arXiv subjects

Elaheh Lotfian

Publications and source records attributed to Elaheh Lotfian.

2 recordsLinked to original sources

arXiv2026

Weak-Curvature AMISE and Plug-in Bandwidth Selection for Kernel Density Estimation

Kernel density estimation risk expansions are commonly expressed through the integrated squared curvature term that enters second-order AMISE and plug-in bandwidth rules. This paper develops a weak-curvature formulation of this classical calculation for densities whose second derivative exists weakly rather than as a continuous classical function. We prove that if a density has square-integrable weak curvature, then the standard second-order AMISE expansion, oracle bandwidth order, and kernel-dependent optimality calculation remain valid with the curvature functional understood in the weak sense. The class $C^{1,1}(\mathbb{R})\setminus C^2(\mathbb{R})$ serves as a concrete and practically relevant subclass: the first derivative is Lipschitz, while curvature may be kinked, discontinuous, or undefined at isolated points. Building on this formulation, we introduce a generalized-curvature plug-in (GCPI) bandwidth selector. The selector estimates the weak-curvature functional by a pilot density-derivative estimator with a leave-one-out U-statistic correction and substitutes this estimate into the AMISE bandwidth formula. We prove first-order oracle equivalence under ratio-consistent weak-curvature estimation and establish consistency of the proposed U-statistic curvature estimator under explicit pilot-bandwidth conditions. We also give a scalar-bandwidth multivariate extension based on weak Hessians and illustrate the theory through nonsmooth density examples, simulations, and a real-data application.

math.ST↗

arXiv2026

HiMARS: Hybrid multi-objective algorithms for recommender systems

In recommender systems, it is well-established that both accuracy and diversity are crucial for generating high-quality recommendation lists. However, achieving a balance between these two typically conflicting objectives remains a significant challenge. In this work, we address this challenge by proposing four novel hybrid multi-objective algorithms inspired by the Non-dominated Neighbor Immune Algorithm (NNIA), Archived Multi-Objective Simulated Annealing (AMOSA), and Non-dominated Sorting Genetic Algorithm-II (NSGA-II), aimed at simultaneously enhancing both accuracy and diversity through multi-objective optimization. Our approach follows a three-stage process: First, we generate an initial top-$k$ list using item-based collaborative filtering for a given user. Second, we solve a bi-objective optimization problem to identify Pareto-optimal top-$s$ recommendation lists, where $s \ll k$, using the proposed hybrid algorithms. Finally, we select an optimal personalized top-$s$ list from the Pareto-optimal solutions. We evaluate the performance of the proposed algorithms on real-world datasets and compare them with existing methods using conventional metrics in recommender systems such as accuracy, diversity, and novelty. Additionally, we assess the quality of the Pareto frontiers using metrics including the spacing metric, mean ideal distance, diversification metric, and spread of non-dominated solutions. Results demonstrate that some of our proposed algorithms significantly improve both accuracy and diversity, offering a novel contribution to multi-objective optimization in recommender systems.

cs.IR↗