Nonparametric Bayesian methods are developed for analysis of multi-channel spike-train data, with the feature learning and spike sorting performed jointly. The feature learning and sorting are performed simultaneously across all channels. Dictionary learning is implemented via the beta-Bernoulli process, with spike sorting performed via the dynamic hierarchical Dirichlet process (dHDP), with these two models coupled. The dHDP is augmented to eliminate refractory-period violations, it allows the "appearance" and "disappearance" of neurons over time, and it models smooth variation in the spike statistics.

We propose a novel inference framework for finding maximal cliques in a weighted graph that satisfy hard constraints. The constraints specify the graph nodes that must belong to the solution as well as mutual exclusions of graph nodes, i.e., sets of nodes that cannot belong to the same solution. The proposed inference is based on a novel particle filter algorithm with state permeations. We apply the inference framework to a challenging problem of learning part-based, deformable object models. Two core problems in the learning framework, matching of image patches and finding salient parts, are formulated as two instances of the problem of finding maximal cliques with hard constraints. Our learning framework yields discriminative part based object models that achieve very good detection rate, and outperform other methods on object classes with large deformation.

We consider a global optimization problem of a deterministic function f in a semimetric space,given a finite budget ofnevaluations. The functionf is assumed to be locally smooth (around one of its global maxima) with respect to a semi-metric l. We describe two algorithms based on optimistic exploration that use a hierarchical partitioningof the space at all scales. A first contribution is an algorithm, DOO, that requires the knowledge of l. We report a finite-sample performance bound in terms of a measure of the quantity of near-optimal states. We then define a second algorithm, SOO, which does not require the knowledge of the semimetric lunder which f is smooth, and whose performance is almost as good as DOO optimally-fitted.

Many nonparametric regressors were recently shown to converge at rates that depend only on the intrinsic dimension of data. These regressors thus escape the curse of dimension when high-dimensional data has low intrinsic dimension (e.g. a manifold). We show that $k$-NN regression is also adaptive to intrinsic dimension. In particular our rates are local to a query $x$ and depend only on the way masses of balls centered at $x$ vary with radius. Furthermore, we show a simple way to choose $k = k(x)$ locally at any $x$ so as to nearly achieve the minimax rate at $x$ in terms of the unknown intrinsic dimension in the vicinity of $x$. We also establish that the minimax rate does not depend on a particular choice of metric space or distribution, but rather that this minimax rate holds for any metric space and doubling measure.

Multi-task learning (MTL) learns multiple related tasks simultaneously to improve generalization performance. Alternating structure optimization (ASO) is a popular MTL method that learns a shared low-dimensional predictive structure on hypothesis spaces from multiple related tasks. It has been applied successfully in many real world applications. As an alternative MTL approach, clustered multi-task learning (CMTL) assumes that multiple tasks follow a clustered structure, i.e., tasks are partitioned into a set of groups where tasks in the same group are similar to each other, and that such a clustered structure is unknown a priori. The objectives in ASO and CMTL differ in how multiple tasks are related. Interestingly, we show in this paper the equivalence relationship between ASO and CMTL, providing significant new insights into ASO and CMTL as well as their inherent relationship. The CMTL formulation is non-convex, and we adopt a convex relaxation to the CMTL formulation. We further establish the equivalence relationship between the proposed convex relaxation of CMTL and an existing convex relaxation of ASO, and show that the proposed convex CMTL formulation is significantly more efficient especially for high-dimensional data. In addition, we present three algorithms for solving the convex CMTL formulation. We report experimental results on benchmark datasets to demonstrate the efficiency of the proposed algorithms.

We study a particular class of cyclic causal models, where each variable is a (possibly nonlinear) function of its parents and additive noise. We prove that the causal graph of such models is generically identifiable in the bivariate, Gaussian-noise case. We also propose a method to learn such models from observational data. In the acyclic case, the method reduces to ordinary regression, but in the more challenging cyclic case, an additional term arises in the loss function, which makes it a special case of nonlinear independent component analysis. We illustrate the proposed method on synthetic data.

In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex forms and better properties than traditional Cauchy and double exponential priors. We first propose a new class of normal scale mixtures through a novel generalized beta distribution that encompasses many interesting priors as special cases. This encompassing framework should prove useful in comparing competing priors, considering properties and revealing close connections. We then develop a class of variational Bayes approximations through the new hierarchy presented that will scale more efficiently to the types of truly massive data sets that are now encountered routinely.

The object people perceive in an image can depend on its orientation relative to the scene it is in (its reference frame). For example, the images of the symbols $\times$ and $+$ differ by a 45 degree rotation. Although real scenes have multiple images and reference frames, psychologists have focused on scenes with only one reference frame. We propose an ideal observer model based on nonparametric Bayesian statistics for inferring the number of reference frames in a scene and their parameters. When an ambiguous image could be assigned to two conflicting reference frames, the model predicts two factors should influence the reference frame inferred for the image: The image should be more likely to share the reference frame of the closer object ({\em proximity}) and it should be more likely to share the reference frame containing the most objects ({\em alignment}). We confirm people use both cues using a novel methodology that allows for easy testing of human reference frame inference.

Discriminative learning when training and test data belong to different distributions is a challenging and complex task. Often times we have very few or no labeled data from the test or target distribution but may have plenty of labeled data from multiple related sources with different distributions. The difference in distributions may be both in marginal and conditional probabilities. Most of the existing domain adaptation work focuses on the marginal probability distribution difference between the domains, assuming that the conditional probabilities are similar. However in many real world applications, conditional probability distribution differences are as commonplace as marginal probability differences. In this paper we propose a two-stage domain adaptation methodology which combines weighted data from multiple sources based on marginal probability differences (first stage) as well as conditional probability differences (second stage), with the target domain data. The weights for minimizing the marginal probability differences are estimated independently, while the weights for minimizing conditional probability differences are computed simultaneously by exploiting the potential interaction among multiple sources. We also provide a theoretical analysis on the generalization performance of the proposed multi-source domain adaptation formulation using the weighted Rademacher complexity measure. Empirical comparisons with existing state-of-the-art domain adaptation methods using three real-world datasets demonstrate the effectiveness of the proposed approach.

Topic models have the potential to improve search and browsing by extracting useful semantic themes from web pages and other text documents. When learned topics are coherent and interpretable, they can be valuable for faceted browsing, results set diversity analysis, and document retrieval. However, when dealing with small collections or noisy text (e.g. web search result snippets or blog posts), learned topics can be less coherent, less interpretable, and less useful. To overcome this, we propose two methods to regularize the learning of topic models. Our regularizers work by creating a structured prior over words that reflect broad patterns in the external data. Using thirteen datasets we show that both regularizers improve topic coherence and interpretability while learning a faithful representation of the collection of interest. Overall, this work makes topic models more useful across a broader range of text data.