arXiv subjects

Panos M. Pardalos

Publications and source records attributed to Panos M. Pardalos.

At least 19 recordsLinked to original sources

arXiv2026

On the Koopman-Based Generalization Bounds for Multi-Task Deep Learning

The paper establishes generalization bounds for multitask deep neural networks using operator-theoretic techniques. The authors propose a tighter bound than those derived from conventional norm based methods by leveraging small condition numbers in the weight matrices and introducing a tailored Sobolev space as an expanded hypothesis space. This enhanced bound remains valid even in single output settings, outperforming existing Koopman based bounds. The resulting framework maintains key advantages such as flexibility and independence from network width, offering a more precise theoretical understanding of multitask deep learning in the context of kernel methods.

cs.LG↗

arXiv2026

Operator-Based Generalization Bound for Deep Learning: Insights on Multi-Task Learning

This paper presents novel generalization bounds for vector-valued neural networks and deep kernel methods, focusing on multi-task learning through an operator-theoretic framework. Our key development lies in strategically combining a Koopman based approach with existing techniques, achieving tighter generalization guarantees compared to traditional norm-based bounds. To mitigate computational challenges associated with Koopman-based methods, we introduce sketching techniques applicable to vector valued neural networks. These techniques yield excess risk bounds under generic Lipschitz losses, providing performance guarantees for applications including robust and multiple quantile regression. Furthermore, we propose a novel deep learning framework, deep vector-valued reproducing kernel Hilbert spaces (vvRKHS), leveraging Perron Frobenius (PF) operators to enhance deep kernel methods. We derive a new Rademacher generalization bound for this framework, explicitly addressing underfitting and overfitting through kernel refinement strategies. This work offers novel insights into the generalization properties of multitask learning with deep learning architectures, an area that has been relatively unexplored until recent developments.

cs.LG↗

arXiv2025

Multi-Task Learning Based on Support Vector Machines and Twin Support Vector Machines: A Comprehensive Survey

Multi-task learning (MTL) enables simultaneous training across related tasks, leveraging shared information to improve generalization, efficiency, and robustness, especially in data-scarce or high-dimensional scenarios. While deep learning dominates recent MTL research, Support Vector Machines (SVMs) and Twin SVMs (TWSVMs) remain relevant due to their interpretability, theoretical rigor, and effectiveness with small datasets. This chapter surveys MTL approaches based on SVM and TWSVM, highlighting shared representations, task regularization, and structural coupling strategies. Special attention is given to emerging TWSVM extensions for multi-task settings, which show promise but remain underexplored. We compare these models in terms of theoretical properties, optimization strategies, and empirical performance, and discuss applications in fields such as computer vision, natural language processing, and bioinformatics. Finally, we identify research gaps and outline future directions for building scalable, interpretable, and reliable margin-based MTL frameworks. This work provides a comprehensive resource for researchers and practitioners interested in SVM- and TWSVM-based multi-task learning.

cs.LG↗

arXiv2025

Maximum Shortest Path Interdiction Problem by Upgrading Nodes on Trees under Unit Cost

Network interdiction problems by deleting critical nodes have wide applications. However, node deletion is not always feasible in certain practical scenarios. We consider the maximum shortest path interdiction problem by upgrading nodes on trees under unit cost (MSPIT-UN$_u$). It aims to upgrade a subset of nodes to maximize the length of the shortest root-leaf distance such that the total upgrade cost under unit cost is upper bounded by a given value. We develop a dynamic programming algorithm with a time complexity of $O(n^3)$ to solve this problem. Furthermore, we consider the related minimum cost problem of (MSPIT-UN$_u$) and propose an $O(n^3\log n)$ binary search algorithm, where a dynamic programming algorithm is exceeded in each iteration to solve its corresponding problem (MSPIT-UN$_u$). Finally, we design numerical experiments to show the effectiveness of the algorithms.

math.OC↗

arXiv2024

Double interdiction problem on trees on the sum of root-leaf distances by upgrading edges

