Related papers: An elementary approach to the problem of column se…
Estimates of the approximate factor model are increasingly used in empirical work. Their theoretical properties, studied some twenty years ago, also laid the ground work for analysis on large dimensional panel data models with cross-section…
Computing more than one eigenvalue for (large sparse) one-parameter polynomial and general nonlinear eigenproblems, as well as for multiparameter linear and nonlinear eigenproblems, is a much harder task than for standard eigenvalue…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
If the assumed model does not accurately capture the underlying structure of the data, a statistical method is likely to yield sub-optimal results, and so model selection is crucial in order to conduct any statistical analysis. However, in…
Linear algebraic expressions are the essence of many computationally intensive problems, including scientific simulations and machine learning applications. However, translating high-level formulations of these expressions to efficient…
It is well known that many problems in interval computation are intractable, which restricts our attempts to solve large problems in reasonable time. This does not mean, however, that all problems are computationally hard. Identifying…
We consider learning the principal subspace of a large set of vectors from an extremely small number of compressive measurements of each vector. Our theoretical results show that even a constant number of measurements per column suffices to…
The column number question asks for the maximal number of columns of an integer matrix with the property that all its rank size minors are bounded by a fixed parameter $\Delta$ in absolute value. Polynomial upper bounds have been proved in…
We develop a linear-algebraic framework for dimensional analysis in systems with constraints, particularly when variables are numerous or related by implicit relations so that direct elimination is impractical. By expressing both…
In this work, we generalize the probability simplex constraint to matrices, i.e., $\mathbf{X}_1 + \mathbf{X}_2 + \ldots + \mathbf{X}_K = \mathbf{I}$, where $\mathbf{X}_i \succeq 0$ is a symmetric positive semidefinite matrix of size…
This paper considers a restriction to non-negative matrix factorization in which at least one matrix factor is stochastic. That is, the elements of the matrix factors are non-negative and the columns of one matrix factor sum to 1. This…
We propose a novel Riemannian method for solving the Extreme multi-label classification problem that exploits the geometric structure of the sparse low-dimensional local embedding models. A constrained optimization problem is formulated as…
A matrix is given in ``shredded'' form if we are presented with the multiset of rows and the multiset of columns, but not told which row is which or which column is which. The matrix is reconstructible if it is uniquely determined by this…
We consider the problem of chance constrained optimization where it is sought to optimize a function and satisfy constraints, both of which are affected by uncertainties. The real world declinations of this problem are particularly…
We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis…
Computing eigenvalues of very large matrices is a critical task in many machine learning applications, including the evaluation of log-determinants, the trace of matrix functions, and other important metrics. As datasets continue to grow in…
In a standard classification framework a set of trustworthy learning data are employed to build a decision rule, with the final aim of classifying unlabelled units belonging to the test set. Therefore, unreliable labelled observations,…
We use the method of interlacing families of polynomials to derive a simple proof of Bourgain and Tzafriri's Restricted Invertibility Principle, and then to sharpen the result in two ways. We show that the stable rank can be replaced by the…
We propose a method for variable selection in discriminant analysis with mixed categorical and continuous variables. This method is based on a criterion that permits to reduce the variable selection problem to a problem of estimating…
Consider the problem of estimating the entries of a large matrix, when the observed entries are noisy versions of a small random fraction of the original entries. This problem has received widespread attention in recent times, especially…