We develop a sampling technique for Hierarchical Dirichlet process models. The parallel algorithm builds upon [1] by proposing large split and merge moves based on learned sub-clusters. The additional global split and merge moves drastically improve convergence in the experimental results. Furthermore, we discover that cross-validation techniques do not adequately determine convergence, and that previous sampling methods converge slower than were previously expected.

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse Gaussian processes. The result of learning is a tractable posterior over nonlinear dynamical systems. In comparison to conventional parametric models, we offer the possibility to straightforwardly trade off model capacity and computational cost whilst avoiding overfitting. Our main algorithm uses a hybrid inference approach combining variational Bayes and sequential Monte Carlo.

Developments in neural recording technology are rapidly enabling the recording of populations of neurons in multiple brain areas simultaneously, as well as the identification of the types of neurons being recorded (e.g., excitatory vs. inhibitory). There is a growing need for statistical methods to study the interaction among multiple, labeled populations of neurons. Rather than attempting to identify direct interactions between neurons (where the number of interactions grows with the number of neurons squared), we propose to extract a smaller number of latent variables from each population and study how these latent variables interact. Specifically, we propose extensions to probabilistic canonical correlation analysis (pCCA) to capture the temporal structure of the latent variables, as well as to distinguish within-population dynamics from across-population interactions (termed Group Latent Auto-Regressive Analysis, gLARA). We then applied these methods to populations of neurons recorded simultaneously in visual areas V1 and V2, and found that gLARA provides a better description of the recordings than pCCA. This work provides a foundation for studying how multiple populations of neurons interact and how this interaction supports brain function.

A wild bootstrap method for nonparametric hypothesis tests based on kernel distribution embeddings is proposed. This bootstrap method is used to construct provably consistent tests that apply to random processes, for which the naive permutation-based bootstrap fails. It applies to a large group of kernel tests based on V-statistics, which are degenerate under the null hypothesis, and nondegenerate elsewhere. To illustrate this approach, we construct a two-sample test, an instantaneous independence test and a multiple lag independence test for time series. In experiments, the wild bootstrap gives strong performance on synthetic examples, on audio data, and in performance benchmarking for the Gibbs sampler.

Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection phase is often ignored. In fact, in theoretical works most of the time assumptions are made, for example, on the prior knowledge of the norm of the optimal solution, while in the practical world validation methods remain the only viable approach. In this paper, we propose a new kernel-based stochastic gradient descent algorithm that performs model selection while training, with no parameters to tune, nor any form of cross-validation. The algorithm builds on recent advancement in online learning theory for unconstrained settings, to estimate over time the right regularization in a data-dependent way. Optimal rates of convergence are proved under standard smoothness assumptions on the target function as well as preliminary empirical results.

We propose a very simple yet effective algorithm that consists of two simple steps: the first step is to complete the sub-matrix corresponding to the labeled examples and the second step is to reconstruct the label matrix from the completed sub-matrix and the provided similarity matrix. Our analysis exhibits that under several mild preconditions we can recover the label matrix with a small error, if the top eigen-space that corresponds to the largest eigenvalues of the similarity matrix covers well the column space of label matrix and is subject to a low coherence, and the number of observed pairwise labels is sufficiently enough. We demonstrate the effectiveness of the proposed algorithm by several experiments.

A major challenge in scaling object detection is the difficulty of obtaining labeled images for large numbers of categories. Recently, deep convolutional neural networks (CNNs) have emerged as clear winners on object classification benchmarks, in part due to training with 1.2M+ labeled classification images. Unfortunately, only a small fraction of those labels are available for the detection task. It is much cheaper and easier to collect large quantities of image-level labels from search engines than it is to collect detection data and label it with precise bounding boxes. In this paper, we propose Large Scale Detection through Adaptation (LSDA), an algorithm which learns the difference between the two tasks and transfers this knowledge to classifiers for categories without bounding box annotated data, turning them into detectors.

The recently established RPCA [4] method provides a convenient way to restore low-rank matrices from grossly corrupted observations. While elegant in theory and powerful in reality, RPCA is not an ultimate solution to the low-rank matrix recovery problem. Indeed, its performance may not be perfect even when data are strictly low-rank. This is because RPCA ignores clustering structures of the data which are ubiquitous in applications. As the number of cluster grows, the coherence of data keeps increasing, and accordingly, the recovery performance of RPCA degrades.

This paper is concerned with compressive sensing of signals drawn from a Gaussian mixture model (GMM) with sparse precision matrices. Previous work has shown: (i) a signal drawn from a given GMM can be perfectly reconstructed from r noise-free measurements if the (dominant) rank of each covariance matrix is less than r; (ii) a sparse Gaussian graphical model can be efficiently estimated from fully-observed training signals using graphical lasso. This paper addresses a problem more challenging than both (i) and (ii), by assuming that the GMM is unknown and each signal is only observed through incomplete linear measurements. Under these challenging assumptions, we develop a hierarchical Bayesian method to simultaneously estimate the GMM and recover the signals using solely the incomplete measurements and a Bayesian shrinkage prior that promotes sparsity of the Gaussian precision matrices. In addition, we provide theoretical performance bounds to relate the reconstruction error to the number of signals for which measurements are available, the sparsity level of precision matrices, and the "incompleteness" of measurements. The proposed method is demonstrated extensively on compressive sensing of imagery and video, and the results with simulated and hardware-acquired real measurements show significant performance improvement over state-of-the-art methods.

The success of pairwise clustering largely depends on the pairwise similarity function defined over the data points, where kernel similarity is broadly used. In this paper, we present a novel pairwise clustering framework by bridging the gap between clustering and multi-class classification. This pairwise clustering framework learns an unsupervised nonparametric classifier from each data partition, and search for the optimal partition of the data by minimizing the generalization error of the learned classifiers associated with the data partitions. We consider two nonparametric classifiers in this framework, i.e. the nearest neighbor classifier and the plug-in classifier. Modeling the underlying data distribution by nonparametric kernel density estimation, the generalization error bounds for both unsupervised nonparametric classifiers are the sum of nonparametric pairwise similarity terms between the data points for the purpose of clustering. Under uniform distribution, the nonparametric similarity terms induced by both unsupervised classifiers exhibit a well known form of kernel similarity. We also prove that the generalization error bound for the unsupervised plugin classifier is asymptotically equal to the weighted volume of cluster boundary [1] for Low Density Separation, a widely used criteria for semi-supervised learning and clustering. Based on the derived nonparametric pairwise similarity using the plug-in classifier, we propose a new nonparametric exemplar-based clustering method with enhanced discriminative capability, whose superiority is evidenced by the experimental results.