, in which we can naturally encode exploration requirements using the cost function. We extend BEETLE, a model-based BRL method, for learning in the environment with cost constraints. We demonstrate the cost-sensitive exploration behaviour in a number of simulated problems.

A new methodology is developed for joint analysis of a matrix and accompanying documents, with the documents associated with the matrix rows/columns. The documents are modeled with a focused topic model, inferring interpretable latent binary features for each document. A new matrix decomposition is developed, with latent binary features associated with the rows/columns, and with imposition of a low-rank constraint. The matrix decomposition and topic model are coupled by sharing the latent binary feature vectors associated with each. The model is applied to roll-call data, with the associated documents defined by the legislation. Advantages of the proposed model are demonstrated for prediction of votes on a new piece of legislation, based only on the observed text of legislation. The coupling of the text and legislation is also shown to yield insight into the properties of the matrix decomposition for roll-call data.

We investigate a curious relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional independence structure of the graph. Our work extends results that have previously been established only in the context of multivariate Gaussian graphical models, thereby addressing an open question about the significance of the inverse covariance matrix of a non-Gaussian distribution. Based on our population-level results, we show how the graphical Lasso may be used to recover the edge structure of certain classes of discrete graphical models, and present simulations to verify our theoretical results.