Related papers: Moment-Matching Polynomials
Mixture modeling is a general technique for making any simple model more expressive through weighted combination. This generality and simplicity in part explains the success of the Expectation Maximization (EM) algorithm, in which updates…
Abstract notions of convexity over the vertices of a graph, and corresponding notions of halfspaces, have recently gained attention from the machine learning community. In this work we study monophonic halfspaces, a notion of graph…
It is well-known that polynomial reproduction is not possible when approximating with Gaussian kernels. Quasi-interpolation schemes have been developed which use a finite number of Gaussians at different scales, which then reproduce…
Polynomial regression is a basic primitive in learning and statistics. In its most basic form the goal is to fit a degree $d$ polynomial to a response variable $y$ in terms of an $n$-dimensional input vector $x$. This is extremely…
In applications such as rank aggregation, mixture models for permutations are frequently used when the population exhibits heterogeneity. In this work, we study the widely used Mallows mixture model. In the high-dimensional setting, we…
The problem of generating random samples of high-dimensional posterior distributions is considered. The main results consist of non-asymptotic computational guarantees for Langevin-type MCMC algorithms which scale polynomially in key…
We consider the basic problem of learning Single-Index Models with respect to the square loss under the Gaussian distribution in the presence of adversarial label noise. Our main contribution is the first computationally efficient algorithm…
We present a polynomial time algorithm to approximately scale tensors of any format to arbitrary prescribed marginals (whenever possible). This unifies and generalizes a sequence of past works on matrix, operator and tensor scaling. Our…
We propose a method to compute an approximation of the moments of a discrete-time stochastic polynomial system. We use the Carleman linearization technique to transform this finite-dimensional polynomial system into an infinite-dimensional…
A low-degree polynomial model for a response curve is used commonly in practice. It generally incorporates a linear or quadratic function of the covariate. In this paper we suggest methods for testing the goodness of fit of a general…
We propose a kernel mixture of polynomials prior for Bayesian nonparametric regression. The regression function is modeled by local averages of polynomials with kernel mixture weights. We obtain the minimax-optimal rate of contraction of…
We initiate the study of \emph{inverse} problems in approximate uniform generation, focusing on uniform generation of satisfying assignments of various types of Boolean functions. In such an inverse problem, the algorithm is given uniform…
Given a finite metric space $(X\cup Y, \mathbf{d})$ the $k$-median problem is to find a set of $k$ centers $C\subseteq Y$ that minimizes $\sum_{p\in X} \min_{c\in C} \mathbf{d}(p,c)$. In general metrics, the best polynomial time algorithm…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the case when each instance has a fixed,…
We study the problem of learning mixtures of $k$ Gaussians in $d$ dimensions. We make no separation assumptions on the underlying mixture components: we only require that the covariance matrices have bounded condition number and that the…
In this paper, we study the problem of multivariate $L_2$-approximation of functions belonging to a weighted Korobov space. We propose and analyze a median lattice-based algorithm, inspired by median integration rules, which have attracted…
Given an input matrix polynomial whose coefficients are floating point numbers, we consider the problem of finding the nearest matrix polynomial which has rank at most a specified value. This generalizes the problem of finding a nearest…
The ability to learn polynomials and generalize out-of-distribution is essential for simulation metamodels in many disciplines of engineering, where the time step updates are described by polynomials. While feed forward neural networks can…
Standard approaches to probabilistic reasoning require that one possesses an explicit model of the distribution in question. But, the empirical learning of models of probability distributions from partial observations is a problem for which…