Search results for " COMPUTATION"

Interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy

2012

Abstract We present an approach to interactive Multiple Criteria Decision Making based on preference driven Evolutionary Multiobjective Optimization with controllable accuracy. The approach relies on formulae for lower and upper bounds on coordinates of the outcome of an arbitrary efficient variant corresponding to preference information expressed by the Decision Maker. In contrast to earlier works on that subject, here lower and upper bounds can be calculated and their accuracy controlled entirely within evolutionary computation framework. This is made possible by exploration of not only the region of feasible variants – a standard within evolutionary optimization, but also the region of i…

Ensemble strategies in Compact Differential Evolution

2011

Differential Evolution is a population based stochastic algorithm with less number of parameters to tune. However, the performance of DE is sensitive to the mutation and crossover strategies and their associated parameters. To obtain optimal performance, DE requires time consuming trial and error parameter tuning. To overcome the computationally expensive parameter tuning different adaptive/self-adaptive techniques have been proposed. Recently the idea of ensemble strategies in DE has been proposed and favorably compared with some of the state-of-the-art self-adaptive techniques. Compact Differential Evolution (cDE) is modified version of DE algorithm which can be effectively used to solve …

Reduced Order Models for Pricing American Options under Stochastic Volatility and Jump-diffusion Models

2016

American options can be priced by solving linear complementary problems (LCPs) with parabolic partial(-integro) differential operators under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. These operators are discretized using finite difference methods leading to a so-called full order model (FOM). Here reduced order models (ROMs) are derived employing proper orthogonal decomposition (POD) and non negative matrix factorization (NNMF) in order to make pricing much faster within a given model parameter variation range. The numerical experiments demonstrate orders of magnitude faster pricing with ROMs. peerReviewed

Higher-order Nonnegative CANDECOMP/PARAFAC Tensor Decomposition Using Proximal Algorithm

2019

Tensor decomposition is a powerful tool for analyzing multiway data. Nowadays, with the fast development of multisensor technology, more and more data appear in higherorder (order > 4) and nonnegative form. However, the decomposition of higher-order nonnegative tensor suffers from poor convergence and low speed. In this study, we propose a new nonnegative CANDECOM/PARAFAC (NCP) model using proximal algorithm. The block principal pivoting method in alternating nonnegative least squares (ANLS) framework is employed to minimize the objective function. Our method can guarantee the convergence and accelerate the computation. The results of experiments on both synthetic and real data demonstrate …

Theoretical and methodological aspects of MCMC computations with noisy likelihoods

2018

Approximate Bayesian computation (ABC) [11, 42] is a popular method for Bayesian inference involving an intractable, or expensive to evaluate, likelihood function but where simulation from the model is easy. The method consists of defining an alternative likelihood function which is also in general intractable but naturally lends itself to pseudo-marginal computations [5], hence making the approach of practical interest. The aim of this chapter is to show the connections of ABC Markov chain Monte Carlo with pseudo-marginal algorithms, review their existing theoretical results, and discuss how these can inform practice and hopefully lead to fruitful methodological developments. peerReviewed

Tractional Motion Machines extend GPAC-generable functions

2012

In late 17th century there appeared the Tractional Motion instruments, mechanical devices which plot the curves solving differential equations by the management of the tangent. In early 20th century Vannevar Bush’s Differential Analyzer got the same aim: in this paper we’ll compare the Differential Analyzer mathematical model (the Shannon’s General Purpose Analog Computer, or GPAC) with the Tractional Motion Machine potentials. Even if we will not arrive in defining the class of the functions generated by Tractional Motion Machines, we’ll see how this class will strictly extend the GPAC-generable functions.

Husserl's Transcendentalization of Mathematical Naturalism

2020

Abstract The paper aims to capture a form of naturalism that can be found “built-in” in phenomenology, namely the idea to take science or mathematics on its own, without postulating extraneous normative “molds” on it. The paper offers a detailed comparison of Penelope Maddy’s naturalism about mathematics and Husserl’s approach to mathematics in Formal and Transcendental Logic (1929). It argues that Maddy’s naturalized methodology is similar to the approach in the first part of the book. However, in the second part Husserl enters into a transcendental clarification of the evidences and presuppositions of the mathematicians’ work, thus “transcendentalizing” his otherwise naturalist approach t…

Pricavy-Preserving Aspects for Data Mining in ICT Services

The steady adoption of systems for profiling users behavior, collecting and critically interpreting as much information as possible about likes and dislikes, interests and habits of Internet residents and generic services consumers have rapidly become some of the hottest keywords within networking research community. Indeed, mining information about users behavior is an advantage for both service providers and service customers: on one side, providers can improve their revenues by focusing on the most successful features of their services, while on the other side, users can enjoy services which reflect closer their specific needs. There are many examples of user profiling applications. Inte…