Related papers: A Simple Algorithm for Exact Multinomial Tests
Checking two probabilistic automata for equivalence has been shown to be a key problem for efficiently establishing various behavioural and anonymity properties of probabilistic systems. In recent experiments a randomised equivalence test…
In this paper, we address the problem of approximating a multivariate function defined on a general domain in $d$ dimensions from sample points. We consider weighted least-squares approximation in an arbitrary finite-dimensional space $P$…
Sparsity finds applications in areas as diverse as statistics, machine learning, and signal processing. Computations over sparse structures are less complex compared to their dense counterparts, and their storage consumes less space. This…
Approximation algorithms are widely used in many engineering problems. To obtain a data set for approximation a factorial design of experiments is often used. In such case the size of the data set can be very large. Therefore, one of the…
Based on two independent samples X_1,...,X_m and X_{m+1},...,X_n drawn from multivariate distributions with unknown Lebesgue densities p and q respectively, we propose an exact multiple test in order to identify simultaneously regions of…
Approximately unbiased tests based on bootstrap probabilities are considered for the exponential family of distributions with unknown expectation parameter vector, where the null hypothesis is represented as an arbitrary-shaped region with…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
In this note we describe experiments on an implementation of two methods proposed in the literature for computing regions that correspond to a notion of order statistics for multidimensional data. Our implementation, which works for any…
We propose a nonconvex estimator for joint multivariate regression and precision matrix estimation in the high dimensional regime, under sparsity constraints. A gradient descent algorithm with hard thresholding is developed to solve the…
This survey provides an exposition of a suite of techniques based on the theory of polynomials, collectively referred to as polynomial methods, which have recently been applied to address several challenging problems in statistical…
Various applications involve assigning discrete label values to a collection of objects based on some pairwise noisy data. Due to the discrete---and hence nonconvex---structure of the problem, computing the optimal assignment (e.g.~maximum…
Decision making or scientific discovery pipelines such as job hiring and drug discovery often involve multiple stages: before any resource-intensive step, there is often an initial screening that uses predictions from a machine learning…
We consider several problems in the field of distributed optimization and hypothesis testing. We show how to obtain convergence times for these problems that scale linearly with the total number of nodes in the network by using a recent…
We introduce a simple, efficient and precise polynomial heuristic for a key NP complete problem, minimum vertex cover. Our method is iterative and operates in probability space. Once a stable probability solution is found we find the true…
The main purpose of this paper is to study the NP-complete subset-sum problem, not in the usual context of time-complexity-based classification of the algorithms (exponential/polynomial), but through a new kind of algorithmic classification…
We consider the problem of uncertainty quantification in change point regressions, where the signal can be piecewise polynomial of arbitrary but fixed degree. That is we seek disjoint intervals which, uniformly at a given confidence level,…
Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…
We study the statistical-computational trade-offs for learning with exact invariances (or symmetries) using kernel regression. Traditional methods, such as data augmentation, group averaging, canonicalization, and frame-averaging, either…
We present a new algorithm for reconstructing an exact algebraic number from its approximate value using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on…
We describe a dynamic programming algorithm for exact counting and exact uniform sampling of matrices with specified row and column sums. The algorithm runs in polynomial time when the column sums are bounded. Binary or non-negative integer…