Nonparametric Model Research Articles

Enabling efficient regional seismic fragility assessment of multi‐component bridge portfolios through Gaussian process regression and active learning

AbstractRegional seismic fragility assessment of bridge portfolios must address the embedded uncertainties and variations stemming from both the earthquake hazard and bridge attributes (e.g., geometry, material, design detail). To achieve bridge‐specific fragility assessment, multivariate probabilistic seismic demand models (PSDM) have recently been developed that use both the ground motion intensity measure and bridge parameters as inputs. However, explicitly utilizing bridge parameters as inputs requires numerous nonlinear response history analyses (NRHAs). In this situation, the associated computational cost increases exponentially for high‐fidelity bridge models with complex component connectivity and sophisticated material constitutive laws. Moreover, it remains unclear how many analyses are sufficient for the response data and the resulting demand model to cover the entire solution space without overfitting. To deal with these issues, this study integrates Gaussian process regression (GPR) and active learning (AL) into a multistep workflow to achieve efficient regional seismic fragility assessment of bridge portfolios. The GPR relaxes the probability distribution assumptions made in typical cloud analysis‐based PSDMs to enable heteroskedastic nonparametric seismic demand modeling. The AL leverages the varying standard deviation to select the least but most representative bridge‐model‐ground‐motion sample pairs to conduct NRHA with much‐improved efficiency. Both independent and correlated multi‐output GPRs are proposed to deal with bridge portfolios with seismic demand correlations among multiple components (column, bearing, shear key, abutment, unseating, and joint seal). Considering a single benchmark highway bridge class in California as the case study, the AL‐GPR framework and the associated component‐level fragility results are investigated in terms of their efficiency, accuracy, and robustness. The fragility results show that 70 AL‐selected samples would enable the GPR to derive bridge‐specific fragility models comparable to the ones using the multiple stripes analysis approach with 1950 ground motions considered for each individual bridge. The AL‐GPR model also successfully captures the physics of how bridge span length, deck area, column slenderness, and steel reinforcement ratio would change the damage state exceedance probabilities of different bridge components. The efficiency of AL stems from the fact that, with the multi‐output independent GPR, a stable and reliable fragility model can be achieved using 50 AL‐selected samples compared to at least 270 randomly chosen samples. The proposed methodology advances the state of the art in enabling more efficient and reliable regional seismic fragility assessment of multi‐component bridge portfolios.

The impact of repayment obligations arising as a by‐product of input use on partial inefficiency: Evidence from Western Australian farm businesses

AbstractFarm businesses often use debt to finance the purchase inputs and meet operational costs. Selected studies have investigated the impact of debt use on farm performance as measured using technical efficiency. However, no prior studies in agriculture have considered treating the debt repayment obligation created as a by‐product of production when benchmarking farm performance. This study employs nonparametric directional distance function models to quantify the impact of debt repayment as a by‐product of input use purchased on credit on farm‐level partial inefficiency using a panel data of 54 mixed enterprise broadacre farms in Western Australia from 2002 to 2011. The study finds that omitting repayment obligations created in the production process in analysis results in underestimating partial inefficiency scores. Farm size, production diversification and rainfall zone are significant drivers of partial inefficiency. The implication of the study's findings is that failure to account for repayment obligations created in the production process may result in erroneous policy suggestions that undermine the efforts of farm businesses to minimise or avoid financial stress.

A Neural Network Approach for Software Reliability Prediction

The increasing reliance on computer software has raised significant concerns regarding software reliability evaluation. Over the past four decades, various software reliability models have been developed, encompassing both parametric and nonparametric approaches. However, no single model has demonstrated effectiveness in handling all types of datasets. In response to this challenge, the deep neural network (DNN), a powerful deep learning model, has emerged as a promising solution. By leveraging the flexibility and adaptability of artificial neural networks (ANN), the DNN model exhibits remarkable prediction performance by capturing training variables and exploring deeper layers. This study presents an approach that utilizes a DNN model based on an ANN architecture with multiple activation functions. This approach aims to estimate software reliability and predict the frequency of software flaws. Through extensive experimental analysis and validation, the proposed DNN model surpasses the predictive accuracy achieved by existing parametric and nonparametric models. These results highlight the potential of the DNN model in effectively addressing the complexities involved in software reliability evaluation. By combining the power of deep learning with the adaptability of ANN, the proposed model offers a promising and accurate solution for software reliability prediction.

