Bayesian Hierarchical Models can Infer Interpretable Predictions of Leaf Area Index From Heterogeneous Datasets

Environmental scientists often face the challenge of predicting a complex phenomenon from a heterogeneous collection of datasets that exhibit systematic differences. Accounting for these differences usually requires including additional parameters in the predictive models, which increases the probability of overfitting, particularly on small datasets. We investigate how Bayesian hierarchical models can help mitigate this problem by allowing the practitioner to incorporate information about the structure of the dataset explicitly. To this end, we look at a typical application in remote sensing: the estimation of leaf area index of white winter wheat, an important indicator for agronomical modeling, using measurements of reflectance spectra collected at different locations and growth stages. Since the insights gained from such a model could be used to inform policy or business decisions, the interpretability of the model is a primary concern. We, therefore, focus on models that capture the association between leaf area index and the spectral reflectance at various wavelengths by spline-based kernel functions, which can be visually inspected and analyzed. We compare models with three different levels of hierarchy: a non-hierarchical baseline model, a model with hierarchical bias parameter, and a model in which bias and kernel parameters are hierarchically structured. We analyze them using Markov Chain Monte Carlo sampling diagnostics and an intervention-based measure of feature importance. The improved robustness and interpretability of this approach show that Bayesian hierarchical models are a versatile tool for the prediction of leaf area index, particularly in scenarios where the available data sources are heterogeneous.

Fault Identification Based on Local Feature Correlation

Industrial data variables show obvious high dimension and strong nonlinear correlation. Traditional multivariate statistical monitoring methods, such as PCA, PLS, CCA, and FDA, are only suitable for solving the high-dimensional data processing with linear correlation. The kernel mapping method is the most common technique to deal with the nonlinearity, which projects the original data in the low-dimensional space to the high-dimensional space through appropriate kernel functions so as to achieve the goal of linear separability in the new space. However, the space projection from the low dimension to the high dimension is contradictory to the actual requirement of dimensionality reduction of the data. So kernel-based method inevitably increases the complexity of data processing.

Long-time dynamics of an epidemic model with nonlocal diffusion and free boundaries

<abstract><p>In this paper, we consider a reaction-diffusion epidemic model with nonlocal diffusion and free boundaries, which generalises the free-boundary epidemic model by Zhao et al. ^{[<xref ref-type="bibr" rid="b1">1</xref>]} by including spatial mobility of the infective host population. We obtain a rather complete description of the long-time dynamics of the model. For the reproduction number $ R_0 $ arising from the corresponding ODE model, we establish its relationship to the spreading-vanishing dichotomy via an associated eigenvalue problem. If $ R_0 \le 1 $, we prove that the epidemic vanishes eventually. On the other hand, if $ R_0 &gt; 1 $, we show that either spreading or vanishing may occur depending on its initial size. In the case of spreading, we make use of recent general results by Du and Ni ^{[<xref ref-type="bibr" rid="b2">2</xref>]} to show that finite speed or accelerated spreading occurs depending on whether a threshold condition is satisfied by the kernel functions in the nonlocal diffusion operators. In particular, the rate of accelerated spreading is determined for a general class of kernel functions. Our results indicate that, with all other factors fixed, the chance of successful spreading of the disease is increased when the mobility of the infective host is decreased, reaching a maximum when such mobility is 0 (which is the situation considered by Zhao et al. ^{[<xref ref-type="bibr" rid="b1">1</xref>]}).</p></abstract>

Support Vector Machines and Support Vector Regression

In this chapter, the support vector machines (svm) methods are studied. We first point out the origin and popularity of these methods and then we define the hyperplane concept which is the key for building these methods. We derive methods related to svm: the maximum margin classifier and the support vector classifier. We describe the derivation of the svm along with some kernel functions that are fundamental for building the different kernels methods that are allowed in svm. We explain how the svm for binary response variables can be expanded for categorical response variables and give examples of svm for binary and categorical response variables with plant breeding data for genomic selection. Finally, general issues for adopting the svm methodology for continuous response variables are provided, and some examples of svm for continuous response variables for genomic prediction are described.

