Related papers: The Generalized Operator Based Prony Method

Pruning aims to accelerate and compress models by removing redundant parameters, identified by specifically designed importance scores which are usually imperfect. This removal is irreversible, often leading to subpar performance in pruned…

We derive fundamental sample complexity bounds for recovering sparse and structured signals for linear and nonlinear observation models including sparse regression, group testing, multivariate regression and problems with missing features.…

We investigate the necessary and sufficient conditions in order that a unitary operator can amplify a pre-assigned component relative to a particular basis of a generic vector at the expense of the other components. This leads to a general…

In this paper we consider several nonlinear systems of algebraic equations which can be called "Prony-type". These systems arise in various reconstruction problems in several branches of theoretical and applied mathematics, such as…

Deep neural networks exploiting millions of parameters are nowadays the norm in deep learning applications. This is a potential issue because of the great amount of computational resources needed for training, and of the possible loss of…

This paper explores sparsification methods as a form of regularization in Graph Neural Networks (GNNs) to address high memory usage and computational costs in large-scale graph applications. Using techniques from Network Science and Machine…

Testing for the significance of a subset of regression coefficients in a linear model, a staple of statistical analysis, goes back at least to the work of Fisher who introduced the analysis of variance (ANOVA). We study this problem under…

Generalised planning (GP) refers to the task of synthesising programs that solve families of related planning problems. We introduce a novel, yet simple method for GP: given a set of training problems, for each problem, compute an optimal…

In the article we propose a general scheme for solutions of some approximation problems under a rather general setting. We illustrate the application of the proposed scheme by a series of examples, in particular we show that many results in…

This paper addresses the topic of sparsifying deep neural networks (DNN's). While DNN's are powerful models that achieve state-of-the-art performance on a large number of tasks, the large number of model parameters poses serious storage and…

A major bottleneck in scientific discovery consists of narrowing an exponentially large set of objects, such as proteins or molecules, to a small set of promising candidates with desirable properties. While this process can rely on expert…

In this work, we develop a simple algorithm for semi-supervised regression. The key idea is to use the top eigenfunctions of integral operator derived from both labeled and unlabeled examples as the basis functions and learn the prediction…

Pruning is a model compression method that removes redundant parameters in deep neural networks (DNNs) while maintaining accuracy. Most available filter pruning methods require complex treatments such as iterative pruning, features…

This investigation pertains to the construction of a class of generalised deformed derivative operators which furnish the familiar finite difference and the q-derivatives as special cases. The procedure involves the introduction of a linear…

As datasets grow larger, they are often distributed across multiple machines that compute in parallel and communicate with a central machine through short messages. In this paper, we focus on sparse regression and propose a new procedure…

This paper proposes an efficient general alternating-direction implicit (GADI) framework for solving large sparse linear systems. The convergence property of the GADI framework is discussed. Most of the existing ADI methods can be viewed as…

In linear inverse problems, we have data derived from a noisy linear transformation of some unknown parameters, and we wish to estimate these unknowns from the data. Separable inverse problems are a powerful generalization in which the…

Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…

There are various inverse problems -- including reconstruction problems arising in medical imaging -- where one is often aware of the forward operator that maps variables of interest to the observations. It is therefore natural to ask…

We present "Amenable Sparse Network Investigator" (ASNI) algorithm that utilizes a novel pruning strategy based on a sigmoid function that induces sparsity level globally over the course of one single round of training. The ASNI algorithm…