The human brain can be described as containing a number of functional regions. For a given task, these regions, as well as the connections between them, play a key role in information processing in the brain. However, most existing multi-voxel pattern analysis approaches either treat multiple functional regions as one large uniform region or several independent regions, ignoring the connections between regions. In this paper, we propose to model such connections in an Hidden Conditional Random Field (HCRF) framework, where the classifier of one region of interest (ROI) makes predictions based on not only its voxels but also the classifier predictions from ROIs that it connects to. Furthermore, we propose a structural learning method in the HCRF framework to automatically uncover the connections between ROIs. Experiments on fMRI data acquired while human subjects viewing images of natural scenes show that our model can improve the top-level (the classifier combining information from all ROIs) and ROI-level prediction accuracy, as well as uncover some meaningful connections between ROIs.

The recent emergence of Graphics Processing Units (GPUs) as general-purpose parallel computing devices provides us with new opportunities to develop scalable learning methods for massive data. In this work, we consider the problem of parallelizing two inference methods on GPUs for latent Dirichlet Allocation (LDA) models, collapsed Gibbs sampling (CGS) and collapsed variational Bayesian (CVB). To address limited memory constraints on GPUs, we propose a novel data partitioning scheme that effectively reduces the memory cost. Furthermore, the partitioning scheme balances the computational cost on each multiprocessor and enables us to easily avoid memory access conflicts. We also use data streaming to handle extremely large datasets. Extensive experiments showed that our parallel inference methods consistently produced LDA models with the same predictive power as sequential training methods did but with 26x speedup for CGS and 196x speedup for CVB on a GPU with 30 multiprocessors; actually the speedup is almost linearly scalable with the number of multiprocessors available. The proposed partitioning scheme and data streaming can be easily ported to many other models in machine learning.

There is a growing body of experimental evidence to suggest that the brain is capable of approximating optimal Bayesian inference in the face of noisy input stimuli. Despite this progress, the neural underpinnings of this computation are still poorly understood. In this paper we focus on the problem of Bayesian filtering of stochastic time series. In particular we introduce a novel neural network, derived from a line attractor architecture, whose dynamics map directly onto those of the Kalman Filter in the limit where the prediction error is small. When the prediction error is large we show that the network responds robustly to change-points in a way that is qualitatively compatible with the optimal Bayesian model. The model suggests ways in which probability distributions are encoded in the brain and makes a number of testable experimental predictions.

Across a wide range of cognitive tasks, recent experience influences behavior. For example, when individuals repeatedly perform a simple two-alternative forcedchoice task(2AFC), response latencies vary dramatically based on the immediately preceding trial sequence. These sequential effects have been interpreted as adaptation to the statistical structure of an uncertain, changing environment (e.g., Jones and Sieck, 2003; Mozer, Kinoshita, and Shettel, 2007; Yu and Cohen, 2008).The Dynamic Belief Model (DBM) (Yu and Cohen, 2008) explains sequential effects in 2AFC tasks as a rational consequence of a dynamic internal representation that tracks second-order statistics of the trial sequence (repetition rates) and predicts whether the upcoming trial will be a repetition or an alternation ofthe previous trial. Experimental results suggest that first-order statistics (base rates) also influence sequential effects. We propose a model that learns both first-and second-order sequence properties, each according to the basic principles ofthe DBM but under a unified inferential framework. This model, the Dynamic BeliefMixture Model (DBM2), obtains precise, parsimonious fits to data. Furthermore, the model predicts dissociations in behavioral (Maloney, Martello, Sahm, and Spillmann, 2005) and electrophysiological studies (Jentzsch and Sommer, 2002),supporting the psychological and neurobiological reality of its two components.

The nested Chinese restaurant process (nCRP) is a powerful nonparametric Bayesian model for learning tree-based hierarchies from data. Since its posterior distribution is intractable, current inference methods have all relied on MCMC sampling. In this paper, we develop an alternative inference technique based on variational methods. To employ variational methods, we derive a tree-based stick-breaking construction of the nCRP mixture model, and a novel variational algorithm that efficiently explores a posterior over a large set of combinatorial structures. We demonstrate the use of this approach for text and hand written digits modeling, where we show we can adapt the nCRP to continuous data as well.

Implementations of topic models typically use symmetric Dirichlet priors with fixed concentration parameters, with the implicit assumption that such smoothing parameters" have little practical effect. In this paper, we explore several classes of structured priors for topic models. We find that an asymmetric Dirichlet prior over the document-topic distributions has substantial advantages over a symmetric prior, while an asymmetric prior over the topic-word distributions provides no real benefit. Approximation of this prior structure through simple, efficient hyperparameter optimization steps is sufficient to achieve these performance gains. The prior structure we advocate substantially increases the robustness of topic models to variations in the number of topics and to the highly skewed word frequency distributions common in natural language. Since this prior structure can be implemented using efficient algorithms that add negligible cost beyond standard inference techniques, we recommend it as a new standard for topic modeling."

In the last few decades, model complexity has received a lot of press. While many methods have been proposed that jointly measure a model’s descriptive adequacy and its complexity, few measures exist that measure complexity in itself. Moreover, existing measures ignore the parameter prior, which is an inherent part of the model and affects the complexity. This paper presents a stand alone measure for model complexity, that takes the number of parameters, the functional form, the range of the parameters and the parameter prior into account. This Prior Predictive Complexity (PPC) is an intuitive and easy to compute measure. It starts from the observation that model complexity is the property of the model that enables it to fit a wide range of outcomes. The PPC then measures how wide this range exactly is.

In the Gaussian process regression the observation model is commonly assumed to be Gaussian, which is convenient in computational perspective. However, the drawback is that the predictive accuracy of the model can be significantly compromised if the observations are contaminated by outliers. A robust observation model, such as the Student-t distribution, reduces the influence of outlying observations and improves the predictions. The problem, however, is the analytically intractable inference. In this work, we discuss the properties of a Gaussian process regression model with the Student-t likelihood and utilize the Laplace approximation for approximate inference. We compare our approach to a variational approximation and a Markov chain Monte Carlo scheme, which utilize the commonly used scale mixture representation of the Student-t distribution.

We introduce a novel multivariate Laplace (MVL) distribution as a sparsity promoting prior for Bayesian source localization that allows the specification of constraints between and within sources. We represent the MVL distribution as a scale mixture that induces a coupling between source variances instead of their means. Approximation of the posterior marginals using expectation propagation is shown to be very efficient due to properties of the scale mixture representation. The computational bottleneck amounts to computing the diagonal elements of a sparse matrix inverse. Our approach is illustrated using a mismatch negativity paradigm for which MEG data and a structural MRI have been acquired. We show that spatial coupling leads to sources which are active over larger cortical areas as compared with an uncoupled prior.

When individuals independently recollect events or retrieve facts from memory, how can we aggregate these retrieved memories to reconstruct the actual set of events or facts? In this research, we report the performance of individuals in a series of general knowledge tasks, where the goal is to reconstruct from memory the order of historic events, or the order of items along some physical dimension. We introduce two Bayesian models for aggregating order information based on a Thurstonian approach and Mallows model. Both models assume that each individuals reconstruction is based on either a random permutation of the unobserved ground truth, or by a pure guessing strategy. We apply MCMC to make inferences about the underlying truth and the strategies employed by individuals. The models demonstrate a wisdom of crowds" effect, where the aggregated orderings are closer to the true ordering than the orderings of the best individual."