The study of point cloud data sampled from a stratification, a collection of manifolds withpossible different dimensions, is pursued in this paper. We present a technique for simultaneously soft clustering and estimating the mixed dimensionality anddensity of such structures. The framework is based on a maximum likelihood estimationof a Poisson mixture model. The presentation of the approach is completed with artificial and real examples demonstrating the importance of extending manifold learning to stratification learning.

Correlation between instances is often modelled via a kernel function using input attributesof the instances. Relational knowledge can further reveal additional pairwise correlations between variables of interest. In this paper, we develop a class of models which incorporates both reciprocal relational information and input attributesusing Gaussian process techniques. This approach provides a novel nonparametric Bayesian framework with a data-dependent covariance function for supervised learning tasks. We also apply this framework to semi-supervised learning. Experimental results on several real world data sets verify the usefulness of this algorithm.

Many recent studies analyze how data from different modalities can be combined. Often this is modeled as a system that optimally combines several sources of information aboutthe same variable. However, it has long been realized that this information combining depends on the interpretation of the data. Two cues that are perceived by different modalities can have different causal relationships: (1) They can both have the same cause, in this case we should fully integrate both cues into a joint estimate.

We consider methods that try to find a good policy for a Markov decision process by choosing one from a given class. The policy is chosen based on its empirical performance in simulations. We are interested in conditions on the complexity of the policy class that ensure the success of such simulation based policy search methods. We show that under bounds on the amount of computation involved in computing policies, transition dynamics and rewards, uniform convergence of empirical estimates to true value functions occurs. Previously, such results were derived by assuming boundedness of pseudodimension and Lipschitz continuity. These assumptions and ours are both stronger than the usual combinatorial complexity measures.We show, via minimax inequalities, that this is essential: boundedness of pseudodimension or fat-shattering dimension alone is not sufficient.

We consider the problem of inferring the structure of a network from cooccurrence data:observations that indicate which nodes occur in a signaling pathway but do not directly reveal node order within the pathway. This problem is motivated by network inference problems arising in computational biology and communication systems, in which it is difficult or impossible to obtain precise time ordering information. Without order information, every permutation of the activated nodes leads to a different feasible solution, resulting in combinatorial explosion of the feasible set. However, physical principles underlying most networked systemssuggest that not all feasible solutions are equally likely. Intuitively, nodes that cooccur more frequently are probably more closely connected. Building on this intuition, we model path co-occurrences as randomly shuffled samples of a random walk on the network. We derive a computationally efficient network inference algorithm and, via novel concentration inequalities for importance samplingestimators, prove that a polynomial complexity Monte Carlo version of the algorithm converges with high probability.

We present a hierarchical Bayesian model for sets of related, but different, classes of time series data. Our model performs alignment simultaneously across all classes, while detecting and characterizing class-specific differences. During inference themodel produces, for each class, a distribution over a canonical representation ofthe class. These class-specific canonical representations are automatically aligned to one another -- preserving common substructures, and highlighting differences.

Everyday inductive reasoning draws on many kinds of knowledge, including knowledge about relationships between properties and knowledge about relationships between objects. Previous accounts of inductive reasoning generally focus on just one kind of knowledge: models of causal reasoning often focus on relationships between properties, and models of similarity-based reasoning often focus on similarity relationships between objects. We present a Bayesian model of inductive reasoning that incorporates both kinds of knowledge, and show that it accounts well for human inferences about the properties of biological species.

Computational gene prediction using generative models has reached a plateau, with several groups converging to a generalized hidden Markov model (GHMM) incorporating phylogenetic models of nucleotide sequence evolution. Further improvements ingene calling accuracy are likely to come through new methods that incorporate additional data, both comparative and species specific. Conditional Random Fields (CRFs), which directly model the conditional probability P (y x) of a vector of hidden states conditioned on a set of observations, provide a unified frameworkfor combining probabilistic and non-probabilistic information and have been shown to outperform HMMs on sequence labeling tasks in natural language processing. We describe the use of CRFs for comparative gene prediction. We implement a model that encapsulates both a phylogenetic-GHMM (our baseline comparative model) and additional non-probabilistic features. We tested our model on the genome sequence of the fungal human pathogen Cryptococcus neoformans.

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.

Bayesian method applied to these models is an attractive approach, used successfully in applications ranging from acoustics t0 bioinformatics.