Related papers: LapSum -- One Method to Differentiate Them All: Ra…
The LASSO is an attractive regularisation method for linear regression that combines variable selection with an efficient computation procedure. This paper is concerned with enhancing the performance of LASSO for square-free hierarchical…
Finite-sum optimization problems are ubiquitous in machine learning, and are commonly solved using first-order methods which rely on gradient computations. Recently, there has been growing interest in \emph{second-order} methods, which rely…
Sorting is one of the most used and well investigated algorithmic problem [1]. Traditional postulation supposes the sorting data archived, and the elementary operation as comparisons of two numbers. In a view of appearance of new processors…
Learning to Rank (LTR) algorithms are usually evaluated using Information Retrieval metrics like Normalised Discounted Cumulative Gain (NDCG) or Mean Average Precision. As these metrics rely on sorting predicted items' scores (and thus, on…
A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…
We introduce a diversified top-k partial MaxSAT problem, a combination of partial MaxSAT problem and enumeration problem. Given a partial MaxSAT formula F and a positive integer k, the diversified top-k partial MaxSAT is to find k maximal…
0-1 knapsack is of fundamental importance in computer science, business, operations research, etc. In this paper, we present a deep learning technique-based method to solve large-scale 0-1 knapsack problems where the number of products…
Recommender systems (RS) aim to retrieve a small set of items that best match individual user preferences. Naturally, RS place primary emphasis on the quality of the Top-$K$ results rather than performance across the entire item set.…
Accurate ranking of important features is a fundamental challenge in interpretable machine learning with critical applications in scientific discovery and decision-making. Unlike feature selection and feature importance, the specific…
The efficiency of exact subset sum problem algorithms which compute individual subset sums is defined as $e=min(T/z, 1)$, where $z$ is the number of subset sums computed. $e$ is related to these algorithms' computational complexity. This…
This paper addresses the anytime sorting problem, aiming to develop algorithms providing tentative estimates of the sorted list at each execution step. Comparisons are treated as steps, and the Spearman's footrule metric evaluates…
The Map-Reduce computing framework rose to prominence with datasets of such size that dozens of machines on a single cluster were needed for individual jobs. As datasets approach the exabyte scale, a single job may need distributed…
The ability to generate multiple plans is central to using planning in real-life applications. Top-quality planners generate sets of such top-cost plans, allowing flexibility in determining equivalent ones. In terms of the order between…
Due to the highly non-convex nature of large-scale robust parameter estimation, avoiding poor local minima is challenging in real-world applications where input data is contaminated by a large or unknown fraction of outliers. In this paper,…
Personalised interactive systems such as recommender systems require selecting relevant items from massive catalogs dependent on context. Reward-driven offline optimisation of these systems can be achieved by a relaxation of the discrete…
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
In this paper we suggest analytical methods and associated algorithms for determining the sum of the subsets $X_m$ of the set $X_n$ (subset sum problem). Our algorithm has time complexity $T=O(C_{n}^{k})$ ($k=[m/2]$, which significantly…
Given a sample covariance matrix, we solve a maximum likelihood problem penalized by the number of nonzero coefficients in the inverse covariance matrix. Our objective is to find a sparse representation of the sample data and to highlight…
This paper introduces a novel and efficient partitioning technique for quicksort, specifically designed for real-world data with duplicate elements (50-year-old problem). The method is referred to as "equal quicksort" or "eqsort". Based on…
One important tool is the optimal clustering of data into useful categories. Dividing similar objects into a smaller number of clusters is of importance in many applications. These include search engines, monitoring of academic performance,…