The double interdiction problem on trees (DIT) for the sum of root-leaf distances (SRD) has significant implications in diverse areas such as transportation networks, military strategies, and counter-terrorism efforts. It aims to maximize the SRD by upgrading edge weights subject to two constraints. One gives an upper bound for the cost of upgrades under certain norm and the other specifies a lower bound for the shortest root-leaf distance (StRD). We utilize both weighted $l_\infty$ norm and Hamming distance to measure the upgrade cost and denote the corresponding (DIT) problem by (DIT$_{H\infty}$) and its minimum cost problem by (MCDIT$_{H\infty}$). We establish the $\mathcal{NP}$-hardness of problem (DIT$_{H\infty}$) by building a reduction from the 0-1 knapsack problem. We solve the problem (DIT$_{H\infty}$) by two scenarios based on the number $N$ of upgrade edges. When $N=1$, a greedy algorithm with $O(n)$ complexity is proposed. For the general case, an exact dynamic programming algorithm within a pseudo-polynomial time is proposed, which is established on a structure of left subtrees by maximizing a convex combination of the StRD and SRD. Furthermore, we confirm the $\mathcal{NP}$-hardness of problem (MCDIT$_{H\infty}$) by reducing from the 0-1 knapsack problem. To tackle problem (MCDIT$_{H\infty}$), a binary search algorithm with pseudo-polynomial time complexity is outlined, which iteratively solves problem (DIT$_{H\infty}$). We culminate our study with numerical experiments, showcasing effectiveness of the algorithm.

math.OC↗

arXiv2024

An Overview of Absolute Value Equations: From Theory to Solution Methods and Challenges

This paper provides a thorough exploration of the absolute value equations $Ax-|x|=b$, a seemingly straightforward concept that has gained heightened attention in recent years. It is an NP-hard and nondifferentiable problem and equivalent with the standard linear complementarity problem. Offering a comprehensive review of existing literature, the study delves into theorems concerning the existence and nonexistence of solutions to the absolute value equations, along with numerical methods for effectively addressing this complex equation. Going beyond conventional approaches, the paper investigates strategies for obtaining solutions with minimal norms, techniques for correcting infeasible systems, and other pertinent topics. By pinpointing challenging issues and emphasizing open problems, this paper serves as a valuable guide for shaping the future research trajectory in this dynamic and multifaceted field.

math.OC↗

arXiv2023

A branch-and-price approach for the nurse rostering problem with multiple units

In this paper, we study the nurse rostering problem that considers multiple units and many soft time-related constraints. An efficient branch and price solution approach that relies on a fast algorithm to solve the pricing subproblem of the column generation process is presented. For the nurse rostering problem, its pricing subproblem can be formulated as a shortest path problem with resource constraints, which has been the backbone of several solutions for several classical problems like vehicle routing problems. However, approaches that perform well on these problems cannot be used since most constraints in the nurse rostering problem are soft. Based on ideas borrowed from global constraints in constraint programming to model rostering problems, an efficient dynamic programming algorithm with novel label definitions and dominating rules specific to soft time-related constraints is proposed. In addition, several acceleration strategies are employed to improve the branch and price algorithm. Computational results on instances of different sizes indicate that the proposed algorithm is a promising solution for the nurse rostering problem with multiple units.

math.OC↗

arXiv2023

Restricted inverse optimal value problem on linear programming under weighted $l_1$ norm

We study the restricted inverse optimal value problem on linear programming under weighted $l_1$ norm (RIOVLP $_1$). Given a linear programming problem $LP_c: \min \{cx|Ax=b,x\geq 0\}$ with a feasible solution $x^0$ and a value $K$, we aim to adjust the vector $c$ to $\bar{c}$ such that $x^0$ becomes an optimal solution of the problem LP$_{\bar c}$ whose objective value $\bar{c}x^0$ equals $K$. The objective is to minimize the distance $\|\bar c - c\|_1=\sum_{j=1}^nd_j|\bar c_j-c_j|$ under weighted $l_1$ norm.Firstly, we formulate the problem (RIOVLP$_1$) as a linear programming problem by dual theories. Secondly, we construct a sub-problem $(D^z)$, which has the same form as $LP_c$, of the dual (RIOVLP$_1$) problem corresponding to a given value $z$. Thirdly, when the coefficient matrix $A$ is unimodular, we design a binary search algorithm to calculate the critical value $z^*$ corresponding to an optimal solution of the problem (RIOVLP$_1$). Finally, we solve the (RIOV) problems on Hitchcock and shortest path problem, respectively, in $O(T_{MCF}\log\max\{d_{max},x^0_{max},n\})$ time, where we solve a sub-problem $(D^z)$ by minimum cost flow in $T_{MCF}$ time in each iteration. The values $d_{max},x^0_{max}$ are the maximum values of $d$ and $x^0$, respectively.

