Related papers: Constructive noncommutative rank computation is in…
In nonadaptive group testing, the main research objective is to design an efficient algorithm to identify a set of up to $t$ positive elements among $n$ samples with as few tests as possible. Disjunct matrices and separable matrices are two…
Using elementary linear algebra, we develop a technique that leads to solutions of two widely known problems on nonnegative matrices. First, we give a short proof of the result by Vavasis stating that the nonnegative rank of a matrix is…
This paper continues research initiated in quant-ph/0201022 . The main subject here is the so-called Edmonds' problem of deciding if a given linear subspace of square matrices contains a nonsingular matrix . We present a deterministic…
We consider the problem of expected cost analysis over nondeterministic probabilistic programs, which aims at automated methods for analyzing the resource-usage of such programs. Previous approaches for this problem could only handle…
Gaussian elimination with full pivoting generates a PLUQ matrix decomposition. Depending on the strategy used in the search for pivots, the permutation matrices can reveal some information about the row or the column rank profiles of the…
This paper studies simultaneous feature selection and extraction in supervised and unsupervised learning. We propose and investigate selective reduced rank regression for constructing optimal explanatory factors from a parsimonious subset…
We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the…
By using of analytical multi-logic expresses in conjunction with non-deterministic Turing machine the proposition was proved that algorithm of deterministic Turing counter machine of polynomial time complexity can be decreased to the…
We consider the problem of Robust PCA in the fully and partially observed settings. Without corruptions, this is the well-known matrix completion problem. From a statistical standpoint this problem has been recently well-studied, and…
We describe a deterministic algorithm that computes an approximate root of n complex polynomial equations in n unknowns in average polynomial time with respect to the size of the input, in the Blum-Shub-Smale model with square root. It…
Consider a matrix $\mathbf{F} \in \mathbb{K}[x]^{m \times n}$ of univariate polynomials over a field $\mathbb{K}$. We study the problem of computing the column rank profile of $\mathbf{F}$. To this end we first give an algorithm which…
This study proposed an exhaustive stable/reproducible rule-mining algorithm combined to a classifier to generate both accurate and interpretable models. Our method first extracts rules (i.e., a conjunction of conditions about the values of…
This note continues the theoretical development of deterministic integer factorization algorithms based on systems of polynomials equations. The main result establishes a new deterministic time complexity bench mark in integer…
In this paper, we study the general problem of optimizing a convex function $F(L)$ over the set of $p \times p$ matrices, subject to rank constraints on $L$. However, existing first-order methods for solving such problems either are too…
Canonical polyadic decomposition (CPD) is at the core of fast matrix multiplication, a computational problem with widespread implications across several seemingly unrelated problems in computer science. Much recent progress in this field…
In this work, we analyze a sublinear-time algorithm for selecting a few rows and columns of a matrix for low-rank approximation purposes. The algorithm is based on an initial uniformly random selection of rows and columns, followed by a…
It is known that the common factors in a large panel of data can be consistently estimated by the method of principal components, and principal components can be constructed by iterative least squares regressions. Replacing least squares…
This article studies how to form CUR decompositions of low-rank matrices via primarily random sampling, though deterministic methods due to previous works are illustrated as well. The primary problem is to determine when a column submatrix…
We focus on \emph{row sampling} based approximations for matrix algorithms, in particular matrix multipication, sparse matrix reconstruction, and \math{\ell_2} regression. For \math{\matA\in\R^{m\times d}} (\math{m} points in \math{d\ll m}…
Recently, fundamental conditions on the sampling patterns have been obtained for finite completability of low-rank matrices or tensors given the corresponding ranks. In this paper, we consider the scenario where the rank is not given and we…