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The paper investigates the problem of performing correlation analysis when the number of observations is very large. In such a case, it is often necessary to combine the random observations to achieve dimensionality reduction of the…
In this paper, we build up a framework for sparse interpolation. We first investigate the theoretical limit of the number of unisolvent points for sparse interpolation under a general setting and try to answer some basic questions of this…
We present a probabilistic algorithm to compute the product of two univariate sparse polynomials over a field with a number of bit operations that is quasi-linear in the size of the input and the output. Our algorithm works for any field of…
In the first part of the series papers, we set out to answer the following question: given specific restrictions on a set of samplers, what kind of signal can be uniquely represented by the corresponding samples attained, as the foundation…
We present new techniques for reducing a multivariate sparse polynomial to a univariate polynomial. The reduction works similarly to the classical and widely-used Kronecker substitution, except that we choose the degrees randomly based on…
Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…
We propose an iterative algorithm for the minimization of a $\ell_1$-norm penalized least squares functional, under additional linear constraints. The algorithm is fully explicit: it uses only matrix multiplications with the three matrices…
A wide range of problems in computational science and engineering require estimation of sparse eigenvectors for high dimensional systems. Here, we propose two variants of the Truncated Orthogonal Iteration to compute multiple leading…
In this paper, a sparse-based method for the estimation of the parameters of multidimensional ($R$-D) modal (harmonic or damped) complex signals in noise is presented. The problem is formulated as $R$ simultaneous sparse approximations of…
Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…
This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…
We propose new compressive parameter estimation algorithms that make use of polar interpolation to improve the estimator precision. Our work extends previous approaches involving polar interpolation for compressive parameter estimation in…
The model interpretation is essential in many application scenarios and to build a classification model with a ease of model interpretation may provide useful information for further studies and improvement. It is common to encounter with a…
In this paper, we investigate the problem of optimization multivariate performance measures, and propose a novel algorithm for it. Different from traditional machine learning methods which optimize simple loss functions to learn prediction…
A linear inverse problem is proposed that requires the determination of multiple unknown signal vectors. Each unknown vector passes through a different system matrix and the results are added to yield a single observation vector. Given the…
Small sample sizes are common in many disciplines, which necessitates pooling roughly similar datasets across multiple institutions to study weak but relevant associations between images and disease outcomes. Such data often manifest…
This work deals with a regularization method enforcing solution sparsity of linear ill-posed problems by appropriate discretization in the image space. Namely, we formulate the so called least error method in an $\ell^1$ setting and perform…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
We consider the problem of reconstructing an infinite set of sparse, finite-dimensional vectors, that share a common sparsity pattern, from incomplete measurements. This is in contrast to the work [17], where the single vector signal can be…
Real-world binary classification tasks are in many cases imbalanced, where the minority class is much smaller than the majority class. This skewness is challenging for machine learning algorithms as they tend to focus on the majority and…