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We study the problem of estimating the size of the maximum matching in the sublinear-time setting. This problem has been extensively studied, with several known upper and lower bounds. A notable result by Behnezhad (FOCS 2021) established a…
We design an algorithm which finds an $\epsilon$-approximate stationary point (with $\|\nabla F(x)\|\le \epsilon$) using $O(\epsilon^{-3})$ stochastic gradient and Hessian-vector products, matching guarantees that were previously available…
Given a set $I \subseteq \mathbb{N}$, consider the sequences $\{d_n(I)\},\{p_n(I)\}$ where for any $n$, $d_n(I)$ and $p_n(I)$ respectively count the number of permutations in the symmetric group $\mathfrak{S}_n$ whose descent set…
New estimates for the population risk are established for two-layer neural networks. These estimates are nearly optimal in the sense that the error rates scale in the same way as the Monte Carlo error rates. They are equally effective in…
The Student-Project Allocation problem with lecturer preferences over Students (SPA-S) comprises three sets of agents, namely students, projects and lecturers, where students have preferences over projects and lecturers have preferences…
A matching in a graph is induced if no two of its edges are joined by an edge, and finding a large induced matching is a very hard problem. Lin et al. (Approximating weighted induced matchings, Discrete Applied Mathematics 243 (2018)…
Despite the intuition that the same population size is not needed throughout the run of an Evolutionary Algorithm (EA), most EAs use a fixed population size. This paper presents an empirical study on the possible benefits of a Simple…
A critical problem in the emerging high-throughput genotyping protocols is to minimize the number of polymerase chain reaction (PCR) primers required to amplify the single nucleotide polymorphism loci of interest. In this paper we study PCR…
Understanding how the time-complexity of evolutionary algorithms (EAs) depend on their parameter settings and characteristics of fitness landscapes is a fundamental problem in evolutionary computation. Most rigorous results were derived…
While evolutionary algorithms are known to be very successful for a broad range of applications, the algorithm designer is often left with many algorithmic choices, for example, the size of the population, the mutation rates, and the…
We study a multi-objective pure exploration problem in a multi-armed bandit model. Each arm is associated to an unknown multi-variate distribution and the goal is to identify the distributions whose mean is not uniformly worse than that of…
The classical non-greedy algorithm (NGA) and the recently proposed proximal alternating minimization method with extrapolation (PAMe) for $L_1$-norm PCA are revisited and their finite-step convergence are studied. It is first shown that NGA…
We consider the problem of computing a Gaussian approximation to the posterior distribution of a parameter given a large number N of observations and a Gaussian prior, when the dimension of the parameter d is also large. To address this…
It has been shown that dimension reduction methods such as PCA may be inherently prone to unfairness and treat data from different sensitive groups such as race, color, sex, etc., unfairly. In pursuit of fairness-enhancing dimensionality…
Given $n$ elements, an integer $k$ and a parameter $\varepsilon$, we study to select an element with rank in $(k-n\varepsilon,k+n\varepsilon]$ using unreliable comparisons where the outcome of each comparison is incorrect independently with…
Recently surrogate functions based on the tail inequalities were developed to evaluate the chance constraints in the context of evolutionary computation and several Pareto optimization algorithms using these surrogates were successfully…
Stochastic optimization lies at the core of most statistical learning models. The recent great development of stochastic algorithmic tools focused significantly onto proximal gradient iterations, in order to find an efficient approach for…
Deep generative models have recently shown success in solving complex engineering design problems where models predict solutions that address the design requirements specified as input. However, there remains a challenge in aligning such…
The compact Genetic Algorithm (cGA), parameterized by its hypothetical population size $K$, offers a low-memory alternative to evolving a large offspring population of solutions. It evolves a probability distribution, biasing it towards…
A genetic algorithm (GA) is a search method that optimises a population of solutions by simulating natural evolution. Good solutions reproduce together to create better candidates. The standard GA assumes that any two solutions can mate.…