Links between probabilistic and non-probabilistic learning algorithms can arise by performing small-variance asymptotics, i.e., letting the variance of particular distributions in a graphical model go to zero. For instance, in the context of clustering, such an approach yields precise connections between the k-means and EM algorithms. In this paper, we explore small-variance asymptotics for exponential family Dirichlet process (DP) and hierarchical Dirichlet process (HDP) mixture models. Utilizing connections between exponential family distributions and Bregman divergences, we derive novel clustering algorithms from the asymptotic limit of the DP and HDP mixtures that feature the scalability of existing hard clustering methods as well as the flexibility of Bayesian nonparametric models. We focus on special cases of our analysis for discrete-data problems, including topic modeling, and we demonstrate the utility of our results by applying variants of our algorithms to problems arising in vision and document analysis.

We present a new variational inference algorithm for Gaussian process regression withnon-conjugate likelihood functions, with application to a wide array of problems including binary and multi-class classification, and ordinal regression. Our method constructs a concave lower bound that is optimized using an efficient fixed-point updating algorithm. We show that the new algorithm has highly competitive computationalcomplexity, matching that of alternative approximate inference methods. We also prove that the use of concave variational bounds provides stable and guaranteed convergence - a property not available to other approaches. We show empirically for both binary and multi-class classification that our new algorithm converges much faster than existing variational methods, and without any degradation in performance.

Fine-grained recognition refers to a subordinate level of recognition, such are recognizing different species of birds, animals or plants. It differs from recognition of basic categories, such as humans, tables, and computers, in that there are global similarities in shape or structure shared within a category, and the differences are in the details of the object parts. We suggest that the key to identifying the fine-grained differences lies in finding the right alignment of image regions that contain the same object parts. We propose a template model for the purpose, which captures common shape patterns of object parts, as well as the co-occurence relation of the shape patterns. Once the image regions are aligned, extracted features are used for classification. Learning of the template model is efficient, and the recognition results we achieve significantly outperform the state-of-the-art algorithms.

While minwise hashing is promising for large-scale learning in massive binary data, the preprocessing cost is prohibitive as it requires applying (e.g.,) $k=500$ permutations on the data. The testing time is also expensive if a new data point (e.g., a new document or a new image) has not been processed. In this paper, we develop a simple \textbf{one permutation hashing} scheme to address this important issue. While it is true that the preprocessing step can be parallelized, it comes at the cost of additional hardware and implementation. Also, reducing $k$ permutations to just one would be much more \textbf{energy-efficient}, which might be an important perspective as minwise hashing is commonly deployed in the search industry. While the theoretical probability analysis is interesting, our experiments on similarity estimation and SVM \& logistic regression also confirm the theoretical results.

The problem of multiple change point estimation is considered for sequences with unknown number of change points. A consistency framework is suggested that is suitable for highly dependent time-series, and an asymptotically consistent algorithm is proposed. In order for the consistency to be established the only assumption required is that the data is generated by stationary ergodic time-series distributions. No modeling, independence or parametric assumptions are made; the data are allowed to be dependent and the dependence can be of arbitrary form. The theoretical results are complemented with experimental evaluations.

We propose a novel stochastic process that is with probability $\alpha_i$ being absorbed at current state $i$, and with probability $1-\alpha_i$ follows a random edge out of it. We analyze its properties and show its potential for exploring graph structures. We prove that under proper absorption rates, a random walk starting from a set $\mathcal{S}$ of low conductance will be mostly absorbed in $\mathcal{S}$. Moreover, the absorption probabilities vary slowly inside $\mathcal{S}$, while dropping sharply outside $\mathcal{S}$, thus implementing the desirable cluster assumption for graph-based learning. Remarkably, the partially absorbing process unifies many popular models arising in a variety of contexts, provides new insights into them, and makes it possible for transferring findings from one paradigm to another. Simulation results demonstrate its promising applications in graph-based learning.

In categorical data there is often structure in the number of variables that take on each label. For example, the total number of objects in an image and the number of highly relevant documents per query in web search both tend to follow a structured distribution. In this paper, we study a probabilistic model that explicitly includes a prior distribution over such counts, along with a count-conditional likelihood that defines probabilities over all subsets of a given size. When labels are binary and the prior over counts is a Poisson-Binomial distribution, a standard logistic regression model is recovered, but for other count distributions, such priors induce global dependencies and combinatorics that appear to complicate learning and inference. However, we demonstrate that simple, efficient learning procedures can be derived for more general forms of this model. We illustrate the utility of the formulation by exploring applications to multi-object classification, learning to rank, and top-K classification.

In many applications classification systems often require in the loop human intervention. In such cases the decision process must be transparent and comprehensible simultaneously requiring minimal assumptions on the underlying data distribution. To tackle this problem, we formulate it as an axis-alligned subspacefinding task under the assumption that query specific information dictates the complementary use of the subspaces. We develop a regression-based approach called RECIP that efficiently solves this problem by finding projections that minimize a nonparametric conditional entropy estimator. Experiments show that the method is accurate in identifying the informative projections of the dataset, picking the correct ones to classify query points and facilitates visual evaluation by users.

Finding maximum aposteriori (MAP) assignments in graphical models is an important task in many applications. Since the problem is generally hard, linear programming (LP) relaxations are often used. Solving these relaxations efficiently is thus an important practical problem. In recent years, several authors have proposed message passing updates corresponding to coordinate descent in the dual LP. However,these are generally not guaranteed to converge to a global optimum. One approach to remedy this is to smooth the LP, and perform coordinate descent on the smoothed dual. However, little is known about the convergence rate of this procedure. Here we perform a thorough rate analysis of such schemes and derive primal and dual convergence rates. We also provide a simple dual to primal mapping that yields feasible primal solutions with a guaranteed rate of convergence. Empirical evaluation supports our theoretical claims and shows that the method is highly competitive with state of the art approaches that yield global optima.

We propose a novel Bayesian approach to solve stochastic optimization problems that involve finding extrema of noisy, nonlinear functions. Previous work has focused on representing possible functions explicitly, which leads to a two-step procedure of first, doing inference over the function space and second, finding the extrema of these functions. Here we skip the representation step and directly model the distribution over extrema. To this end, we devise a non-parametric conjugate prior where the natural parameter corresponds to a given kernel function and the sufficient statistic is composed of the observed function values. The resulting posterior distribution directly captures the uncertainty over the maximum of the unknown function.