A Bayesian approach to partitioning distance matrices is presented. It is inspired by the 'Translation-Invariant Wishart-Dirichlet' process (TIWD) in (Vogt et al., 2010) and shares a number of advantageous properties like the fully probabilistic nature of the inference model, automatic selection of the number of clusters and applicability in semi-supervised settings. In addition, our method (which we call 'fastTIWD') overcomes the main shortcoming of the original TIWD, namely its high computational costs. The fastTIWD reduces the workload in each iteration of a Gibbs sampler from O(n^3) in the TIWD to O(n^2). Our experiments show that this cost reduction does not compromise the quality of the inferred partitions. With this new method it is now possible to 'mine' large relational datasets with a probabilistic model, thereby automatically detecting new and potentially interesting clusters.

We study the problem of learning to track a large quantity of homogeneous objects such as cell tracking in cell culture study and developmental biology. Reliable cell tracking in time-lapse microscopic image sequences is important for modern biomedical research. Existing cell tracking methods are usually kept simple and use only a small number of features to allow for manual parameter tweaking or grid search. We propose a structured learning approach that allows to learn optimum parameters automatically from a training set. This allows for the use of a richer set of features which in turn affords improved tracking compared to recently reported methods on two public benchmark sequences.

In recent years semidefinite optimization has become a tool of major importance in various optimization and machine learning problems. In many of these problems the amount of data in practice is so large that there is a constant need for faster algorithms. In this work we present the first sublinear time approximation algorithm for semidefinite programs which we believe may be useful for such problems in which the size of data may cause even linear time algorithms to have prohibitive running times in practice. We present the algorithm and its analysis alongside with some theoretical lower bounds and an improved algorithm for the special problem of supervised learning of a distance metric.

An important task in exploring and analyzing real-world data sets is to detect unusual and interesting phenomena. In this paper, we study the group anomaly detection problem. Unlike traditional anomaly detection research that focuses on data points, our goal is to discover anomalous aggregated behaviors of groups of points. For this purpose, we propose the Flexible Genre Model (FGM). FGM is designed to characterize data groups at both the point level and the group level so as to detect various types of group anomalies. We evaluate the effectiveness of FGM on both synthetic and real data sets including images and turbulence data, and show that it is superior to existing approaches in detecting group anomalies.

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.

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.

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.

In this paper we describe a maximum likelihood likelihood approach for dictionary learning in the multiplicative exponential noise model. This model is prevalent in audio signal processing where it underlies a generative composite model of the power spectrogram. Maximum joint likelihood estimation of the dictionary and expansion coefficients leads to a nonnegative matrix factorization problem where the Itakura-Saito divergence is used. The optimality of this approach is in question because the number of parameters (which include the expansion coefficients) grows with the number of observations. In this paper we describe a variational procedure for optimization of the marginal likelihood, i.e., the likelihood of the dictionary where the activation coefficients have been integrated out (given a specific prior). We compare the output of both maximum joint likelihood estimation (i.e., standard Itakura-Saito NMF) and maximum marginal likelihood estimation (MMLE) on real and synthetical datasets. The MMLE approach is shown to embed automatic model order selection, akin to automatic relevance determination.