Latent Dirichlet allocation (LDA) is a Bayesian network that has recently gained much popularity in applications ranging from document modeling to computer vision. Due to the large scale nature of these applications, current inference procedures like variational Bayes and Gibbs sampling have been found lacking. In this paper we propose the collapsed variational Bayesian inference algorithm for LDA, and show that it is computationally efficient, easy to implement and significantly more accurate than standard variational Bayesian inference for LDA.

We propose a nonlinear generative model for human motion data that uses an undirected model with binary latent variables and real-valued "visible" variables that represent joint angles. The latent and visible variables at each time step receive directed connections from the visible variables at the last few time-steps. Such an architecture makes online inference efficient and allows us to use a simple approximate learning procedure. After training, the model finds a single set of parameters that simultaneously capture several different kinds of motion. We demonstrate the power of our approach by synthesizing various motion sequences and by performing online filling in of data lost during motion capture.

In supervised learning there is a typical presumption that the training and test points are taken from the same distribution. In practice this assumption is commonly violated. The situations where the training and test data are from different distributions is called covariate shift. Recent work has examined techniques for dealing with covariate shift in terms of minimisation of generalisation error. As yet the literature lacks a Bayesian generative perspective on this problem. This paper tackles this issue for regression models. Recent work on covariate shift can be understood in terms of mixture regression. Using this view, we obtain a general approach to regression under covariate shift, which reproduces previous work as a special case. The main advantages of this new formulation over previous models for covariate shift are that we no longer need to presume the test and training densities are known, the regression and density estimation are combined into a single procedure, and previous methods are reproduced as special cases of this procedure, shedding light on the implicit assumptions the methods are making.

We establish a general oracle inequality for clipped approximate minimizers of regularized empirical risks and apply this inequality to support vector machine (SVM) type algorithms. We then show that for SVMs using Gaussian RBF kernels for classification this oracle inequality leads to learning rates that are faster than the ones established in [9]. Finally, we use our oracle inequality to show that a simple parameter selection approach based on a validation set can yield the same fast learning rates without knowing the noise exponents which were required to be known a-priori in [9].

Establishing correspondence between distinct objects is an important and nontrivial task: correctness of the correspondence hinges on properties which are difficult to capture in an a priori criterion. While previous work has used a priori criteria which in some cases led to very good results, the present paper explores whether it is possible to learn a combination of features that, for a given training set of aligned human heads, characterizes the notion of correct correspondence. By optimizing this criterion, we are then able to compute correspondence and morphs for novel heads.

We present a new statistical framework called hidden Markov Dirichlet process (HMDP) to jointly model the genetic recombinations among possibly infinite number of founders and the coalescence-with-mutation events in the resulting genealogies. The HMDP posits that a haplotype of genetic markers is generated by a sequence of recombination events that select an ancestor for each locus from an unbounded set of founders according to a 1st-order Markov transition process. Conjoining this process with a mutation model, our method accommodates both between-lineage recombination and within-lineage sequence variations, and leads to a compact and natural interpretation of the population structure and inheritance process underlying haplotype data. We have developed an efficient sampling algorithm for HMDP based on a two-level nested Pólya urn scheme. On both simulated and real SNP haplotype data, our method performs competitively or significantly better than extant methods in uncovering the recombination hotspots along chromosomal loci; and in addition it also infers the ancestral genetic patterns and offers a highly accurate map of ancestral compositions of modern populations.

Starting with the work of Jaakkola and Haussler, a variety of approaches have been proposed for coupling domain-specific generative models with statistical learning methods. The link is established by a kernel function which provides a similarity measure based inherently on the underlying model. In computational biology, the full promise of this framework has rarely ever been exploited, as most kernels are derived from very generic models, such as sequence profiles or hidden Markov models. Here, we introduce the MTreeMix kernel, which is based on a generative model tailored to the underlying biological mechanism.

We describe a method to learn to make sequential stopping decisions, such as those made along a processing pipeline. We envision a scenario in which a series of decisions must be made as to whether to continue to process. Further processing costs time and resources, but may add value. Our goal is to create, based on historic data, a series of decision rules (one at each stage in the pipeline) that decide, based on information gathered up to that point, whether to continue processing the part. We demonstrate how our framework encompasses problems from manufacturing to vision processing. We derive a quadratic (in the number of decisions) bound on testing performance and provide empirical results on object detection.

Independent Component Analysis (ICA) is a popular method for extracting independent features from visual data. However, as a fundamentally linear technique, there is always nonlinear residual redundancy that is not captured by ICA. Hence there have been many attempts to try to create a hierarchical version of ICA, but so far none of the approaches have a natural way to apply them more than once. Here we show that there is a relatively simple technique that transforms the absolute values of the outputs of a previous application of ICA into a normal distribution, to which ICA maybe applied again. This results in a recursive ICA algorithm that may be applied any number of times in order to extract higher order structure from previous layers.

We describe an algorithmic framework for an abstract game which we term a convex repeated game. We show that various online learning and boosting algorithms can be all derived as special cases of our algorithmic framework. This unified view explains the properties of existing algorithms and also enables us to derive several new interesting algorithms. Our algorithmic framework stems from a connection that we build between the notions of regret in game theory and weak duality in convex optimization.