Related papers: A cost-scaling algorithm for computing the degree …
Efficient matrix determinant calculations have been studied since the 19th century. Computers expand the range of determinants that are practically calculable to include matrices with symbolic entries. However, the fastest determinant…
We study the problem of high-dimensional robust mean estimation in the presence of a constant fraction of adversarial outliers. A recent line of work has provided sophisticated polynomial-time algorithms for this problem with…
One of the most attractive recent approaches to processing well-structured large-scale convex optimization problems is based on smooth convex-concave saddle point reformu-lation of the problem of interest and solving the resulting problem…
We describe a new algorithm for calculating the topological degree deg (f, B, 0) where B \subseteq Rn is a product of closed real intervals and f : B \rightarrow Rn is a real-valued continuous function given in the form of arithmetical…
We present an iterative algorithm for computing an invariant subspace associated with the algebraically smallest eigenvalues of a large sparse or structured Hermitian matrix A. We are interested in the case in which the dimension of the…
We study algorithms for construction of composable coresets for the task of Determinant Maximization under partition constraint. Given a point set $V\subset \mathbb{R}^d$ that is partitioned into $s$ groups $V_1,\cdots, V_s$, and integers…
The pseudo-determinant Det(A) of a square matrix A is defined as the product of the nonzero eigenvalues of A. It is a basis-independent number which is up to a sign the first nonzero entry of the characteristic polynomial of A. We prove…
We use a variety of computational tools to obtain a degree-$\binom{m + n - 2}{m - 1}$ polynomial equation conjecturally satisfied by the top-left entry of the Sinkhorn limit of a positive $m \times n$ matrix. The degree of this equation has…
We study the problem of optimal subset selection from a set of correlated random variables. In particular, we consider the associated combinatorial optimization problem of maximizing the determinant of a symmetric positive definite matrix…
An algorithm is devised for solving minimization problems with equality constraints. The algorithm uses first-order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest-descent…
Let $g: \{-1,1\}^k \to \{-1,1\}$ be any Boolean function and $q_1,\dots,q_k$ be any degree-2 polynomials over $\{-1,1\}^n.$ We give a \emph{deterministic} algorithm which, given as input explicit descriptions of $g,q_1,\dots,q_k$ and an…
We extend our techniques developed in our earlier paper appeared in Computational Complexity, 2017 (preprint: arXiv:1508.00690) to obtain a deterministic polynomial time algorithm for computing the non-commutative rank together with…
This paper presents a method for expressing the determinant of an N {\times} N complex block matrix in terms of its constituent blocks. The result allows one to reduce the determinant of a matrix with N^2 blocks to the product of the…
In this paper, we develop a polynomial time algorithm to compute a Dulmage-Mendelsohn-type decomposition of a matrix partitioned into submatrices of rank at most $1$.
In this paper, we consider the online proximal mirror descent for solving the time-varying composite optimization problems. For various applications, the algorithm naturally involves the errors in the gradient and proximal operator. We…
The problem of expressing a specific polynomial as the determinant of a square matrix of affine-linear forms arises from algebraic geometry, optimisation, complexity theory, and scientific computing. Motivated by recent developments in this…
In this paper, we introduce a novel algorithm for calculating arbitrary order cumulants of multidimensional data. Since the $d^\text{th}$ order cumulant can be presented in the form of an $d$-dimensional tensor, the algorithm is presented…
We consider a class of optimization problems over stochastic variables where the algorithm can learn information about the value of any variable through a series of costly steps; we model this information acquisition process as a Markov…
A class of derivatives is defined for the pseudo determinant $Det(A)$ of a Hermitian matrix $A$. This class is shown to be non-empty and to have a unique, canonical member $\mathbf{\nabla Det}(A)=Det(A)A^+$, where $A^+$ is the Moore-Penrose…
The minimum degree algorithm is one of the most widely-used heuristics for reducing the cost of solving large sparse systems of linear equations. It has been studied for nearly half a century and has a rich history of bridging techniques…