Related papers: A multivariate generalization of Prony's method
We present a sampling theory for a class of binary images with finite rate of innovation (FRI). Every image in our model is the restriction of $\mathds{1}_{\{p\leq0\}}$ to the image plane, where $\mathds{1}$ denotes the indicator function…
Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step…
Suppose $\mathbb{K}$ is a large enough field and $\mathcal{P} \subset \mathbb{K}^2$ is a fixed, generic set of points which is available for precomputation. We introduce a technique called \emph{reshaping} which allows us to design…
A quadrature rule of a measure $\mu$ on the real line represents a convex combination of finitely many evaluations at points, called nodes, that agrees with integration against $\mu$ for all polynomials up to some fixed degree. In this…
Undersampling is a common method in Magnetic Resonance Imaging (MRI) to subsample the number of data points in k-space, reducing acquisition times at the cost of decreased image quality. A popular approach is to employ undersampling…
The main aim of this work is to compare two Borel measures thorough their moment matrices using a new notion of smallest and largest generalized eigenvalues. With this approach we provide information in problems as the localization of the…
In order to process a potential moment sequence by the entropy optimization method one has to be assured that the original measure is absolutely continuous with respect to Lebesgue measure. We propose a non-linear exponential transform of…
In many applications of tomography, the acquired projections are either limited in number or contain a significant amount of noise. In these cases, standard reconstruction methods tend to produce artifacts that can make further analysis…
This article explores the generalized analysis-of-variance or ANOVA dimensional decomposition (ADD) for multivariate functions of dependent random variables. Two notable properties, stemming from weakened annihilating conditions, reveal…
We study recovery of amplitudes and nodes of a finite impulse train from noisy frequency samples. This problem is known as super-resolution under sparsity constraints and has numerous applications. An especially challenging scenario occurs…
This paper describes a novel method to approximate the polynomial coefficients of regression functions, with particular interest on multi-dimensional classification. The derivation is simple, and offers a fast, robust classification…
This paper studies a machine learning regression problem as a multivariate approximation problem using the framework of the theory of random functions. An ab initio derivation of a regression method is proposed, starting from postulates of…
An estimation method is presented for polynomial phase signals, i.e., those adopting the form of a complex exponential whose phase is polynomial in its indices. Transcending the scope of existing techniques, the proposed estimator can…
The pre-trained foundation models (PFMs) have become essential for facilitating large-scale multimodal learning. Researchers have effectively employed the ``pre-train, prompt, and predict'' paradigm through prompt learning to induce…
We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…
A general method is given for revising degrees of belief and arriving at consistent decisions about a system of logically constrained issues. In contrast to other works about belief revision, here the constraints are assumed to be fixed.…
Multinomial probit models are routinely-implemented representations for learning how the class probabilities of categorical response data change with p observed predictors. Although several frequentist methods have been developed for…
The Method of Moments [Pea94] is one of the most widely used methods in statistics for parameter estimation, by means of solving the system of equations that match the population and estimated moments. However, in practice and especially…
In many applications, the information about the number of eigenvalues inside a given region is required. In this paper, we propose a contour-integral based method for this purpose. The new method is motivated by two findings. There exist…
The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable…