Search results for "a posteriori"
showing 10 items of 144 documents
Probabilistic cross-validation estimators for Gaussian process regression
2018
Gaussian Processes (GPs) are state-of-the-art tools for regression. Inference of GP hyperparameters is typically done by maximizing the marginal log-likelihood (ML). If the data truly follows the GP model, using the ML approach is optimal and computationally efficient. Unfortunately very often this is not case and suboptimal results are obtained in terms of prediction error. Alternative procedures such as cross-validation (CV) schemes are often employed instead, but they usually incur in high computational costs. We propose a probabilistic version of CV (PCV) based on two different model pieces in order to reduce the dependence on a specific model choice. PCV presents the benefits from both…
A posteriori error majorants of the modeling errors for elliptic homogenization problems
2013
In this paper, we derive new two-sided a posteriori estimates of the modeling errors for linear elliptic boundary value problems with periodic coefficients solved by homogenization. Our approach is based on the concept of functional a posteriori error estimation. The estimates are obtained for the energy norm and use solely the global flux of the non-oscillatory solution of the homogenized model and solution of a boundary value problem on the cell of periodicity.
A posteriori modelling-discretization error estimate for elliptic problems with L ∞-Coefficients
2017
We consider elliptic problems with complicated, discontinuous diffusion tensor A0. One of the standard approaches to numerically treat such problems is to simplify the coefficient by some approximation, say Aϵ, and to use standard finite elements. In [19] a combined modelling-discretization strategy has been proposed which estimates the discretization and modelling errors by a posteriori estimates of functional type. This strategy allows to balance these two errors in a problem adapted way. However, the estimate of the modelling error was derived under the assumption that the difference A0 - Aϵ becomes small with respect to the L∞-norm. This implies in particular that interfaces/discontinui…
Adaptive dual control in one biomedical problem
2003
In this paper, the following biomedical problem is considered. People are subjected to a certain chemotherapeutic treatment. The optimal dosage is the maximal dose for which an individual patient will have toxicity level that does not cross the allowable limit. We discuss sequential procedures for searching the optimal dosage, which are based on the concept of dual control and the principle of optimality. According to the dual control theory, the control has two purposes that might be conflicting: one is to help learning about unknown parameters and/or the state of the system (estimation); the other is to achieve the control objective. Thus the resulting control sequence exhibits the closed…
Macrostructural EEG characterization based on nonparametric change point segmentation: application to sleep analysis
2001
In the present investigation a new methodology for macrostructural EEG characterization based on automatic segmentation has been applied to sleep analysis. A nonparametric statistical approach for EEG segmentation was chosen, because it minimizes the need for a priori information about a signal. The method provides the detection of change-points i.e. boundaries between quasi-stationary EEG segments based on the EEG characteristics within four fundamental frequency bands (delta, theta, alpha and beta). Polysomnographic data of 18 healthy subjects were analyzed. Our findings show that nonparametric change-point segmentation in combination with cluster analysis enables us to obtain a clear pic…
A posteriori estimates for the stationary Stokes problem in exterior domains
2020
This paper is concerned with the analysis of the inf-sup condition arising in the stationary Stokes problem in exterior domains and applications to the derivation of computable bounds for the distance between the exact solution of the exterior Stokes problem and a certain approximation (which may be of a rather general form). In the first part, guaranteed bounds are deduced for the constant in the stability lemma associated with the exterior domain. These bounds depend only on known constants and the stability constant related to bounded domains that arise after suitable truncations of the unbounded domains. The lemma in question implies computable estimates of the distance to the set of di…
Principal component analysis for the selection of variables in the application of the H-point and generalised H-point standard addition method
2000
The present paper deals with the selection of variables for the H-point and generalised H-point standard additions methods (HPSAM and GHPSAM, respectively). Both methods are applied for the resolution of spectroscopic interfered signals in the UV-vis range. The HPSAM is a suitable method for the resolution of binary and ternary mixtures when the interferent is known. The GHPSAM is applied for the resolution of samples that contain unknown interferents. In this paper, a method based on the study of a principal components analysis (PCA) for the selection of variables for the HPSAM and GHPSAM is proposed. The PCA results show the isolation of the analyte signal from the sample signal, achieved…
Reduced complexity models in the identification of dynamical networks: Links with sparsification problems
2009
In many applicative scenarios it is important to derive information about the topology and the internal connections of more dynamical systems interacting together. Examples can be found in fields as diverse as Economics, Neuroscience and Biochemistry. The paper deals with the problem of deriving a descriptive model of a network, collecting the node outputs as time series with no use of a priori insight on the topology. We cast the problem as the optimization of a cost function operating a trade-off between accuracy and complexity in the final model. We address the problem of reducing the complexity by fixing a certain degree of sparsity, and trying to find the solution that “better” satisfi…
Comparative Study of the a Posteriori Error Estimators for the Stokes Problem
2007
The research presented is focused on a comparative study of a posteriori error estimation methods to various approximations of the Stokes problem. Mainly, we are interested in the performance of functional type a posterior error estimates and their comparison with other methods. We show that functional type a posteriori error estimators are applicable to various types of approximations (including non-Galerkin ones) and robust with respect to the mesh structure, type of the finite element and computational procedure used. This allows the construction of effective mesh adaptation procedures in all cases considered. Numerical tests justify the approach suggested.
Medical Data Mining for Heart Diseases and the Future of Sequential Mining in Medical Field
2018
Data Mining in general is the act of extracting interesting patterns and discovering non-trivial knowledge from a large amount of data. Medical data mining can be used to understand the events happened in the past, i.e. studying a patients vital signs to understand his complications and discover why he has died, or to predict the future by analyzing the events that had happened. In this chapter we are presenting an overview on studies that use data mining to predict heart failure and heart diseases classes. We will also focus on one of the trendiest data-mining field, namely the Sequential Mining, which is a very promising paradigm. Due to its important results in many fields, this chapter …