Related papers: Approximating the Permanent via Nonabelian Determi…
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 consider approximating analytic functions on the interval $[-1,1]$ from their values at a set of $m+1$ equispaced nodes. A result of Platte, Trefethen \& Kuijlaars states that fast and stable approximation from equispaced samples is…
We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions…
A maximal matching can be maintained in fully dynamic (supporting both addition and deletion of edges) $n$-vertex graphs using a trivial deterministic algorithm with a worst-case update time of O(n). No deterministic algorithm that…
We study a variable length Markov chain model associated with a group of stationary processes that share the same context tree but each process has potentially different conditional probabilities. We propose a new model selection and…
We present a randomized, inverse-free algorithm for producing an approximate diagonalization of any $n \times n$ matrix pencil $(A,B)$. The bulk of the algorithm rests on a randomized divide-and-conquer eigensolver for the generalized…
We present a new sublinear time algorithm for approximating the spectral density (eigenvalue distribution) of an $n\times n$ normalized graph adjacency or Laplacian matrix. The algorithm recovers the spectrum up to $\epsilon$ accuracy in…
We consider the fundamental learning problem of estimating properties of distributions over large domains. Using a novel piecewise-polynomial approximation technique, we derive the first unified methodology for constructing sample- and…
Finding a good approximation of the top eigenvector of a given $d\times d$ matrix $A$ is a basic and important computational problem, with many applications. We give two different quantum algorithms that, given query access to the entries…
In this paper we consider the problem of computing the likelihood of the profile of a discrete distribution, i.e., the probability of observing the multiset of element frequencies, and computing a profile maximum likelihood (PML)…
The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical…
We solve principal component regression (PCR), up to a multiplicative accuracy $1+\gamma$, by reducing the problem to $\tilde{O}(\gamma^{-1})$ black-box calls of ridge regression. Therefore, our algorithm does not require any explicit…
This paper describes an algorithm which computes the characteristic polynomial of a matrix over a field within the same asymptotic complexity, up to constant factors, as the multiplication of two square matrices. Previously, this was only…
We consider irreversible Markov chains on finite commutative rings randomly generated using both addition and multiplication. We restrict ourselves to the case where the addition is uniformly random and multiplication is arbitrary. We first…
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…
A novel class of non-reversible Markov chain Monte Carlo schemes relying on continuous-time piecewise-deterministic Markov Processes has recently emerged. In these algorithms, the state of the Markov process evolves according to a…
The covariance matrix of measurements of Markov random fields (processes) has useful properties that allow to develop effective computational algorithms for many problems in the study of Markov fields on the basis of field observations…
Initiated by Mulmuley, Vazirani, and Vazirani (1987), many algebraic algorithms have been developed for matching and related problems. In this paper, we review basic facts and discuss possible improvements with the aid of fast computation…
Exact calculation and even multiplicative error estimation of matrix permanent are challenging for both classical and quantum computers. Regarding the permanents of random Gaussian matrices, the additive error estimation is closely linked…
Zero-free based algorithm is a major technique for deterministic approximate counting. In Barvinok's original framework[Bar17], by calculating truncated Taylor expansions, a quasi-polynomial time algorithm was given for estimating zero-free…