Related papers: A Theoretical Framework of Approximation Error Ana…
This work proposes a machine-learning framework for constructing statistical models of errors incurred by approximate solutions to parameterized systems of nonlinear equations. These approximate solutions may arise from early termination of…
In Tri-clustering, a sub-matrix is being created, which exhibit highly similar behavior with respect to genes, conditions and time-points. In this technique, genes with same expression values are discovered across some fragment of time…
The range of applications of traditional optimization methods are limited by the features of the object variables, and of both the objective and the constraint functions. In contrast, population-based algorithms whose optimization…
Population-based evolutionary algorithms have great potential to handle multiobjective optimisation problems. However, these algorithms depends largely on problem characteristics, and there is a need to improve their performance for a wider…
We give a detailed analysis of the cost used by the (1+1)-evolutionary algorithm. The problem has been approached in the evolutionary algorithm literature under various views, formulation and degree of rigor. Our asymptotic approximations…
In this paper we propose a novel method for learning how algorithms perform. Classically, algorithms are compared on a finite number of existing (or newly simulated) benchmark datasets based on some fixed metrics. The algorithm(s) with the…
Deep learning algorithms have been applied very successfully in recent years to a range of problems out of reach for classical solution paradigms. Nevertheless, there is no completely rigorous mathematical error and convergence analysis…
Evolutionary algorithms, such as Differential Evolution, excel in solving real-parameter optimization challenges. However, the effectiveness of a single algorithm varies across different problem instances, necessitating considerable efforts…
Mappings to structured output spaces (strings, trees, partitions, etc.) are typically learned using extensions of classification algorithms to simple graphical structures (eg., linear chains) in which search and parameter estimation can be…
Robust iterative methods for solving large sparse systems of linear algebraic equations often suffer from the problem of optimizing the corresponding tuning parameters. To improve the performance of the problem of interest, specific…
This paper presents an application of evolutionary search procedures to artificial neural networks. Here, we can distinguish among three kinds of evolution in artificial neural networks, i.e. the evolution of connection weights, of…
This article is a review on basic concepts and tools devoted to a posteriori error estimation for problems solved with the Finite Element Method. For the sake of simplicity and clarity, we mostly focus on linear elliptic diffusion problems,…
Recent works have investigated the sample complexity necessary for fair machine learning. The most advanced of such sample complexity bounds are developed by analyzing multicalibration uniform convergence for a given predictor class. We…
The paper proposes a novel nature-inspired technique of optimization. It mimics the perching nature of eagles and uses mathematical formulations to introduce a new addition to metaheuristic algorithms. The nature of the proposed algorithm…
This paper is concerned with the two--phase obstacle problem, a type of a variational free boundary problem. We recall the basic estimates of Repin and Valdman (2015) and verify them numerically on two examples in two space dimensions. A…
This paper deals with some nonlinear problems which exponential and biexponential decays are involved in. A proof of the quasiconvexity of the error function in some of these problems of optimization is presented. This proof is restricted…
We derive computable upper bounds for the difference between an exact solution of the evolutionary convection-diffusion problem and an approximation of this solution. The estimates are obtained by certain transformations of the integral…
Population-based evolutionary algorithms (EAs) have been widely applied to solve various optimization problems. The question of how the performance of a population-based EA depends on the population size arises naturally. The performance of…
In this work, we propose an extensive numerical study on approximating the absolute value function. The methods presented in this paper compute approximants in the form of rational functions and have been proposed relatively recently, e.g.,…
Theoretical studies on evolutionary algorithms have developed vigorously in recent years. Many such algorithms have theoretical guarantees in both running time and approximation ratio. Some approximation mechanism seems to be inherently…