Related papers: On approximating two distributions from a single c…
We propose an algorithm for reduction of the problem of maximization of fraction of two functionals to the equivalent procedure including maximization of difference between the functionals and the solution of an equation of scalar unknown.…
A confidence distribution is a complete tool for making frequentist inference for a parameter of interest $\psi$ based on an assumed parametric model. Indeed, it allows to reach point estimates, to assess their precision, to set up tests…
We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…
We design efficient distance approximation algorithms for several classes of structured high-dimensional distributions. Specifically, we show algorithms for the following problems: - Given sample access to two Bayesian networks $P_1$ and…
The construction of a multiresolution analysis starts with specification of a scale function. The Fourier transform of this function is defined by an infinite product. The convergence of this product is usually discussed in the context of…
We consider discrete best approximation problems in the setting of tropical algebra, which is concerned with the theory and application of algebraic systems with idempotent operations. Given a set of input--output pairs of an unknown…
This paper mainly addresses the optimization of $p$-th moment of $\mathbb{R}^n$-valued random variable. Through an ingenious approximation mechanism, one transforms the maximization problem into a sequence of minimization problems, which…
We revisit the optimization from samples (OPS) model, which studies the problem of optimizing objective functions directly from the sample data. Previous results showed that we cannot obtain a constant approximation ratio for the maximum…
Parameterization and approximation are two popular ways of coping with NP-hard problems. More recently, the two have also been combined to derive many interesting results. We survey developments in the area both from the algorithmic and…
In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several…
The subset sum problem is known to be an NP-hard problem in the field of computer science with the fastest known approach having a run-time complexity of $O(2^{0.3113n})$. A modified version of this problem is known as the perfect sum…
We investigate the use of the Metropolis-Hastings algorithm to sample posterior distribution in a Bayesian inverse problem, where the likelihood function is random. Concretely, we consider the case where one has full field observations of a…
The Poisson distribution arises naturally when dealing with data involving counts, and it has found many applications in inverse problems and imaging. In this work, we develop an approximate Bayesian inference technique based on expectation…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
We study the impact of quantum computation on the fundamental problem of testing the property of distributions. In particular, we focus on testing whether two unknown classical distributions are close or far enough, and propose the…
Let $p$ and $q$ be two imprecise points, given as probability density functions on $\mathbb R^2$, and let $\cal R$ be a set of $n$ line segments (obstacles) in $\mathbb R^2$. We study the problem of approximating the probability that $p$…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
Computing and storing probabilities is a hard problem as soon as one has to deal with complex distributions over multiple random variables. The problem of efficient representation of probability distributions is central in term of…
Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…
In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…