Related papers: FPRAS Approximation of the Matrix Permanent in Pra…
The permanent of a square matrix is defined in a way similar to the determinant, but without using signs. The exact computation of the permanent is hard, but there are Monte-Carlo algorithms that can estimate general permanents. Given a…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
Finding the largest cardinality feasible subset of an infeasible set of linear constraints is the Maximum Feasible Subsystem problem (MAX FS). Solving this problem is crucial in a wide range of applications such as machine learning and…
We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method utilizes a recurrence relation satisfied by the fractional…
Some important applicative problems require the evaluation of functions $\Psi$ of large and sparse and/or \emph{localized} matrices $A$. Popular and interesting techniques for computing $\Psi(A)$ and $\Psi(A)\mathbf{v}$, where $\mathbf{v}$…
The problem of (approximately) counting the independent sets of a bipartite graph (#BIS) is the canonical approximate counting problem that is complete in the intermediate complexity class #RH\Pi_1. It is believed that #BIS does not have an…
In this work, we study two simple yet general complexity classes, based on logspace Turing machines, which provide a unifying framework for efficient query evaluation in areas like information extraction and graph databases, among others.…
The polynomial-time computability of the permanent over fields of characteristic 3 for k-semi-unitary matrices (i.e. square matrices such that the differences of their Gram matrices and the corresponding identity matrices are of rank k) in…
We show an algorithm for computing the permanent of a random matrix with vanishing mean in quasi-polynomial time. Among special cases are the Gaussian, and biased-Bernoulli random matrices with mean 1/lnln(n)^{1/8}. In addition, we can…
Propositional model counting is a fundamental problem in artificial intelligence with a wide variety of applications, such as probabilistic inference, decision making under uncertainty, and probabilistic databases. Consequently, the problem…
We study the problem of approximating the partition function of the ferromagnetic Ising model in graphs and hypergraphs. Our first result is a deterministic approximation scheme (an FPTAS) for the partition function in bounded degree graphs…
Matrix Completion is the problem of recovering an unknown real-valued low-rank matrix from a subsample of its entries. Important recent results show that the problem can be solved efficiently under the assumption that the unknown matrix is…
Evaluating the permanent of a matrix is a fundamental computation that emerges in many domains, including traditional fields like computational complexity theory, graph theory, many-body quantum theory and emerging disciplines like machine…
We present a method to approximate functionals $\text{Tr} \, f(A)$ of very high-dimensional hermitian matrices $A$ represented as Matrix Product Operators (MPOs). Our method is based on a reformulation of a block Lanczos algorithm in tensor…
Matrix permanent plays a key role in data association probability calculations. Exact algorithms (such as Ryser's) scale exponentially with matrix size. Fully polynomial time randomized approximation schemes exist but are quite complex.…
We propose a Fully Polynomial-Time Approximation Scheme (FPTAS) for stochastic dynamic programs with multidimensional action, scalar state, convex costs and linear state transition function. The action spaces are polyhedral and described by…
Computing the permanent of a non-negative matrix is a computationally challenging, \#P-complete problem with wide-ranging applications. We introduce a novel permanental analogue of Schur's determinant formula, leveraging a newly defined…
Binary quadratic programming problems have attracted much attention in the last few decades due to their potential applications. This type of problems are NP-hard in general, and still considered a challenge in the design of efficient…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Counting problems are fundamental across mathematics and computer science. Among the most subtle are those whose associated decision problem is solvable in polynomial time, yet whose exact counting version appears intractable. For some such…