Reverse engineering morphogenesis through Bayesian optimization of physics-based models

Morphogenetic programs coordinate cell signaling and mechanical interactions to shape organs. In systems and synthetic biology, a key challenge is determining optimal cellular interactions for predicting organ shape, size, and function. Physics-based models defining the subcellular force distribution facilitate this, but it is challenging to calibrate parameters in these models from data. To solve this inverse problem, we created a Bayesian optimization framework to determine the optimal cellular force distribution such that the predicted organ shapes match the experimentally observed organ shapes. This integrative framework employs Gaussian Process Regression, a non-parametric kernel-based probabilistic machine learning modeling paradigm, to learn the mapping functions relating to the morphogenetic programs that maintain the final organ shape. We calibrated and tested the method on Drosophila wing imaginal discs to study mechanisms that regulate epithelial processes ranging from development to cancer. The parameter estimation framework successfully infers the underlying changes in core parameters needed to match simulation data with imaging data of wing discs perturbed with collagenase. The computational pipeline identifies distinct parameter sets mimicking wild-type shapes. It enables a global sensitivity analysis to support the regulation of actomyosin contractility and basal ECM stiffness to generate and maintain the curved shape of the wing imaginal disc. The optimization framework, combined with experimental imaging, identified that Piezo, a mechanosensitive ion channel, impacts fold formation by regulating the apical-basal balance of actomyosin contractility and elasticity of ECM. This workflow is extensible toward reverse-engineering morphogenesis across organ systems and for real-time control of complex multicellular systems.

Modelling diffusion of innovation curves using radiocarbon data

Archaeological data provide a potential to investigate the diffusion of technological and cultural traits. However, much of this research agenda currently needs more formal quantitative methods to address small sample sizes and chronological uncertainty. This paper introduces a novel Bayesian framework for inferring the shape of diffusion curves using radiocarbon data associated with the presence/absence of a particular innovation. We developed two distinct approaches: 1) a hierarchical model that enables the fitting of an s-shaped diffusion curve whilst accounting for inter-site variations in the probability of sampling the innovation itself, and 2) a non-parametric model that can estimate the changing proportion of the innovation across user-defined time-blocks. The robustness of the two approaches was first tested against simulated datasets and then applied to investigate three case studies, the first pair on the diffusion of farming in prehistoric Japan and Britain and the third on cycles of changes in the burial practices of later prehistoric Britain.

Stability and economic performances in the banking industry: The case of China

We estimate stability performances in the Chinese banking industry over the 2007–2017 period using four risk indicators under nonparametric modelling. We are the first to calculate the risk indicator shadow prices, and we use a new way of studying the relationship between stability and economic performance. In particular, we reexamine stability performances when banks achieve their best economic performances. This questions the existence of stability rents, which form a prime reason for the banking authority to consider economic performance. Finally, we verify whether ownership has an impact on our results and investigate the role of the interest rate liberalization reforms.

Development and validation of health-oriented personal evaluation for the community-dwelling older person based on the International Classification of Functioning, Disability and Health.