On a special class of modified integral operators preserving some exponential functions

<p style='text-indent:20px;'>In the present paper, we consider a general class of operators enriched with some properties in order to act on <inline-formula><tex-math id="M1">\begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}</tex-math></inline-formula>. We establish uniform convergence of the operators for every function in <inline-formula><tex-math id="M2">\begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}</tex-math></inline-formula> on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R} _{0}^{+} $\end{document}</tex-math></inline-formula>. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.</p>

A comparative study of Gaussian process regression with other three machine learning approaches in the performance prediction of centrifugal pump

Accurate prediction of performance indices using impeller parameters is of great importance for the initial and optimal design of centrifugal pump. In this study, a kernel-based non-parametric machine learning method named with Gaussian process regression (GPR) was proposed, with the purpose of predicting the performance of centrifugal pump with less effort based on available impeller parameters. Nine impeller parameters were defined as model inputs, and the pump performance indices, that is, the head and efficiency, were determined as model outputs. The applicability of three widely used nonlinear kernel functions of GPR including squared exponential (SE), rational quadratic (RQ) and Matern5/2 was investigated, and it was found by comparing with the experimental data that the SE kernel function is more suitable to capture the relationship between impeller parameters and performance indices because of the highest R square and the lowest values of max absolute relative error (MARE), mean absolute proportional error (MAPE), and root mean square error (RMSE). In addition, the results predicted by GPR with SE kernel function were compared with the results given by other three machine learning models. The comparison shows that the GPR with SE kernel function is more accurate and robust than other models in centrifugal pump performance prediction, and its prediction errors and uncertainties are both acceptable in terms of engineering applications. The GPR method is less costly in the performance prediction of centrifugal pump with sufficient accuracy, which can be further used to effectively assist the design and manufacture of centrifugal pump and to speed up the optimization design process of impeller coupled with stochastic optimization methods.

An EMD and IMF Energy Entropy Based Optimized Feature Extraction and Classification Scheme for Single Trial EEG Signal

For the purpose of improving the classification accuracy of single trial EEG signal during motor imagery (MI) process, this study proposed a classification method which combined IMF energy entropy and improved EMD scheme. Singular value decomposition (SVD), Gaussian mixture model, EMD and IMF energy entropy were employed for the newly designed scheme. After removing noise and artifacts from acquired EEG signals in EEGLAB, SVD was applied, and the singular values were clustered by Gaussian mixture model. The insignificant characteristics indicated by the small SVD values were then removed, and the signals were reconstructed, feeding to EMD algorithm. Those IMFs mapping to δ、θ、α and β frequencies were selected as the major features of the EEG signal. The SVM classifier with RBF, linear, and polynomial kernel functions and voting mechanism then kicked in for classification. The results were compared with that of the traditional EMD and EEMD through simulation, showing that the proposed scheme can eliminate mode mixing effectively and improve the single trial EEG signal classification accuracy significantly, suggesting the probability of designing a more efficient EEG control system based on the proposed scheme.

INSOLE-BASED ESTIMATION OF COMPLETE GROUND REACTION FORCE WITH GAUSSIAN KERNEL REGRESSION AND DATA EXPANSION

A method for estimating ground reaction force (GRF) with plantar pressure was proposed in this paper. The estimation model was constructed to approximate the nonlinear relationships between GRF and the plantar pressure according to the linear combinations of Gaussian kernel functions. Partial least squares regression (PLSR) was adopted to obtain model parameters and eliminate multicollinearity among the pressure components. The general model and subject-specific models were constructed for 12 male and 4 female subjects. Moreover, a data expansion method was introduced for the establishment of subject-specific model, which is implemented by searching and adopting the data with consistent statistical characteristics in a pre-established database. That approach is particularly meaningful for the group whose walking ability is limited or clinic where the force platform is not available. The NRMSEs (%) for general model were 5.27–7.85% (GRF_V), 7.35–8.53% (GRF_ML), and 8.82–10.54% (GRF_AP). The maximum NRMSEs (%) for subject-specific models were 5.02% (GRF_V), 9.91% (GRF_ML), and 10.23% (GRF_AP). Results showed that both general and subject-specific models achieved higher accuracy than existing methods such as linear regression and neural network methods.