Difficulty In Model Selection Research Articles

Analytical and Numerical Connections between Fractional Fickian and Intravoxel Incoherent Motion Models of Diffusion MRI

Impaired tissue perfusion underlies many chronic disease states and aging. Diffusion-weighted imaging (DWI) is a noninvasive MRI technique that has been widely used to characterize tissue perfusion. Parametric models based on DWI measurements can characterize microvascular perfusion modulated by functional and microstructural alterations in the skeletal muscle. The intravoxel incoherent motion (IVIM) model uses a biexponential form to quantify the incoherent motion of water molecules in the microvasculature at low b-values of DWI measurements. The fractional Fickian diffusion (FFD) model is a parsimonious representation of anomalous superdiffusion that uses the stretched exponential form and can be used to quantify the microvascular volume of skeletal muscle. Both models are established measures of perfusion based on DWI, and the prognostic value of model parameters for identifying pathophysiological processes has been studied. Although the mathematical properties of individual models have been previously reported, quantitative connections between IVIM and FFD models have not been examined. This work provides a mathematical framework for obtaining a direct, one-way transformation of the parameters of the stretched exponential model to those of the biexponential model. Numerical simulations are implemented, and the results corroborate analytical results. Additionally, analysis of in vivo DWI measurements in skeletal muscle using both biexponential and stretched exponential models is shown and compared with analytical and numerical models. These results demonstrate the difficulty of model selection based on goodness of fit to experimental data. This analysis provides a framework for better interpreting and harmonizing perfusion parameters from experimental results using these two different models.

Aerosol-type retrieval and uncertainty quantification from OMI data

Abstract. We discuss uncertainty quantification for aerosol-type selection in satellite-based atmospheric aerosol retrieval. The retrieval procedure uses precalculated aerosol microphysical models stored in look-up tables (LUTs) and top-of-atmosphere (TOA) spectral reflectance measurements to solve the aerosol characteristics. The forward model approximations cause systematic differences between the modelled and observed reflectance. Acknowledging this model discrepancy as a source of uncertainty allows us to produce more realistic uncertainty estimates and assists the selection of the most appropriate LUTs for each individual retrieval.This paper focuses on the aerosol microphysical model selection and characterisation of uncertainty in the retrieved aerosol type and aerosol optical depth (AOD). The concept of model evidence is used as a tool for model comparison. The method is based on Bayesian inference approach, in which all uncertainties are described as a posterior probability distribution. When there is no single best-matching aerosol microphysical model, we use a statistical technique based on Bayesian model averaging to combine AOD posterior probability densities of the best-fitting models to obtain an averaged AOD estimate. We also determine the shared evidence of the best-matching models of a certain main aerosol type in order to quantify how plausible it is that it represents the underlying atmospheric aerosol conditions.The developed method is applied to Ozone Monitoring Instrument (OMI) measurements using a multiwavelength approach for retrieving the aerosol type and AOD estimate with uncertainty quantification for cloud-free over-land pixels. Several larger pixel set areas were studied in order to investigate the robustness of the developed method. We evaluated the retrieved AOD by comparison with ground-based measurements at example sites. We found that the uncertainty of AOD expressed by posterior probability distribution reflects the difficulty in model selection. The posterior probability distribution can provide a comprehensive characterisation of the uncertainty in this kind of problem for aerosol-type selection. As a result, the proposed method can account for the model error and also include the model selection uncertainty in the total uncertainty budget.