The International Classification of Functioning, Disability and Health (ICF) offers a standardized international terminology to operationalize function management across multiple domains, but the summary score of the ICF qualifier scale provides limited information on the comparison of personal abilities and functioning difficulties. To enhance the interpretative power of the ICF-based Health-oriented Personal Evaluation for the community-dwelling older person (iHOPE-OP) scale through the implementation of the item response theory (IRT) modelling. This cross-sectional, multi-centre study administrated 161 ICF categories (58 on body functions, 15 on body structures, 60 on activities or participation and 28 on environmental factors) to evaluate the functional level of 338 older citizens (female = 158, male = 180) residing in community or supportive living facilities. The validation process encompassed assessing the IRT model fitness and evaluating the psychometric properties of the IRT-derived iHOPE-OP scale. The age of participants ranged from 60 to 94.57, with the mean age of 70. The analysis of non-parametric and parametric models revealed that the three-parameter logistic IRT model, with a dichotomous scoring principle, exhibited the best fit. The 53-item iHOPE-OP scale demonstrated high reliability (Cronbach's α = 0.9729, Guttman's lambda-2 = 0.9749, Molenaar-Sijtsma Statistic = 0.9803, latent class reliability coefficient = 0.9882). There was a good validity between person abilities and the Barthel Index (p < .001, r = .83), as well as instrumental activities of daily living (p < .001, r = .84). IRT methods generate the reliable and valid iHOPE-OP scale with the most discriminable and minimal items to represent the older person's functional performance at a comprehensive level. The use of the Wright map can aid in presby-functioning management by visualizing item difficulties and person abilities. Considering the intricate and heterogeneous health status of older persons, a single functional assessment tool might not fulfil the need to fully understand the multifaceted health status. For use in conjunction with the IRT and ICF framework, the reliable and valid iHOPE-OP scale was developed and can be applied to capture presby-functioning. The Wright map depicts the distribution of item difficulties and person abilities on the same scale that facilitates person-centred goal setting and tailors intervention.

Degradation modeling and remaining useful lifetime prediction based on functional variance process

AbstractDynamic fluctuation is a common phenomenon in degradation processes. Hence, how to model it properly has a great impact on the degradation modeling as well as the remaining useful lifetime prediction. To capture the dynamic features and to avoid the risk of the model mis‐specification, a nonparametric degradation model based on functional variance process is proposed in this article. The model is composed of a unit‐specific mean trend and a degradation fluctuation which follows a stochastic process. The mean trend is estimated by the local smoother method, while the stochastic fluctuation is estimated by the functional principal component analysis method. The asymptotic properties of the estimators are proved. Also, the prediction for the remaining useful lifetime is discussed and the estimator is proved to converge in distribution. Moreover, a Bayesian scheme is developed to forecast the remaining useful lifetime for units with incomplete degradation observations. Simulation results show the superiority of the proposed method by comparing it with some existing methods. Finally, two real data sets are analyzed and used to illustrate the application of the method.

Does Environmental, Social, and Governance (ESG) Performance Improve Financial Institutions’ Efficiency? Evidence from China

Nowadays, the call for sustainable development is becoming stronger in all countries of the world, and environmental, social, and governance (ESG) performance, as a vivid practice of this concept, has gradually received extensive attention from enterprises and investors. Financial institutions have an important position in the national economy as an important tool for the state to regulate the macroeconomy. Whether ESG performance can improve financial institutions’ efficiency is of key significance for boosting sustainable development. Based on data from China’s listed financial institutions from 2015 to 2021, this study aims to investigate the impact of ESG performance on financial institutions. The robust nonparametric boundary model and fixed-effects model are employed for analysis. The empirical results demonstrate that ESG performance and its sub-indicators of environmental performance and social responsibility performance can significantly enhance financial institutions’ efficiency. In particular, this effect is more pronounced in the securities industry and diversified financial industry, as well as in non-state and small-scale financial institutions. The results remain unchanged after a series of robustness tests. Furthermore, the mechanism tests indicate that ESG performance can enhance financial institutions’ efficiency by reducing downside risk and agency costs.

