Related papers: Data approximation with time-frequency invariant s…
We propose a method of data quantization of finite discrete-time signals which optimizes the error estimate of low frequency Haar coefficients. We also discuss the error/noise bounds of this quantization in the Fourier space. Our result…
The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those…
We study (constrained) least-squares regression as well as multiple response least-squares regression and ask the question of whether a subset of the data, a coreset, suffices to compute a good approximate solution to the regression. We…
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…
We present an algorithm for minimizing the sum of a strongly convex time-varying function with a time-invariant, convex, and nonsmooth function. The proposed algorithm employs the prediction-correction scheme alongside the forward-backward…
Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods that are effective in the small-noise regime are suboptimal…
We study best approximation to a given function, in the least square sense on a subset of the unit circle, by polynomials of given degree which are pointwise bounded on the complementary subset. We show that the solution to this problem, as…
Many popular learning algorithms (E.g. Regression, Fourier-Transform based algorithms, Kernel SVM and Kernel ridge regression) operate by reducing the problem to a convex optimization problem over a vector space of functions. These methods…
Unitary best approximation to the exponential function on an interval on the imaginary axis has been introduced recently. In the present work two algorithms are considered to compute this best approximant: an algorithm based on rational…
We develop fixed-point algorithms for the approximation of structured matrices with rank penalties. In particular we use these fixed-point algorithms for making approximations by sums of exponentials, or frequency estimation. For the basic…
Invariance to nuisance transformations is one of the desirable properties of effective representations. We consider transformations that form a \emph{group} and propose an approach based on kernel methods to derive local group invariant…
We introduce new finite-dimensional spaces specifically designed to approximate the solutions to high-frequency Helmholtz problems with smooth variable coefficients in dimension $d$. These discretization spaces are spanned by Gaussian…
We propose a novel approximate factor model tailored for analyzing time-dependent curve data. Our model decomposes such data into two distinct components: a low-dimensional predictable factor component and an unpredictable error term. These…
We obtain robust and computationally efficient estimators for learning several linear models that achieve statistically optimal convergence rate under minimal distributional assumptions. Concretely, we assume our data is drawn from a…
This work aims to address an open problem in data valuation literature concerning the efficient computation of Data Shapley for weighted $K$ nearest neighbor algorithm (WKNN-Shapley). By considering the accuracy of hard-label KNN with…
We study time-uniform statistical inference for parameters in stochastic approximation (SA), which encompasses a bunch of applications in optimization and machine learning. To that end, we analyze the almost-sure convergence rates of the…
Analysis of big data has become an increasingly relevant area of research, with data often represented on discrete networks both constructed and organic. While for structured domains, there exist intuitive definitions of signals and…
We propose the use of low bit-depth Sigma-Delta and distributed noise-shaping methods for quantizing the Random Fourier features (RFFs) associated with shift-invariant kernels. We prove that our quantized RFFs -- even in the case of $1$-bit…
Precise measurements from sensors are crucial, but data is usually collected from low-cost, low-tech systems, which are often inaccurate. Thus, they require further calibrations. To that end, we first identify three requirements for…
We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…