math.OC↗

arXiv2023

The sum of root-leaf distance interdiction problem with cardinality constraint by upgrading edges on trees

A network for the transportation of supplies can be described as a rooted tree with a weight of a degree of congestion for each edge. We take the sum of root-leaf distance (SRD) on a rooted tree as the whole degree of congestion of the tree. Hence, we consider the SRD interdiction problem on trees with cardinality constraint by upgrading edges (denoted by (SDIPTC) in brief). It aims to maximize the SRD by upgrading the weights of $N$ critical edges such that the total upgrade cost under some measurement is upper-bounded by a given value. The relevant minimum cost problem (MCSDIPTC) aims to minimize the total upgrade cost on the premise that the SRD is lower-bounded by a given value. We develop two different norms including weighted $l_\infty$ norm and weighted bottleneck Hamming distance to measure the upgrade cost. We propose two binary search algorithms within O($n\log n$) time for the problems (SDIPTC) under the two norms, respectively. For problems (MCSDIPTC),we propose two binary search algorithms within O($N n^2$) and O($n \log n$) under weighted $l_\infty$ norm and weighted bottleneck Hamming distance, respectively. These problems are solved through their subproblems (SDIPT) and (MCSDIPT), in which we ignore the cardinality constraint on the number of upgraded edges. Finally, we design numerical experiments to show the effectiveness of these algorithms.

math.OC↗

arXiv2023

A Brief Review of Explainable Artificial Intelligence in Healthcare

XAI refers to the techniques and methods for building AI applications which assist end users to interpret output and predictions of AI models. Black box AI applications in high-stakes decision-making situations, such as medical domain have increased the demand for transparency and explainability since wrong predictions may have severe consequences. Model explainability and interpretability are vital successful deployment of AI models in healthcare practices. AI applications' underlying reasoning needs to be transparent to clinicians in order to gain their trust. This paper presents a systematic review of XAI aspects and challenges in the healthcare domain. The primary goals of this study are to review various XAI methods, their challenges, and related machine learning models in healthcare. The methods are discussed under six categories: Features-oriented methods, global methods, concept models, surrogate models, local pixel-based methods, and human-centric methods. Most importantly, the paper explores XAI role in healthcare problems to clarify its necessity in safety-critical applications. The paper intends to establish a comprehensive understanding of XAI-related applications in the healthcare field by reviewing the related experimental results. To facilitate future research for filling research gaps, the importance of XAI models from different viewpoints and their limitations are investigated.

cs.AI↗

arXiv2023

A New Approximation Algorithm for Minimum-Weight $(1,m)$--Connected Dominating Set

Consider a graph with nonnegative node weight. A vertex subset is called a CDS (connected dominating set) if every other node has at least one neighbor in the subset and the subset induces a connected subgraph. Furthermore, if every other node has at least $m$ neighbors in the subset, then the node subset is called a $(1,m)$CDS. The minimum-weight $(1,m)$CDS problem aims at finding a $(1,m)$CDS with minimum total node weight. In this paper, we present a new polynomial-time approximation algorithm for this problem with approximation ratio $2H(δ_{\max}+m-1)$, where $δ_{\max}$ is the maximum degree of the given graph and $H(\cdot)$ is the Harmonic function, i.e., $H(k)=\sum_{i=1}^k \frac{1}{i}$.

cs.DS↗

arXiv2022

Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches

This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting a thorough description and analysis of the known methods capable of finding one or many solutions to SNEs, and to assist interested readers seeking to identify solution techniques which are well suited for solving the various classes of SNEs which one may encounter in real world applications. To accomplish these objectives, we present a multi-part survey. In part one, we focus on root-finding approaches which can be used to search for solutions to a SNE without transforming it into an optimization problem. In part two, we will introduce the various transformations which have been utilized to transform a SNE into an optimization problem, and we discuss optimization algorithms which can then be used to search for solutions. In part three, we will present a robust quantitative comparative analysis of methods capable of searching for solutions to SNEs.

cs.MS↗

arXiv2022

Survey of Methods for Solving Systems of Nonlinear Equations, Part II: Optimization Based Approaches

