In bioinformatics it is often desirable to combine data from various measurement sources and thus structured feature vectors are to be analyzed that possess different intrinsic blocking characteristics (e.g., different patterns of missing values, observation noise levels, effective intrinsic dimensionalities). We propose a new machine learning tool, heterogeneous component analysis (HCA), for feature extraction in order to better understand the factors that underlie such complex structured heterogeneous data. HCA is a linear block-wise sparse Bayesian PCA based not only on a probabilistic model with block-wise residual variance terms but also on a Bayesian treatment of a block-wise sparse factor-loading matrix. We study various algorithms that implement our HCA concept extracting sparse heterogeneous structure by obtaining common components for the blocks and specific components within each block. Simulations on toy and bioinformatics data underline the usefulness of the proposed structured matrix factorization concept.

We investigate the problem of learning a widely-used latent-variable model - the Latent Dirichlet Allocation (LDA) or "topic" model - using distributed computation, where each of

We present a nonparametric Bayesian method of estimating variable order Markov processes up to a theoretically infinite order. By extending a stick-breaking prior, which is usually defined on a unit interval, "vertically" to the trees of infinite depth associated with a hierarchical Chinese restaurant process, our model directly infers the hidden orders of Markov dependencies from which each symbol originated. Experiments on character and word sequences in natural language showed that the model has a comparative performance with an exponentially large full-order model, while computationally much efficient in both time and space. We expect that this basic model will also extend to the variable order hierarchical clustering of general data.

The learning of probabilistic models with many hidden variables and nondecomposable dependencies is an important and challenging problem. In contrast to traditional approaches based on approximate inference in a single intractable model, our approach is to train a set of tractable submodels by encouraging them to agree on the hidden variables. This allows us to capture non-decomposable aspects of the data while still maintaining tractability. We propose an objective function for our approach, derive EMstyle algorithms for parameter estimation, and demonstrate their effectiveness on three challenging real-world learning tasks.

Statistical models on full and partial rankings of n items are often of limited practical use for large n due to computational consideration. We explore the use of nonparametric models for partially ranked data and derive efficient procedures for their use for large n. The derivations are largely possible through combinatorial and algebraic manipulations based on the lattice of partial rankings. In particular, we demonstrate for the first time a nonparametric coherent and consistent model capable of efficiently aggregating partially ranked data of different types.

Clustering is often formulated as the maximum likelihood estimation of a mixture model that explains the data. The EM algorithm widely used to solve the resulting optimization problem is inherently a gradient-descent method and is sensitive to initialization. The resulting solution is a local optimum in the neighborhood of the initial guess. This sensitivity to initialization presents a significant challenge in clustering large data sets into many clusters. In this paper, we present a different approach to approximate mixture fitting for clustering. We introduce an exemplar-based likelihood function that approximates the exact likelihood. This formulation leads to a convex minimization problem and an efficient algorithm with guaranteed convergence to the globally optimal solution. The resulting clustering can be thought of as a probabilistic mapping of the data points to the set of exemplars that minimizes the average distance and the information-theoretic cost of mapping.

We extend position and phase-shift tuning, concepts already well established in the disparity energy neuron literature, to motion energy neurons. We show that Reichardt-like detectors can be considered examples of position tuning, and that motion energy filters whose complex valued spatiotemporal receptive fields are space-time separable can be considered examples of phase tuning. By combining these two types of detectors, we obtain an architecture for constructing motion energy neurons whose center frequencies can be adjusted by both phase and position shifts. Similar to recently described neurons in the primary visual cortex, these new motion energy neurons exhibit tuning that is between purely spacetime separable and purely speed tuned. We propose a functional role for this intermediate level of tuning by demonstrating that comparisons between pairs of these motion energy neurons can reliably discriminate between inputs whose velocities lie above or below a given reference velocity.

We utilize the ensemble of trees framework, a tractable mixture over superexponential number of tree-structured distributions [1], to develop a new model for multivariate density estimation. The model is based on a construction of treestructured copulas - multivariate distributions with uniform on [0, 1] marginals.

Point-based algorithms have been surprisingly successful in computing approximately optimal solutions for partially observable Markov decision processes (POMDPs) in high dimensional belief spaces. In this work, we seek to understand the belief-space properties that allow some POMDP problems to be approximated efficiently and thus help to explain the point-based algorithms' success often observed in the experiments. We show that an approximately optimal POMDP solution can be computed in time polynomial in the covering number of a reachable belief space, which is the subset of the belief space reachable from a given belief point. We also show that under the weaker condition of having a small covering number for an optimal reachable space, which is the subset of the belief space reachable under an optimal policy, computing an approximately optimal solution is NPhard. However, given a suitable set of points that "cover" an optimal reachable space well, an approximate solution can be computed in polynomial time. The covering number highlights several interesting properties that reduce the complexity of POMDP planning in practice, e.g., fully observed state variables, beliefs with sparse support, smooth beliefs, and circulant state-transition matrices.

A discriminative method is proposed for learning monotonic transformations of the training data while jointly estimating a large-margin classifier. In many domains such as document classification, image histogram classification and gene microarray experiments, fixed monotonic transformations can be useful as a preprocessing step. However, most classifiers only explore these transformations through manual trial and error or via prior domain knowledge. The proposed method learns monotonic transformations automatically while training a large-margin classifier without any prior knowledge of the domain. A monotonic piecewise linear function is learned which transforms data for subsequent processing by a linear hyperplane classifier. Two algorithmic implementations of the method are formalized. The first solves a convergent alternating sequence of quadratic and linear programs until it obtains a locally optimal solution. An improved algorithm is then derived using a convex semidefinite relaxation that overcomes initialization issues in the greedy optimization problem. The effectiveness of these learned transformations on synthetic problems, text data and image data is demonstrated.