116,777 research outputs found
Nonlinear Robust Identification using Evolutionary Algorithms. Application to a Biomedical Process
[EN] This work describes a new methodology for robust identification (RI), meaning the identification of the parameters of a model and the characterization of uncertainties. The alternative proposed handles non-linear models and can take into account the different properties demanded by the model. The indicator that leads the identification process is the identification error (IE), that is, the difference between experimental data and model response. In particular, the methodology obtains the feasible parameter set (FPS, set of parameter values which satisfy a bounded IE) and a nominal model in a non-linear identification problem. To impose different properties on the model, several norms of the IE are used and bounded simultaneously. This improves the model quality, but increases the problem complexity. The methodology proposes that the RI problem is transformed into a multimodal optimization problem with an infinite number of global minima which constitute the FPS. For the optimization task, a special genetic algorithm (epsilon-GA), inspired by Multiobjective Evolutionary Algorithms, is presented. This algorithm characterizes the FPS by means of a discrete set of models well distributed along the FPS. Finally, an application for a biomedical model which shows the blockage that a given drug produces on the ionic currents of a cardiac cell is presented to illustrate the methodology. (C) 2008 Elsevier Ltd. All rights reserved.Partially supported by MEC (Spanish government) and FEDER funds: Projects DP12005-07835, DP12004-8383-CO3-02 and Generalitat Valenciana (Spain) Project GVA-026.Herrero Durá, JM.; Blasco, X.; Martínez Iranzo, MA.; Ramos Fernández, C.; Sanchís Saez, J. (2008). Nonlinear Robust Identification using Evolutionary Algorithms. Application to a Biomedical Process. Engineering Applications of Artificial Intelligence. 21(8):1397-1408. https://doi.org/10.1016/j.engappai.2008.05.001S1397140821
Membership-set estimation using random scanning and principal component analysis
A set-theoretic approach to parameter estimation based on the bounded-error concept is an appropriate choice when incomplete knowledge of observation error statistics and unavoidable structural model error invalidate the presuppositions of stochastic methods. Within this class the estimation of non-linear-in-the-parameters models is examined. This situation frequently occurs in modelling natural systems. The output error method proposed is based on overall random scanning with iterative reduction of the size of the scanned region. In order to overcome the problem of computational inefficiency, which is particularly serious when there is interaction between the parameter estimates, two modifications to the basic method are introduced. The first involves the use of principal component transformations to provide a rotated parameter space in the random scanning because large areas of the initial parameter space are thus excluded from further examination. The second improvement involves the standardization of the parameters so as to obtain an initial space with equal size extension in all directions. This proves to largely increase the computational robustness of the method. The modified algorithm is demonstrated by application to a simple three-parameter model of diurnal dissolved oxygen patterns in a lake
Nonparametric identification of positive eigenfunctions
Important features of certain economic models may be revealed by studying
positive eigenfunctions of appropriately chosen linear operators. Examples
include long-run risk-return relationships in dynamic asset pricing models and
components of marginal utility in external habit formation models. This paper
provides identification conditions for positive eigenfunctions in nonparametric
models. Identification is achieved if the operator satisfies two mild
positivity conditions and a power compactness condition. Both existence and
identification are achieved under a further non-degeneracy condition. The
general results are applied to obtain new identification conditions for
external habit formation models and for positive eigenfunctions of pricing
operators in dynamic asset pricing models
Nonlinear system identification using wavelet based SDP models
System identification has played an increasingly dominant role in a wide range of engineering applications. While linear system's theory is mature, nonlinear system identification remains an open research area in recent years. This thesis develops a new, efficient and systematic approach to the identification of nonlinear dynamic systems using wavelet based State Dependent Parameter (SDP) models, from structure determination to parameter estimation. In this approach, the system's nonlinearities are analysed and effectively represented by a SDP model structure in the form of wavelets. This provides a computationally efficient tool to open up the `black-box', offering valuable insights into the system's dynamics. In this thesis, 1-dimensional (1-D) approach is first developed based on a conventional SDP model structure which relies on a single state variable dependency. It is then extended into a multi-dimensional approach in order to solve the identification problem of systems with significant multi-variable dependence nonlinear dynamics. Here, parametrically efficient nonlinear model is obtained by the application of an effective model structure selection algorithm based on the Predicted Residual Sums of Squares (PRESS) criterion in conjunction with Orthogonal Decomposition (OD) to avoid any ill-conditioning problems associated with the parameter estimation. This thesis also investigates the aspects of noise, stability and other engineering application of the proposed approaches. More specifically, this includes: (1) nonlinear identification in the presence of noise, (2) development of bounded characteristics of the estimated models and (3) application studies where the developed approaches have been used in various engineering applications. Particularly, the modelling and forecast of daily peak power demand in the state of Victoria, Australia have been effectively studied using the proposed approaches. This strongly motivates a great deal of potential future research to be carried out in the area of power system modelling
Machine Learning for Set-Identified Linear Models
This paper provides estimation and inference methods for an identified set
where the selection among a very large number of covariates is based on modern
machine learning tools. I characterize the boundary of the identified set
(i.e., support function) using a semiparametric moment condition. Combining
Neyman-orthogonality and sample splitting ideas, I construct a root-N
consistent, uniformly asymptotically Gaussian estimator of the support function
and propose a weighted bootstrap procedure to conduct inference about the
identified set. I provide a general method to construct a Neyman-orthogonal
moment condition for the support function. Applying my method to Lee (2008)'s
endogenous selection model, I provide the asymptotic theory for the sharp
(i.e., the tightest possible) bounds on the Average Treatment Effect in the
presence of high-dimensional covariates. Furthermore, I relax the conventional
monotonicity assumption and allow the sign of the treatment effect on the
selection (e.g., employment) to be determined by covariates. Using JobCorps
data set with very rich baseline characteristics, I substantially tighten the
bounds on the JobCorps effect on wages under weakened monotonicity assumption
On Bayesian Oracle Properties
When model uncertainty is handled by Bayesian model averaging (BMA) or
Bayesian model selection (BMS), the posterior distribution possesses a
desirable "oracle property" for parametric inference, if for large enough data
it is nearly as good as the oracle posterior, obtained by assuming
unrealistically that the true model is known and only the true model is used.
We study the oracle properties in a very general context of quasi-posterior,
which can accommodate non-regular models with cubic root asymptotics and
partial identification. Our approach for proving the oracle properties is based
on a unified treatment that bounds the posterior probability of model
mis-selection. This theoretical framework can be of interest to Bayesian
statisticians who would like to theoretically justify their new model selection
or model averaging methods in addition to empirical results. Furthermore, for
non-regular models, we obtain nontrivial conclusions on the choice of prior
penalty on model complexity, the temperature parameter of the quasi-posterior,
and the advantage of BMA over BMS.Comment: 31 page
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