Related papers: Optimally selecting the top $k$ values from $X+Y$ …
From a machine learning point of view, identifying a subset of relevant features from a real data set can be useful to improve the results achieved by classification methods and to reduce their time and space complexity. To achieve this…
We introduce and analyse a new, extremely simple, randomised sorting algorithm: - choose a pair of indices $\{i, j\}$ according to some distribution $q$; - sort the elements in positions $i$ and $j$ of the array in ascending order. Choosing…
We prove in this paper that the expected value of the objective function of the $k$-means++ algorithm for samples converges to population expected value. As $k$-means++, for samples, provides with constant factor approximation for $k$-means…
We design efficient approximation algorithms for maximizing the expectation of the supremum of families of Gaussian random variables. In particular, let $\mathrm{OPT}:=\max_{\sigma_1,\cdots,\sigma_n}\mathbb{E}\left[\sum_{j=1}^{m}\max_{i\in…
We propose a simple iterative (SI) algorithm for the maxcut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the cut…
Identifying a set of homogeneous clusters in a heterogeneous dataset is one of the most important classes of problems in statistical modeling. In the realm of unsupervised partitional clustering, k-means is a very important algorithm for…
The k-means algorithm is a well-known method for partitioning n points that lie in the d-dimensional space into k clusters. Its main features are simplicity and speed in practice. Theoretically, however, the best known upper bound on its…
Bilevel optimization, a hierarchical mathematical framework where one optimization problem is nested within another, has emerged as a powerful tool for modeling complex decision-making processes in various fields such as economics,…
We propose a hierarchical architecture for efficiently computing high-quality solutions to structured mixed-integer programs (MIPs). To reduce computational effort, our approach decouples the original problem into a higher level problem and…
Let D be a database of N objects where each object has m fields. The objects are given in m sorted lists (where the ith list is sorted according to the ith field). Our goal is to find the top k objects according to a monotone aggregation…
Mixed-integer optimisation problems can be computationally challenging. Here, we introduce and analyse two efficient algorithms with a specific sequential design that are aimed at dealing with sampled problems within this class. At each…
State-of-the-art clustering algorithms use heuristics to partition the feature space and provide little insight into the rationale for cluster membership, limiting their interpretability. In healthcare applications, the latter poses a…
Finding the k-medianin a network involves identifying a subset of k vertices that minimize the total distance to all other vertices in a graph. This problem has been extensively studied in computer science, graph theory, operations…
The sliding window model of computation captures scenarios in which data is arriving continuously, but only the latest $w$ elements should be used for analysis. The goal is to design algorithms that update the solution efficiently with each…
The maximum-entropy sampling problem is a fundamental and challenging combinatorial-optimization problem, with application in spatial statistics. It asks to find a maximum-determinant order-$s$ principal submatrix of an order-$n$ covariance…
Sorting is an essential operation which is widely used and is fundamental to some very basic day to day utilities like searches, databases, social networks and much more. Optimizing this basic operation in terms of complexity as well as…
This paper introduces a general technique for estimating the absolute value of pure Gaussian sums of order k over a prime p for a class of composite order k. The new estimate improves the classical estimate by a factor of about 2 or better…
Q-learning is a stochastic approximation version of the classic value iteration. The literature has established that Q-learning suffers from both maximization bias and slower convergence. Recently, multi-step algorithms have shown practical…
The current best approximation algorithms for $k$-median rely on first obtaining a structured fractional solution known as a bi-point solution, and then rounding it to an integer solution. We improve this second step by unifying and…
A widely used method to create a continuous representation of a discrete data-set is regression analysis. When the regression model is not based on a mathematical description of the physics underlying the data, heuristic techniques play a…