Principles and guidelines of deterioration modelling for water and waste water assets

Deterioration modelling is an important analytical component in risk-informed infrastructure asset management. Many asset managers find it very challenging because of its technicality, paucity of deterioration data and difficulty in model selection. Traditional approaches emphasised the mean deterioration trend and heeded too little the characterisation of uncertainty involved. This paper attempts to revert this trend and bring stochastic deterioration modelling back to focus. Following a systems approach, the author argues that deterioration modelling involves not only the data-driven process that asset managers have traditionally perceived, but also a system analysis that carries the empirical deterioration modelling at the level of performance data up to the level of the performance hierarchy at which decisions are made. In addition, deterioration modelling is an important and integral component of risk analysis, and therefore, the characterisation and quantification of aleatory uncertainty and epistemic uncertainty become an essential component of deterioration modelling. Moreover, deterioration data include not only hard data collected from inspection and condition assessment, but also soft data that can be gleaned from expert opinions, design manuals and professional judgements. Although mainly for water and waste water assets, the principles, guidelines and model selection flow chart are equally applicable to other infrastructure assets.

An ensemble evolutionary approach in evaluation of surface finish reduction of vibratory finishing process

Purpose – The functioning of multi-gene genetic programming (MGGP) algorithm suffers from the problem of difficulty in model selection. During the preliminary analysis, it is observed that there are many models in the population whose performance is better than that of the model selected with a little compromise on training error. Therefore, an ensemble evolutionary (Ensemble-MGGP) approach is proposed and applied to the data obtained from the vibratory finishing process. The paper aims to discuss these issues. Design/methodology/approach – Unlike the standard GP, each model participating in Ensemble-MGGP approach is made by combining the set of genes. Predicted residual sum of squares criterion (PRESS) criterion is integrated to improve its evolutionary search. The parametric analysis and sensitivity analysis (SA) conducted on the proposed model validates its robustness by unveiling dominant input parameters and hidden non-linear relationships. Findings – The results indicate that the proposed Ensemble-MGGP model outperforms the standardized MGGP model. SA and parametric analysis reveals relationships and insights into vibratory finishing process. Originality/value – Literature emphasises on characterization of vibratory finishing process using the experimental-based-studies. In addition, the issue of difficulty in model selection in genetic programming is addressed. This work proposes a new ensemble evolutionary approach to counter these issues.

A new simulation approach of genetic programming in modelling of soil water retention property of unsaturated soil

Purpose – For measuring the effect of crop root content on soil water retention curves (SWRC), a simulation approach (multi-gene genetic programming (MGGP)), which develops the model structure and its coefficients automatically can be applied. However, it does not perform well due to two vital issues related to its generalization: inappropriate formulation procedure of the multi-gene model and the difficulty in model selection. The purpose of this paper is to propose a heuristic-based-MGGP (N-MGGP) to formulate the functional relationship between the water content and two input parameters (soil suction and volumetric crop root content). Design/methodology/approach – A new simulation approach (heuristic-based-MGGP (N-MGGP)), was proposed to formulate the functional relationship between the water content and two input parameters (soil suction and volumetric crop root content). The proposed approach makes use of a statistical approach of stepwise regression and classification methods (Bayes naïve and artificial neural network (ANN)) to tackle the two issues. Simulated data obtained from the models was evaluated against the experimental data. Findings – The performance of proposed approach was found to better than that of standardized MGGP. Sensitivity and parametric analysis conducted validates the robustness of model by unveiling dominant input parameters and hidden non-linear relationships. Originality/value – To the best of authors’ knowledge, an empirical model is developed that measures the effect of crop root content on the SWRCs. The authors also proposed a new genetic programming approach in simulating the crop root content dependent SWRCs.

Improving environmental sustainability by formulation of generalized power consumption models using an ensemble based multi-gene genetic programming approach

