Related papers: A Christoffel-like function for high-dimensional s…
Statistical inferences for quadratic functionals of linear regression parameter have found wide applications including signal detection, global testing, inferences of error variance and fraction of variance explained. Classical theory based…
Stochastic Boolean Function Evaluation is the problem of determining the value of a given Boolean function f on an unknown input x, when each bit of x_i of x can only be determined by paying an associated cost c_i. The assumption is that x…
In this paper, based on Newton interpolation we have proposed a numerical scheme of predictor-corrector type in order to solve fractional differential equations with the fractional derivative involving the Mittag-Leffler function. We have…
While generalized linear mixed models are a fundamental tool in applied statistics, many specifications, such as those involving categorical factors with many levels or interaction terms, can be computationally challenging to estimate due…
Shapley values have seen widespread use in machine learning as a way to explain model predictions and estimate the importance of covariates. Accurately explaining models is critical in real-world models to both aid in decision making and to…
In this paper, we focus on distributed estimation and support recovery for high-dimensional linear quantile regression. Quantile regression is a popular alternative tool to the least squares regression for robustness against outliers and…
We introduce and study natural derivatives for Christoffel and finite standard words, as well as for characteristic Sturmian words. These derivatives, which are realized as inverse images under suitable morphisms, preserve the…
The inverse of a large matrix can often be accurately approximated by a polynomial of degree significantly lower than the order of the matrix. The iteration polynomial generated by a run of the GMRES algorithm is a good candidate, and its…
The Morse-Smale complex of a function $f$ decomposes the sample space into cells where $f$ is increasing or decreasing. When applied to nonparametric density estimation and regression, it provides a way to represent, visualize, and compare…
This paper demonstrates how to explicitly construct a bidiagonal factorization of the banded recurrence matrix that appears in mixed multiple orthogonality on the step-line in terms of the coeffcients of the mixed multiple orthogonal…
Models with intractable normalizing functions have numerous applications. Because the normalizing constants are functions of the parameters of interest, standard Markov chain Monte Carlo cannot be used for Bayesian inference for these…
We describe CFW, a computationally efficient algorithm for collaborative filtering that uses posteriors over weights of evidence. In experiments on real data, we show that this method predicts as well or better than other methods in…
The problem of recovering a moment-determinate multivariate function $f$ via its moment sequence is studied. Under mild conditions on $f$, the point-wise and $L_1$-rates of convergence for the proposed constructions are established. The…
A new version of the convexification method is developed analytically and tested numerically for a 1-D coefficient inverse problem in the frequency domain. Unlike the previous version, this one does not use the so-called "tail function",…
We propose a dimension reduction framework for feature extraction and moment reconstruction in dynamical systems that operates on spaces of probability measures induced by observables of the system rather than directly in the original data…
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…
In this manuscript we consider the problem of jointly estimating multiple graphical models in high dimensions. We assume that the data are collected from n subjects, each of which consists of T possibly dependent observations. The graphical…
Because of the high approximation power and simplicity of computation of smooth radial basis functions (RBFs), in recent decades they have received much attention for function approximation. These RBFs contain a shape parameter that…
We present a FFT-based algorithm for the computation of a polynomial's coefficients from its roots, and apply it to obtain the coefficients of interpolation polynomials, to invert Vandermondians and to evaluate the symmetric functions of a…
Stochastic gradient descent is a simple approach to find the local minima of a cost function whose evaluations are corrupted by noise. In this paper, we develop a procedure extending stochastic gradient descent algorithms to the case where…