We construct a distribution-free Bayes optimal classifier called the Minimum Error Minimax Probability Machine (MEMPM) in a worst-case setting, i.e., under all possible choices of class-conditional densities with a given mean and covariance matrix. By assuming no specific distributions for the data

ABSTRACT We consider the problem of designing a linear transformation ` 2 IRp\Theta n, of rank p ^ n, which projects the features of a classifier x 2 IRn onto y = `x 2 IRp such as to achieve minimum Bayes error (or probability of misclassification). Two avenues will be explored: the first

Let X be a data matrix of rank ρ, representing n points in d-dimensional space. The linear support vector machine constructs a hyperplane separator that maximizes the 1-norm soft margin. We develop a new oblivious dimension reduction technique which is precomputed and can be applied to any input

criterion which minimizes the probability of overlap. The resulting optimization problem can be solved efficiently and we show how the global minimum of the error term is guaranteed under mild conditions. We provide extensive experimental results, demonstrating the superiority of the proposed approach over

reduction by elimination of non-binding resources and by conditional decomposition based on special structure, an effective scaling algorithm to control errors in the inversion, efficient treatment of multiple classes with identical parameters and truncation of large sums. We show that the computational

waveforms, which in turn are chosen from a large class of spreading codes. We derive the probability-of-error when using two methods for recovery of active users and their transmitted symbols: the reduced-dimension decorrelating (RDD) detector, which combines subspace projection and thresholding

We compute the singular values of an m×n tall and skinny (m ≫ n) sparse matrix A without dependence on m, for very large m. In particular, we give a simple nonadaptive sampling scheme where the singular values of A are estimated within relative error with high probability. Our proven bounds focus

Abstract — We consider minimum variance estimation within the sparse linear Gaussian model (SLGM). A sparse vector is to be estimated from a linearly transformed version embedded in Gaussian noise. Our analysis is based on the theory of reproducing kernel Hilbert spaces (RKHS). After a

Abstract A master equation describes the continuous-time evolution of a probability distribution, and is characterized by a simple bilinear structure and an often-high dimension. We develop a model reduction approach in which the number of possible configurations and corresponding dimension

proposed by Cayrel et al. in [14]. Our proposed scheme benefits of a performance gain as a result of the reduction in the soundness error from 2/3 for Stern’s scheme to 1/2 per round for the q-SD scheme. Our threshold ring signature scheme uses random linear codes over the field Fq, secure in the random