Related papers: Roos' Matrix Permanent Approximation Bounds for Da…
We construct a deterministic approximation algorithm for computing a permanent of a $0,1$ $n$ by $n$ matrix to within a multiplicative factor $(1+\epsilon)^n$, for arbitrary $\epsilon>0$. When the graph underlying the matrix is a constant…
Counting the number of all the matchings on a bipartite graph has been transformed into calculating the permanent of a matrix obtained from the extended bipartite graph by Yan Huo, and Rasmussen presents a simple approach (RM) to…
Counting the number of all the matchings on a bipartite graph has been transformed into calculating the permanent of a matrix obtained from the extended bipartite graph by Yan Huo, and Rasmussen presents a simple approach (RM) to…
Data association, the problem of reasoning over correspondence between targets and measurements, is a fundamental problem in tracking. This paper presents a graphical model formulation of data association and applies an approximate…
Characterizing the risk of operations is a fundamental requirement in robotics, and a crucial ingredient of safe planning. The problem is multifaceted, with multiple definitions arising in the vast recent literature fitting different…
Low-rank matrix approximations are often used to help scale standard machine learning algorithms to large-scale problems. Recently, matrix coherence has been used to characterize the ability to extract global information from a subset of…
Matrix approximation is a common tool in machine learning for building accurate prediction models for recommendation systems, text mining, and computer vision. A prevalent assumption in constructing matrix approximations is that the…
We propose a framework for the exact probabilistic analysis of window-based pattern matching algorithms, such as Boyer-Moore, Horspool, Backward DAWG Matching, Backward Oracle Matching, and more. In particular, we show how to efficiently…
In this paper, we develop deterministic fully dynamic algorithms for computing approximate distances in a graph with worst-case update time guarantees. In particular, we obtain improved dynamic algorithms that, given an unweighted and…
The algorithm and complexity of approximating the permanent of a matrix is an extensively studied topic. Recently, its connection with quantum supremacy and more specifically BosonSampling draws special attention to the average-case…
Given a real matrix A with n columns, the problem is to approximate the Gram product AA^T by c << n weighted outer products of columns of A. Necessary and sufficient conditions for the exact computation of AA^T (in exact arithmetic) from c…
The CUR matrix decomposition is an important extension of Nystr\"{o}m approximation to a general matrix. It approximates any data matrix in terms of a small number of its columns and rows. In this paper we propose a novel randomized CUR…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
Estimating conditional dependence graphs and precision matrices are some of the most common problems in modern statistics and machine learning. When data are fully observed, penalized maximum likelihood-type estimators have become standard…
We present a randomized approximation scheme for the permanent of a matrix with nonnegative entries. Our scheme extends a recursive rejection sampling method of Huber and Law (SODA 2008) by replacing the upper bound for the permanent with a…
We document a connection between constraint reasoning and probabilistic reasoning. We present an algorithm, called {em probabilistic arc consistency}, which is both a generalization of a well known algorithm for arc consistency used in…
Belief updating in Bayes nets, a well known computationally hard problem, has recently been approximated by several deterministic algorithms, and by various randomized approximation algorithms. Deterministic algorithms usually provide…
Global data association is an essential prerequisite for robot operation in environments seen at different times or by different robots. Repetitive or symmetric data creates significant challenges for existing methods, which typically rely…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Relational Continuous Models (RCMs) represent joint probability densities over attributes of objects, when the attributes have continuous domains. With relational representations, they can model joint probability distributions over large…