Amino acid profiles, which capture position-specific mutation probabilities, are a richer encoding of biological sequences than the individual sequences themselves. However, profile comparisons are much more computationally expensive than discrete symbol comparisons, making profiles impractical for many large datasets. Furthermore, because they are such a rich representation, profiles can be difficult to visualize. To overcome these problems, we propose a discretization for profiles using an expanded alphabet representing not just individual amino acids, but common profiles. By using an extension of information bottleneck (IB) incorporating constraints and priors on the class distributions, we find an informationally optimal alphabet. This discretization yields a concise, informative textual representation for profile sequences. Also alignments between these sequences, while nearly as accurate as the full profile-profile alignments, can be computed almost as quickly as those between individual or consensus sequences. A full pairwise alignment of SwissProt would take years using profiles, but less than 3 days using a discrete IB encoding, illustrating how discrete encoding can expand the range of sequence problems to which profile information can be applied.

We present an algorithm based on convex optimization for constructing kernels for semi-supervised learning. The kernel matrices are derived from the spectral decomposition of graph Laplacians, and combine labeled and unlabeled data in a systematic fashion. Unlike previous work using diffusion kernels and Gaussian random field kernels, a nonparametric kernel approach is presented that incorporates order constraints during optimization. This results in flexible kernels and avoids the need to choose among different parametric forms. Our approach relies on a quadratically constrained quadratic program (QCQP), and is computationally feasible for large datasets. We evaluate the kernels on real datasets using support vector machines, with encouraging results.

We relate the algorithm to the stochastic approximation literature. This enables us to specify conditions under which the algorithm is guaranteed to converge to the optimal solution (with probability 1). This includes necessary and sufficient conditions for the solution to be unbiased.

Unfortunately, the required optimization problem is often intractable because there is a combinatorial increase in the number of local minima as the number of candidate basis vectors increases.

We present a novel approach to collaborative prediction, using low-norm instead of low-rank factorizations. The approach is inspired by, and has strong connections to, large-margin linear discrimination. We show how to learn low-norm factorizations by solving a semi-definite program, and discuss generalization error bounds for them.

A novel linear feature selection algorithm is presented based on the global minimization of a data-dependent generalization error bound. Feature selection and scaling algorithms often lead to non-convex optimization problems, which in many previous approaches were addressed through gradient descent procedures that can only guarantee convergence to a local minimum. We propose an alternative approach, whereby the global solution of the non-convex optimization problem is derived via an equivalent optimization problem. Moreover, the convex optimization task is reduced to a conic quadratic programming problem for which efficient solvers are available. Highly competitive numerical results on both artificial and real-world data sets are reported.

We do this by first defining a decomposition tree representation for G, which is closely related to the junction-tree representation for G. We then give an algorithm which uses this representation to compute the optimal H H. Gavril [2] and Tarjan [3] have used graph separation properties to solve several combinatorial optimization problems when the size of the minimal separators in the graph is bounded. We present an extension of this technique which applies to some important choices of H even when the size of the minimal separators of G are arbitrarily large. In particular, this applies to problems such as finding an optimal subgraphical model over a (k 1)-tree of a graphical model over a k-tree (for arbitrary k) and selecting an optimal subgraphical model with (a constant) d fewer edges with respect to KL-divergence can be solved in time polynomial in V (G) using this formulation.

Bayesian Regularization and Nonnegative Deconvolution (BRAND) is proposed for estimating time delays of acoustic signals in reverberant environments.

Various problems in machine learning, databases, and statistics involve pairwise distances among a set of objects. It is often desirable for these distances to satisfy the properties of a metric, especially the triangle inequality. Applications where metric data is useful include clustering, classification, metric-based indexing, and approximation algorithms for various graph problems. This paper presents the Metric Nearness Problem: Given a dissimilarity matrix, find the "nearest" matrix of distances that satisfy the triangle inequalities.

We consider the problem of structured classification, where the task is to predict a label y from an input x, and y has meaningful internal structure. Our framework includes supervised training of Markov random fields and weighted context-free grammars as special cases. We describe an algorithm that solves the large-margin optimization problem defined in [12], using an exponential-family (Gibbs distribution) representation of structured objects. The algorithm is efficient--even in cases where the number of labels y is exponential in size--provided that certain expectations under Gibbs distributions can be calculated efficiently. The method for structured labels relies on a more general result, specifically the application of exponentiated gradient updates [7, 8] to quadratic programs.