Related papers: Pursuing the limit of chirp parameter identifiabil…
We propose, analyze, and test a proximal-gradient method for solving regularized optimization problems with general constraints. The method employs a decomposition strategy to compute trial steps and uses a merit function to determine step…
We propose a new (theoretical) computational model for the study of massive data processing with limited computational resources. Our model measures the complexity of reading the very large data sets in terms of the data size N and analyzes…
In this paper, we propose some estimation techniques to estimate the elementary chirp model parameters, which are encountered in sonar, radar, acoustics, and other areas. We derive asymptotic theoretical properties of least squares…
We revisit the problem of computing submatrices of the Cram\'er-Rao bound (CRB), which lower bounds the variance of any unbiased estimator of a vector parameter $\vth$. We explore iterative methods that avoid direct inversion of the Fisher…
Some consequences of the Restricted Isometry Property (RIP) of matrices have been applied to develop a greedy algorithm called "ROMP" (Regularized Orthogonal Matching Pursuit) to recover sparse signals and to approximate non-sparse ones.…
Maximizing the precision in estimating parameters in a quantum system subject to instrumentation constraints is cast as a convex optimization problem. We account for prior knowledge about the parameter range by developing a worst-case and…
Given an edge-weighted graph, how many minimum $k$-cuts can it have? This is a fundamental question in the intersection of algorithms, extremal combinatorics, and graph theory. It is particularly interesting in that the best known bounds…
The problem of online checkpointing is a classical problem with numerous applications which had been studied in various forms for almost 50 years. In the simplest version of this problem, a user has to maintain $k$ memorized checkpoints…
In this paper the problem of finding the sparsest (i.e., minimum cardinality) critical $k$-tuple including one arbitrarily specified measurement is considered. The solution to this problem can be used to identify weak points in the…
We consider the classical $k$-means clustering problem in the setting bi-criteria approximation, in which an algoithm is allowed to output $\beta k > k$ clusters, and must produce a clustering with cost at most $\alpha$ times the to the…
This paper investigates the fundamental limits for detecting a high-dimensional sparse matrix contaminated by white Gaussian noise from both the statistical and computational perspectives. We consider $p\times p$ matrices whose rows and…
We study the Stochastic Shortest Path (SSP) problem with a linear mixture transition kernel, where an agent repeatedly interacts with a stochastic environment and seeks to reach certain goal state while minimizing the cumulative cost.…
In this paper, we study the problem of maximizing $k$-submodular functions subject to a knapsack constraint. For monotone objective functions, we present a $\frac{1}{2}(1-e^{-2})\approx 0.432$ greedy approximation algorithm. For the…
The primary focus of this paper is on designing an inexact first-order algorithm for solving constrained nonlinear optimization problems. By controlling the inexactness of the subproblem solution, we can significantly reduce the…
In this paper, we present a new approach which qualifies or not a solution found by a heuristic as a potential optimal solution. Our approach is based on the following observation: for a minimization problem, the number of admissible…
Straightforward methods for adapting the familiar chi^2 statistic to histograms of discrete events and other Poisson distributed data generally yield biased estimates of the parameters of a model. The bias can be important even when the…
Quantitative assessment of the growth of biological organisms has produced many mathematical equations. Many efforts have been given on statistical identification of the correct growth model from experimental data. Every growth equation is…
We study approximation algorithms for two natural generalizations of the Maximum Quadratic Assignment Problem (MaxQAP). In the Maximum List-Restricted Quadratic Assignment Problem, each node in one partite set may only be matched to nodes…
Top-k selection, which identifies the largest or smallest k elements from a data set, is a fundamental operation in data-intensive domains such as databases and deep learning, so its scalability and efficiency are critical for these…
The Capacitated Vehicle Routing Problem (CVRP) is one of the most extensively studied problems in combinatorial optimization. Based on customer demand, we distinguish three variants of CVRP: unit-demand, splittable, and unsplittable. In…