A new computational framework for log-concave density estimation

AbstractIn statistics, log-concave density estimation is a central problem within the field of nonparametric inference under shape constraints. Despite great progress in recent years on the statistical theory of the canonical estimator, namely the log-concave maximum likelihood estimator, adoption of this method has been hampered by the complexities of the non-smooth convex optimization problem that underpins its computation. We provide enhanced understanding of the structural properties of this optimization problem, which motivates the proposal of new algorithms, based on both randomized and Nesterov smoothing, combined with an appropriate integral discretization of increasing accuracy. We prove that these methods enjoy, both with high probability and in expectation, a convergence rate of order 1/T up to logarithmic factors on the objective function scale, where T denotes the number of iterations. The benefits of our new computational framework are demonstrated on both synthetic and real data, and our implementation is available in a github repository (Log-Concave Computation).

Nonparametric Modelling of Ship Dynamics Using Puma Optimizer Algorithm-Optimized Twin Support Vector Regression

Ship dynamic models serve as the foundation for designing ship controllers, trajectory planning, and obstacle avoidance. Support vector regression (SVR) is a commonly used nonparametric modelling method for ship dynamics. Achieving high accuracy SVR models requires a substantial amount of training samples. Additionally, as the number of training samples increases, the computational efficiency for solving the quadratic programming problem (QPP) of SVR decreases. Ship controllers demand dynamic models with both high accuracy and computational efficiency. Therefore, to enhance the prediction accuracy and computational efficiency of SVR, this paper proposes a nonparametric modelling method based on twin SVR (TSVR). TSVR replaces a large QPP with a set of smaller QPPs, significantly enhancing generalizability and computational efficiency. To further improve the predictive accuracy of TSVR, the puma optimizer algorithm is employed to determine the optimal hyperparameters. The performance of the proposed method is validated using a Mariner class vessel. Gaussian white noise is introduced into the modelling data to simulate measurement error. The TSVR model accurately predicts various zigzag and turning circle manoeuvring motions under disturbance conditions, demonstrating its robustness and generalizability. Compared to the SVR model, the TSVR model achieves lower root mean square error and computational time, confirming its superior predictive accuracy and computational efficiency.

Genomic prediction of blood biomarkers of metabolic disorders in Holstein cattle using parametric and nonparametric models

BackgroundMetabolic disturbances adversely impact productive and reproductive performance of dairy cattle due to changes in endocrine status and immune function, which increase the risk of disease. This may occur in the post-partum phase, but also throughout lactation, with sub-clinical symptoms. Recently, increased attention has been directed towards improved health and resilience in dairy cattle, and genomic selection (GS) could be a helpful tool for selecting animals that are more resilient to metabolic disturbances throughout lactation. Hence, we evaluated the genomic prediction of serum biomarkers levels for metabolic distress in 1353 Holsteins genotyped with the 100K single nucleotide polymorphism (SNP) chip assay. The GS was evaluated using parametric models best linear unbiased prediction (GBLUP), Bayesian B (BayesB), elastic net (ENET), and nonparametric models, gradient boosting machine (GBM) and stacking ensemble (Stack), which combines ENET and GBM approaches.ResultsThe results show that the Stack approach outperformed other methods with a relative difference (RD), calculated as an increment in prediction accuracy, of approximately 18.0% compared to GBLUP, 12.6% compared to BayesB, 8.7% compared to ENET, and 4.4% compared to GBM. The highest RD in prediction accuracy between other models with respect to GBLUP was observed for haptoglobin (hapto) from 17.7% for BayesB to 41.2% for Stack; for Zn from 9.8% (BayesB) to 29.3% (Stack); for ceruloplasmin (CuCp) from 9.3% (BayesB) to 27.9% (Stack); for ferric reducing antioxidant power (FRAP) from 8.0% (BayesB) to 40.0% (Stack); and for total protein (PROTt) from 5.7% (BayesB) to 22.9% (Stack). Using a subset of top SNPs (1.5k) selected from the GBM approach improved the accuracy for GBLUP from 1.8 to 76.5%. However, for the other models reductions in prediction accuracy of 4.8% for ENET (average of 10 traits), 5.9% for GBM (average of 21 traits), and 6.6% for Stack (average of 16 traits) were observed.ConclusionsOur results indicate that the Stack approach was more accurate in predicting metabolic disturbances than GBLUP, BayesB, ENET, and GBM and seemed to be competitive for predicting complex phenotypes with various degrees of mode of inheritance, i.e. additive and non-additive effects. Selecting markers based on GBM improved accuracy of GBLUP.

