Related papers: Computation of Induced Orthogonal Polynomial Distr…
We present some properties of measures (q-Gaussian) that orthogonalize the set of q-Hermite polynomials. We also present an algorithm for simulating i.i.d. sequences of random variables having q-Gaussian distribution.
In this paper, we present a wideband subspace estimation method that characterizes the signal subspace through its orthogonal projection matrix at each frequency. Fundamentally, the method models this projection matrix as a function of…
This paper addresses a fundamental problem in random variate generation: given access to a random source that emits a stream of independent fair bits, what is the most accurate and entropy-efficient algorithm for sampling from a discrete…
We present the new Orthogonal Polynomials Approximation Algorithm (OPAA), a parallelizable algorithm that estimates probability distributions using functional analytic approach: first, it finds a smooth functional estimate of the…
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…
Sample- and computationally-efficient distribution estimation is a fundamental tenet in statistics and machine learning. We present SURF, an algorithm for approximating distributions by piecewise polynomials. SURF is: simple, replacing…
The principal support vector machines method (Li et al., 2011) is a powerful tool for sufficient dimension reduction that replaces original predictors with their low-dimensional linear combinations without loss of information. However, the…
We propose efficient techniques for generating independent identically distributed uniform random samples inside semialgebraic sets. The proposed algorithm leverages recent results on the approximation of indicator functions by polynomials…
A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient…
We develop a computationally efficient and robust algorithm for generating pseudo-random samples from a broad class of smooth probability distributions in one and two dimensions. The algorithm is based on inverse transform sampling with a…
In this paper we investigate polynomial interpolation using orthogonal polynomials. We use weight functions associated with orthogonal polynomials to define a weighted form of Lagrange interpolation. We introduce an upper bound of error…
This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…
This paper presents a novel method for polynomial approximation (Hermite approximation) using the fusion of value and derivative information. Therefore, the least-squares error in both domains is simultaneously minimized. A covariance…
We discuss an algorithm to compute transport maps that couple the uniform measure on $[0,1]^d$ with a specified target distribution $\pi$ on $[0,1]^d$. The primary objectives are either to sample from or to compute expectations w.r.t.…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…
The purpose of the paper is to provide a characterization of the error of the best polynomial approximation of composite functions in weighted spaces. Such a characterization is essential for the convergence analysis of numerical methods…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
This paper describes a very efficient algorithm for image signal extrapolation. It can be used for various applications in image and video communication, e.g. the concealment of data corrupted by transmission errors or prediction in video…
This work addresses the distributed estimation problem in a set membership framework. The agents of a network collect measurements which are affected by bounded errors, thus implying that the unknown parameters to be estimated belong to a…
When deploying a trained machine learning model in the real world, it is inevitable to receive inputs from out-of-distribution (OOD) sources. For instance, in continual learning settings, it is common to encounter OOD samples due to the…