Wyniki wyszukiwania - BazTech

Ograniczanie wyników

2 International Journal of Applied Mathematics and Computer Science

Znaleziono wyników: 2

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: estymacja regresji

Sortuj według:

Ogranicz wyniki do:

Probabilities of discrepancy between minima of cross-validation, Vapnik bounds and true risks

Klęsk P.

International Journal of Applied Mathematics and Computer Science

2010

Vol. 20, no 3

525-544

Two known approaches to complexity selection are taken under consideration: n-fold cross-validation and structural risk minimization. Obviously, in either approach, a discrepancy between the indicated optimal complexity (indicated as the minimum of a generalization error estimate or a bound) and the genuine minimum of unknown true risks is possible. In the paper, this problem is posed in a novel quantitative way. We state and prove theorems demonstrating how one can calculate pessimistic probabilities of discrepancy between these minima for given for given conditions of an experiment. The probabilities are calculated in terms of all relevant constants: the sample size, the number of cross-validation folds, the capacity of the set of approximating functions and bounds on this set. We report experiments carried out to validate the results.

Robust parameter design using the weighted metric method - The case of 'the smaller the better'

Ardakani M. K., Noorossana R., Niaki S. T. A., Lahijanian H.

International Journal of Applied Mathematics and Computer Science

2009

Vol. 19, no 1

59-68

In process robustness studies, it is desirable to minimize the influence of noise factors on the system and simultaneously determine the levels of controllable factors optimizing the overall response or outcome. In the cases when a random effects model is applicable and a fixed effects model is assumed instead, an increase in the variance of the coefficient vector should be expected. In this paper, the impacts of this assumption on the results of the experiment in the context of robust parameter design are investigated. Furthermore, two criteria are considered to determine the optimum settings for the control factors. In order to better understand the proposed method and to evaluate its performances, a numerical example for the case of 'the smaller the better' is included.