Related papers: From Sampling to Optimization on Discrete Domains …
We study the problem of extracting a small subset of representative items from a large data stream. In many data mining and machine learning applications such as social network analysis and recommender systems, this problem can be…
It is known that greedy methods perform well for maximizing monotone submodular functions. At the same time, such methods perform poorly in the face of non-monotonicity. In this paper, we show - arguably, surprisingly - that invoking the…
For any $\varepsilon > 0$, we prove that $k$-Dimensional Matching is hard to approximate within a factor of $k/(12 + \varepsilon)$ for large $k$ unless $\textsf{NP} \subseteq \textsf{BPP}$. Listed in Karp's 21 $\textsf{NP}$-complete…
In this paper, we propose a new feature selection method for unsupervised domain adaptation based on the emerging optimal transportation theory. We build upon a recent theoretical analysis of optimal transport in domain adaptation and show…
We analyze statistical features of the ``optimization landscape'' in a random version of one of the simplest constrained optimization problems of the least-square type: finding the best approximation for the solution of an overcomplete…
An efficient algorithm to solve the $k$ shortest non-homotopic path planning ($k$-SNPP) problem in a 2D environment is proposed in this paper. Motivated by accelerating the inefficient exploration of the homotopy-augmented space of the 2D…
We analyze the accuracy of the discrete least-squares approximation of a function $u$ in multivariate polynomial spaces $\mathbb{P}_\Lambda:={\rm span} \{y\mapsto y^\nu \,: \, \nu\in \Lambda\}$ with $\Lambda\subset \mathbb{N}_0^d$ over the…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
Pattern matching can be used to calculate the support of patterns, and is a key issue in sequential pattern mining (or sequence pattern mining). Nonoverlapping pattern matching means that two occurrences cannot use the same character in the…
Performing random walks in networks is a fundamental primitive that has found numerous applications in communication networks such as token management, load balancing, network topology discovery and construction, search, and peer-to-peer…
In this paper, we propose a novel framework that converts streaming algorithms for monotone submodular maximization into streaming algorithms for non-monotone submodular maximization. This reduction readily leads to the currently tightest…
The aim of this paper is to check feasibility of using the maximal-entropy random walk in algorithms finding communities in complex networks. A number of such algorithms exploit an ordinary or a biased random walk for this purpose. Their…
For obtaining optimal first-order convergence guarantee for stochastic optimization, it is necessary to use a recurrent data sampling algorithm that samples every data point with sufficient frequency. Most commonly used data sampling…
In this paper, we address the problem of approximating a multivariate function defined on a general domain in $d$ dimensions from sample points. We consider weighted least-squares approximation in an arbitrary finite-dimensional space $P$…
Running machine learning algorithms on large and rapidly growing volumes of data is often computationally expensive, one common trick to reduce the size of a data set, and thus reduce the computational cost of machine learning algorithms,…
Diversity maximization aims to select a diverse and representative subset of items from a large dataset. It is a fundamental optimization task that finds applications in data summarization, feature selection, web search, recommender…
We consider the problem of determining the top-$k$ largest measurements from a dataset distributed among a network of $n$ agents with noisy communication links. We show that this scenario can be cast as a distributed convex optimization…
The Densest $k$-Subgraph (D$k$S) is a fundamental combinatorial problem known for its theoretical hardness and breadth of applications. Recently, Lu et al. (AAAI 2025) introduced a penalty-based non-convex relaxation that achieves promising…
A determinantal point process (DPP) is an elegant model that assigns a probability to every subset of a collection of $n$ items. While conventionally a DPP is parameterized by a symmetric kernel matrix, removing this symmetry constraint,…
We propose subsampling as a unified algorithmic technique for submodular maximization in centralized and online settings. The idea is simple: independently sample elements from the ground set, and use simple combinatorial techniques (such…