Related papers: A PTAS for $\ell_0$-Low Rank Approximation: Solvin…
Semidefinite programming (SDP) is a central topic in mathematical optimization with extensive studies on its efficient solvers. In this paper, we present a proof-of-principle sublinear-time algorithm for solving SDPs with low-rank…
Makespan minimization on unrelated machines is a classic problem in approximation algorithms. No polynomial time $(2-\delta)$-approximation algorithm is known for the problem for constant $\delta> 0$. This is true even for certain special…
The subset sum problem (SSP) can be briefly stated as: given a target integer $E$ and a set $A$ containing $n$ positive integer $a_j$, find a subset of $A$ summing to $E$. The \textit{density} $d$ of an SSP instance is defined by the ratio…
To accelerate DNNs inference, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pre-trained model by low-rank…
Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…
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 $\ell_2^2$ min-sum $k$-clustering problem is to partition an input set into clusters $C_1,\ldots,C_k$ to minimize $\sum_{i=1}^k\sum_{p,q\in C_i}\|p-q\|_2^2$. Although $\ell_2^2$ min-sum $k$-clustering is NP-hard, it is not known whether…
We continue the investigation of polynomial-time sparsification for NP-complete Boolean Constraint Satisfaction Problems (CSPs). The goal in sparsification is to reduce the number of constraints in a problem instance without changing the…
This thesis investigates the extent to which the optimal value of a constraint satisfaction problem (CSP) can be approximated by some sentence of fixed point logic with counting (FPC). It is known that, assuming $\mathsf{P} \neq…
We prove that the Bounded Occurrence Ordering k-CSP Problem is not approximation resistant. We give a very simple local search algorithm that always performs better than the random assignment algorithm. Specifically, the expected value of…
The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational…
We study the Sparse Plus Low-Rank decomposition problem (SLR), which is the problem of decomposing a corrupted data matrix into a sparse matrix of perturbations plus a low-rank matrix containing the ground truth. SLR is a fundamental…
The problem of low-rank approximation with convex constraints, which appears in data analysis, system identification, model order reduction, low-order controller design and low-complexity modelling is considered. Given a matrix, the…
This paper introduces a novel algorithm to approximate the matrix with minimum nuclear norm among all matrices obeying a set of convex constraints. This problem may be understood as the convex relaxation of a rank minimization problem, and…
Low-rank matrix approximation is one of the central concepts in machine learning, with applications in dimension reduction, de-noising, multivariate statistical methodology, and many more. A recent extension to LRMA is called low-rank…
Many problems in computer vision and recommender systems involve low-rank matrices. In this work, we study the problem of finding the maximum entry of a stochastic low-rank matrix from sequential observations. At each step, a learning agent…
Given a predicate $P: \{-1, 1\}^k \to \{-1, 1\}$, let $CSP(P)$ be the set of constraint satisfaction problems whose constraints are of the form $P$. We say that $P$ is approximable if given a nearly satisfiable instance of $CSP(P)$, there…
Matrix low rank approximation including the classical PCA and the robust PCA (RPCA) method have been applied to solve the background modeling problem in video analysis. Recently, it has been demonstrated that a special weighted low rank…
We work in the space of $m$-by-$n$ real matrices with the Frobenius inner product. Consider the following Problem: Given an m-by-n real matrix A and a positive integer k, find the m-by-n matrix with rank k that is closest to A. I discuss a…
We study approximation algorithms for satisfiable and nearly satisfiable instances of ordering constraint satisfaction problems (ordering CSPs). Ordering CSPs arise naturally in ranking and scheduling, yet their approximability remains…