Related papers: Approximation of Functions: Optimal Sampling and C…
Low-rank approximation is a fundamental technique in modern data analysis, widely utilized across various fields such as signal processing, machine learning, and natural language processing. Despite its ubiquity, the mechanics of low-rank…
The reconstruction of unknown functions from a finite number of samples is a fundamental challenge in pure and applied mathematics. This survey provides a comprehensive overview of recent developments in sampling recovery, focusing on the…
The exploration of complex physical or technological processes usually requires exploiting available information from different sources: (i) physical laws often represented as a family of parameter dependent partial differential equations…
Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…
Rejection Sampling is a fundamental Monte-Carlo method. It is used to sample from distributions admitting a probability density function which can be evaluated exactly at any given point, albeit at a high computational cost. However,…
We introduce a sampling theoretic framework for the recovery of smooth surfaces and functions living on smooth surfaces from few samples. The proposed approach can be thought of as a nonlinear generalization of union of subspace models…
We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
This is a continuation of our earlier paper \cite{PT3}. We consider here operator-valued functions (or infinite matrix functions) on the unit circle $\T$ and study the problem of approximation by bounded analytic operator functions. We…
The paper investigates possibility of recovery of sequences from their decimated subsequences. It is shown that this recoverability is associated with certain spectrum degeneracy of a new kind, and that a sequences of a general kind can be…
The motivation for this paper stems from the desire to develop an adaptive sampling method for solving constrained optimization problems in which the objective function is stochastic and the constraints are deterministic. The method…
We study the problem of maximizing a function that is approximately submodular under a cardinality constraint. Approximate submodularity implicitly appears in a wide range of applications as in many cases errors in evaluation of a…
We introduce several generalizations of classical computer science problems obtained by replacing simpler objective functions with general submodular functions. The new problems include submodular load balancing, which generalizes load…
The question of what can be computed, and how efficiently, are at the core of computer science. Not surprisingly, in distributed systems and networking research, an equally fundamental question is what can be computed in a…
The aim of this chapter is to give an overview of the recent advances related to sampling and recovery of signals defined over graphs. First, we illustrate the conditions for perfect recovery of bandlimited graph signals from samples…
This work proposes an implementable proximal-type method for a broad class of optimization problems involving nonsmooth and nonconvex objective and constraint functions. In contrast to existing methods that rely on an ad hoc model…
Natural Language Processing has moved rather quickly from modelling specific tasks to taking more general pre-trained models and fine-tuning them for specific tasks, to a point where we now have what appear to be inherently generalist…
The performance of the Monte Carlo sampling methods relies on the crucial choice of a proposal density. The notion of optimality is fundamental to design suitable adaptive procedures of the proposal density within Monte Carlo schemes. This…
For many tasks of data analysis, we may only have the information of the explanatory variable and the evaluation of the response values are quite expensive. While it is impractical or too costly to obtain the responses of all units, a…
We study the problem of experiment planning with function approximation in contextual bandit problems. In settings where there is a significant overhead to deploying adaptive algorithms -- for example, when the execution of the data…