Related papers: On High-Resolution Adaptive Sampling of Determinis…
A wide variety of numerical methods are evaluated and compared for solving the stochastic differential equations encountered in molecular dynamics. The methods are based on the application of deterministic impulses, drifts, and Brownian…
In this article, recent results about point processes are used in sampling theory. Precisely, we define and study a new class of sampling designs: determinantal sampling designs. The law of such designs is known, and there exists a simple…
In modern data analysis, random sampling is an efficient and widely-used strategy to overcome the computational difficulties brought by large sample size. In previous studies, researchers conducted random sampling which is according to the…
We study distributed optimization algorithms for minimizing the average of \emph{heterogeneous} functions distributed across several machines with a focus on communication efficiency. In such settings, naively using the classical stochastic…
Measurement samples are often taken in various monitoring applications. To reduce the sensing cost, it is desirable to achieve better sensing quality while using fewer samples. Compressive Sensing (CS) technique finds its role when the…
Maximum consensus estimation plays a critically important role in robust fitting problems in computer vision. Currently, the most prevalent algorithms for consensus maximization draw from the class of randomized hypothesize-and-verify…
In this chapter, we discuss recent work on learning sparse approximations to high-dimensional functions on data, where the target functions may be scalar-, vector- or even Hilbert space-valued. Our main objective is to study how the…
The adaptive perturbation chooses a non-standard decomposition. The Hamiltonian becomes a sum of solvable and perturbation parts. We calculate the spectrum using the adaptive perturbation method at the leading-order to compare to numerical…
Discovering valuable insights from data through meaningful associations is a crucial task. However, it becomes challenging when trying to identify representative patterns in quantitative databases, especially with large datasets, as…
This paper is concerned with the problem of low rank plus sparse matrix decomposition for big data. Conventional algorithms for matrix decomposition use the entire data to extract the low-rank and sparse components, and are based on…
Sampling of signals defined over the nodes of a graph is one of the crucial problems in graph signal processing. While in classical signal processing sampling is a well defined operation, when we consider a graph signal many new challenges…
Compressed Sensing refers to extracting a low-dimensional structured signal of interest from its incomplete random linear observations. A line of recent work has studied that, with the extra prior information about the signal, one can…
In this paper, we consider signal interpolation of discrete-time signals which are decimated nonuniformly. A conventional interpolation method is based on the sampling theorem, and the resulting system consists of an ideal filter with…
The structure of Magnetic Resonance Images (MRI) and especially their compressibility in an appropriate representation basis enables the application of the compressive sensing theory, which guarantees exact image recovery from incomplete…
Topological measurements are increasingly being accepted as an important tool for quantifying complex structures. In many applications, these structures can be expressed as nodal domains of real-valued functions and are obtained only…
The note studies the problem of selecting a good enough subset out of a finite number of alternatives under a fixed simulation budget. Our work aims to maximize the posterior probability of correctly selecting a good subset. We formulate…
Probabilistic Regression refers to predicting a full probability density function for the target conditional on the features. We present a nonparametric approach to this problem which combines base classifiers (typically gradient boosted…
We present an adaptive regularization algorithm that can be effectively applied to the optimization problem in deep learning framework. Our regularization algorithm aims to take into account the fitness of data to the current state of model…
We study the optimal sample complexity of variable selection in linear regression under general design covariance, and show that subset selection is optimal while under standard complexity assumptions, efficient algorithms for this problem…
In this study, energy-efficient deterministic adaptive beamforming algorithms are proposed for distributed sensor/relay networks. Specifically, DBSA, D-QESA, D-QESA-E, and a hybrid algorithm, hybrid-QESA, that combines the benefits of both…