This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting a thorough description and analysis of the known methods capable of finding one or many solutions to SNEs, and to assist interested readers seeking to identify solution techniques which are well suited for solving the various classes of SNEs which one may encounter in real world applications. To accomplish these objectives, we present a multi-part survey. In part one, we focused on root-finding approaches which can be used to search for solutions to a SNE without transforming it into an optimization problem. In part two, we introduce the various transformations which have been utilized to transform a SNE into an optimization problem, and we discuss optimization algorithms which can then be used to search for solutions. We emphasize the important characteristics of each method, and we discuss promising directions for future research. In part three, we will present a robust quantitative comparative analysis of methods capable of searching for solutions to SNEs.

cs.MS↗

arXiv2021

Homography augumented momentum constrastive learning for SAR image retrieval

Deep learning-based image retrieval has been emphasized in computer vision. Representation embedding extracted by deep neural networks (DNNs) not only aims at containing semantic information of the image, but also can manage large-scale image retrieval tasks. In this work, we propose a deep learning-based image retrieval approach using homography transformation augmented contrastive learning to perform large-scale synthetic aperture radar (SAR) image search tasks. Moreover, we propose a training method for the DNNs induced by contrastive learning that does not require any labeling procedure. This may enable tractability of large-scale datasets with relative ease. Finally, we verify the performance of the proposed method by conducting experiments on the polarimetric SAR image datasets.

cs.CV↗

arXiv2021

NC-MOPSO: Network centrality guided multi-objective particle swarm optimization for transport optimization on networks

Transport processes are universal in real-world complex networks, such as communication and transportation networks. As the increase of the traffic in these complex networks, problems like traffic congestion and transport delay are becoming more and more serious, which call for a systematic optimization of these networks. In this paper, we formulate a multi-objective optimization problem (MOP) to deal with the enhancement of network capacity and efficiency simultaneously, by appropriately adjusting the weights of edges in networks. To solve this problem, we provide a multi-objective evolutionary algorithm (MOEA) based on particle swarm optimization (PSO), namely network centrality guided multi-objective PSO (NC-MOPSO). Specifically, in the framework of PSO, we propose a hybrid population initialization mechanism and a local search strategy by employing the network centrality theory to enhance the quality of initial solutions and strengthen the exploration of the search space, respectively. Simulation experiments performed on network models and real networks show that our algorithm has better performance than four state-of-the-art alternatives on several most-used metrics.

cs.NI↗

arXiv2021

Deep Data Density Estimation through Donsker-Varadhan Representation

Estimating the data density is one of the challenging problems in deep learning. In this paper, we present a simple yet effective method for estimating the data density using a deep neural network and the Donsker-Varadhan variational lower bound on the KL divergence. We show that the optimal critic function associated with the Donsker-Varadhan representation on the KL divergence between the data and the uniform distribution can estimate the data density. We also present the deep neural network-based modeling and its stochastic learning. The experimental results and possible applications of the proposed method demonstrate that it is competitive with the previous methods and has a lot of possibilities in applied to various applications.

cs.LG↗

arXiv2020

Machine Learning Methods for Data Association in Multi-Object Tracking

Data association is a key step within the multi-object tracking pipeline that is notoriously challenging due to its combinatorial nature. A popular and general way to formulate data association is as the NP-hard multidimensional assignment problem (MDAP). Over the last few years, data-driven approaches to assignment have become increasingly prevalent as these techniques have started to mature. We focus this survey solely on learning algorithms for the assignment step of multi-object tracking, and we attempt to unify various methods by highlighting their connections to linear assignment as well as to the MDAP. First, we review probabilistic and end-to-end optimization approaches to data association, followed by methods that learn association affinities from data. We then compare the performance of the methods presented in this survey, and conclude by discussing future research directions.

cs.CV↗

arXiv2020

Interpreting Rate-Distortion of Variational Autoencoder and Using Model Uncertainty for Anomaly Detection

Building a scalable machine learning system for unsupervised anomaly detection via representation learning is highly desirable. One of the prevalent methods is using a reconstruction error from variational autoencoder (VAE) via maximizing the evidence lower bound. We revisit VAE from the perspective of information theory to provide some theoretical foundations on using the reconstruction error, and finally arrive at a simpler and more effective model for anomaly detection. In addition, to enhance the effectiveness of detecting anomalies, we incorporate a practical model uncertainty measure into the metric. We show empirically the competitive performance of our approach on benchmark datasets.

cs.LG↗