Environmental sustainability is an important aspect for accessing the performance of any machining industry. Growing demand of customers for better product quality has resulted in an increase in energy consumption and thus a lower environmental performance. Optimization of both product quality and energy consumption is needed for improving economic and environmental performance of the machining operations. However, for achieving the global multi-objective optimization, the models formulated must be able to generalize the data accurately. In this context, an evolutionary approach of multi-gene genetic programming (MGGP) can be used to formulate the models for product quality (surface roughness and tool life) and power consumption. MGGP develops the model structure and its coefficients based on the principles of genetic algorithm (GA). Despite being widely applied, MGGP generates models that may not give satisfactory performance on the test data. The main reason behind this is the inappropriate formulation procedure of the multi-gene model and the difficulty in model selection. Therefore, the present work proposes a new ensemble-based-MGGP (EN-MGGP) framework that makes use of statistical and classification strategies for improving the generalization ability. The EN-MGGP approach is applied on the reliable experimental database (outputs: surface roughness, tool life and power consumption) obtained from the literature, and its performance is compared to that of the standardized MGGP. The proposed EN-MGGP models outperformed the standardized MGGP models. The conducted sensitivity and parametric analysis validates the robustness of the models by unveiling the non-linear relationships between the outputs (surface roughness, tool life and power consumption) and input parameters. It was also found that the cutting speed has the most significant impact on the power consumption in turning of AISI 1045 steel and the turning of 7075 Al alloy- 15 wt% SIC composites. The generalized EN-MGGP models obtained can easily be optimized analytically for attaining the optimum input parameter settings that optimize the product quality and power consumption simultaneously.

A new computational intelligence approach in formulation of functional relationship of open porosity of the additive manufacturing process

An additive manufacturing process of selective laser sintering (SLS) builds components of complex 3D shapes directly from metal powder. Past studies reveal that the properties of an SLS-fabricated prototype such as porosity, surface roughness, waviness, compressive strength, tensile strength, wear strength, and dimensional accuracy depend on the parameter settings of the SLS setup and can be improved by appropriate adjustment. In this context, the computational intelligence (CI) approach of multi-gene genetic programming (MGGP) can be used to formulate the model for understanding the process behavior. MGGP develops the model structure and its coefficients automatically. Despite being widely applied, MGGP generates models that may not give satisfactory performance on test data. The underlying reason is the inappropriate formulation procedure of the multi-gene model and the difficulty in model selection. Therefore, the present work proposes a new CI approach (ensemble-based MGGP (EN-MGGP)) that makes use of statistical and classification strategies for improving its generalization. The EN-MGGP approach is applied to the open porosity data obtained from the experiments conducted on an SLS machine, and its performance is compared to that of the standardized MGGP. The proposed EN-MGGP model outperforms the standardized model and is proven to capture the dynamics of the SLS process by unveiling dominant input process parameters and the hidden non-linear relationships.

Learning with many experts: Model selection and sparsity

AbstractExperts classifying data are often imprecise. Recently, several models have been proposed to train classifiers using the noisy labels generated by these experts. How to choose between these models? In such situations, the true labels are unavailable. Thus, one cannot perform model selection using the standard versions of methods such as empirical risk minimization and cross validation. In order to allow model selection, we present a surrogate loss and provide theoretical guarantees that assure its consistency. Next, we discuss how this loss can be used to tune a penalization which introduces sparsity in the parameters of a traditional class of models. Sparsity provides more parsimonious models and can avoid overfitting. Nevertheless, it has seldom been discussed in the context of noisy labels owing to the difficulty in model selection and, therefore, in choosing tuning parameters. We apply these techniques to several sets of simulated and real data. © 2013 Wiley Periodicals, Inc. Statistical Analysis and Data Mining, 2013

Incremental Regression Function Construction with Small Landmarks

In automatic control and its related applications, many problems can be formulated as the regression estimation problem. In this paper, we construct a nonlinear regression model by using kernels as basis functions in a dictionary and applying the L1 norm as the regularizer. The regression function obtained from this model possesses the sparseness property where only a subset of points are used to represent the function. We call this subset of points as landmarks. It is a convex optimization problem. However, instead of using the standard optimization tools to solve a convex problem for a particular regularization value, we develop an efficient regularization path algorithm that can trace all solutions for all possible regularization parameter values. It overcomes the computational difficulty in model selection. Since the algorithm generally adds basis functions incrementally to improve the prediction accuracy, the regression function can be represented concisely with small landmarks.