For many pattern recognition tasks, the ideal input feature would be invariant to multiple confounding properties (such as illumination and viewing angle, in computer visionapplications). Recently, deep architectures trained in an unsupervised manner have been proposed as an automatic method for extracting useful features. However, it is difficult to evaluate the learned features by any means other than using them in a classifier. In this paper, we propose a number of empirical tests that directly measure the degree to which these learned features are invariant to different input transformations. We find that stacked autoencoders learn modestly increasingly invariant features with depth when trained on natural images. We find that convolutional deep belief networks learn substantially more invariant features in each layer. These results further justify the use of "deep" vs. "shallower" representations, butsuggest that mechanisms beyond merely stacking one autoencoder on top of another may be important for achieving invariance. Our evaluation metrics canalso be used to evaluate future work in deep learning, and thus help the development of future algorithms.

We develop the syntactic topic model (STM), a nonparametric Bayesian model of parsed documents. The STM generates words that are both thematically and syntactically constrained, which combines the semantic insights of topic models with the syntactic information available from parse trees. Each word of a sentence is generated by a distribution that combines document-specific topic weights and parse-tree-specific syntactic transitions. Words are assumed to be generated in an order that respects the parse tree. We derive an approximate posterior inference method based on variational methods for hierarchical Dirichlet processes, and we report qualitative and quantitative results on both synthetic data and hand-parsed documents.

We present a general Bayesian approach to probabilistic matrix factorization subject to linear constraints. The approach is based on a Gaussian observation model and Gaussian priors with bilinear equality and inequality constraints. We present an efficient Markov chain Monte Carlo inference procedure based on Gibbs sampling. Special cases of the proposed model are Bayesian formulations of non-negative matrix factorization and factor analysis. The method is evaluated on a blind source separation problem. We demonstrate that our algorithm can be used to extract meaningful and interpretable features that are remarkably different from features extracted using existing related matrix factorization techniques.

We provide sharp bounds for Rademacher and Gaussian complexities of (constrained) linear classes. These bounds make short work of providing a number of corollaries including: risk bounds for linear prediction (including settings where the weight vectors are constrained by either $L_2$ or $L_1$ constraints), margin bounds (including both $L_2$ and $L_1$ margins, along with more general notions based on relative entropy), a proof of the PAC-Bayes theorem, and $L_2$ covering numbers (with $L_p$ norm constraints and relative entropy constraints). In addition to providing a unified analysis, the results herein provide some of the sharpest risk and margin bounds (improving upon a number of previous results). Interestingly, our results show that the uniform convergence rates of empirical risk minimization algorithms tightly match the regret bounds of online learning algorithms for linear prediction (up to a constant factor of 2).

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."

Multilevel hierarchical models provide an attractive framework for incorporating correlations induced in a response variable that is organized hierarchically. Model fitting is challenging, especially for a hierarchy with a large number of nodes. We provide a novel algorithm based on a multi-scale Kalman filter that is both scalable and easy to implement. For Gaussian response, we show our method provides the maximum a-posteriori (MAP) parameter estimates; for non-Gaussian response, parameter estimation is performed through a Laplace approximation. However, the Laplace approximation provides biased parameter estimates that is corrected through a parametric bootstrap procedure. We illustrate through simulation studies and analyses of real world data sets in health care and online advertising.

Mixture of Gaussian processes models extended a single Gaussian process with ability of modeling multi-modal data and reduction of training complexity. Previous inference algorithms for these models are mostly based on Gibbs sampling, which can be very slow, particularly for large-scale data sets. We present a new generative mixture of experts model. Each expert is still a Gaussian process but is reformulated by a linear model. This breaks the dependency among training outputs and enables us to use a much faster variational Bayesian algorithm for training. Our gating network is more flexible than previous generative approaches as inputs for each expert are modeled by a Gaussian mixture model. The number of experts and number of Gaussian components for an expert are inferred automatically. A variety of tests show the advantages of our method.

Dynamic Bayesian networks have been applied widely to reconstruct the structure of regulatory processes from time series data. The standard approach is based on the assumption of a homogeneous Markov chain, which is not valid in many real-world scenarios. Recent research efforts addressing this shortcoming have considered undirected graphs, directed graphs for discretized data, or over-flexible models that lack any information sharing between time series segments. In the present article, we propose a non-stationary dynamic Bayesian network for continuous data, in which parameters are allowed to vary between segments, and in which a common network structure provides essential information sharing across segments. Our model is based on a Bayesian change-point process, and we apply a variant of the allocation sampler of Nobile and Fearnside to infer the number and location of the change-points.

Adaptation of visually guided reaching movements in novel visuomotor environments (e.g.wearing prism goggles) comprises not only motor adaptation but also substantial sensory adaptation, corresponding to shifts in the perceived spatial location of visual and proprioceptive cues. Previous computational modelsof the sensory component of visuomotor adaptation have assumed that it is driven purely by the discrepancy introduced between visual andproprioceptive estimates of hand position and is independent of any motor component of adaptation. We instead propose a unified model in which sensory and motor adaptation are jointly driven by optimal Bayesian estimation of the sensory and motor contributions to perceived errors. Our model is able to account for patterns of performance errors during visuomotor adaptationas well as the subsequent perceptual aftereffects. This unified model also makes the surprising prediction that force field adaptation willelicit similar perceptual shifts, even though there is never any discrepancy between visual and proprioceptive observations. We confirm this prediction with an experiment.

In this paper we present a novel approach to learn directed acyclic graphs (DAG) and factor models within the same framework while also allowing for model comparison between them. For this purpose, we exploit the connection between factor models and DAGs to propose Bayesian hierarchies based on spike and slab priors to promote sparsity, heavy-tailed priors to ensure identifiability and predictive densities to perform the model comparison. We require identifiability to be able to produce variable orderings leading to valid DAGs and sparsity to learn the structures. The effectiveness of our approach is demonstrated through extensive experiments on artificial and biological data showing that our approach outperform a number of state of the art methods.