Combining Nonparametric and Parametric Item Response Theory to Explore Data Quality: Illustrations and a Simulation Study

ABSTRACT Researchers who use measurement models for evaluation purposes often select models with stringent requirements, such as Rasch models, which are parametric. Mokken Scale Analysis (MSA) offers a theory-driven nonparametric modeling approach that may be more appropriate for some measurement applications. Researchers have discussed using MSA as a preliminary procedure with which to evaluate data quality before applying a parametric model. However, the literature includes only a few examples in which researchers have integrated MSA techniques with parametric models throughout the analytic procedure. We consider a systematic approach for integrating results from nonparametric MSA techniques with parametric measurement models to evaluate measurement quality and construct scales with useful measurement properties. We use real-data illustrations and a simulation study to demonstrate and systematically explore our approach. We discuss implications for research and practice.

Extended Asymptotic Identifiability of Nonparametric Item Response Models.

Nonparametric item response models provide a flexible framework in psychological and educational measurements. Douglas (Psychometrika 66(4):531-540, 2001) established asymptotic identifiability for a class of models with nonparametric response functions for long assessments. Nevertheless, the model class examined in Douglas (2001) excludes several popular parametric item response models. This limitation can hinder the applications in which nonparametric and parametric models are compared, such as evaluating model goodness-of-fit. To address this issue, We consider an extended nonparametric model class that encompasses most parametric models and establish asymptotic identifiability. The results bridge the parametric and nonparametric item response models and provide a solid theoretical foundation for the applications of nonparametric item response models for assessments with many items.

Optimal smoothing parameter selection in single-index model derivative estimation

. Single-index model is one of the most popular semiparametric models in applied econometrics. Estimation of the derivative function is often of crucial importance, as studying “marginal effects” serves as a cornerstone of microeconomics. A prerequisite for the successful application of nonparametric/semiparametric kernel estimation methods is to select smoothing parameters properly to balance the estimation squared bias and variance. Henderson et al. (2015) propose a novel method for selecting the smoothing parameters optimally for derivative function estimation. However, their method suffers from the “curse of diemnsionality” problem in a multivariate nonparametric regression model. In this article, we extend the work of Henderson et al. (2015) to estimation of the derivative function of a single-index model. Specifically, we propose a data-driven method to select smoothing parameters optimally for single-index model derivative function estimation. We also derive the asymptotic distribution of the resulting local linear estimator of the derivative function. Both simulations and empirical applications show that the proposed method works well in practice.

Non-parametric quantile regression-based modelling of additive effects to solar irradiation in Southern Africa

Modelling of solar irradiation is paramount to renewable energy management. This warrants the inclusion of additive effects to predict solar irradiation. Modelling of additive effects to solar irradiation can improve the forecasting accuracy of prediction frameworks. To help develop the frameworks, this current study modelled the additive effects using non-parametric quantile regression (QR). The approach applies quantile splines to approximate non-parametric components when finding the best relationships between covariates and the response variable. However, some additive effects are perceived as linear. Thus, the study included the partial linearly additive quantile regression model (PLAQR) in the quest to find how best the additive effects can be modelled. As a result, a comparative investigation on the forecasting performances of the PLAQR, an additive quantile regression (AQR) model and the new quantile generalised additive model (QGAM) using out-of-sample and probabilistic forecasting metric evaluations was done. Forecasted density plots, Murphy diagrams and results from the Diebold–Mariano (DM) hypothesis test were also analysed. The density plot, the curves on the Murphy diagram and most metric scores computed for the QGAM were slightly better than for the PLAQR and AQR models. That is, even though the DM test indicates that the PLAQR and AQR models are less accurate than the QGAM, we could not conclude an outright greater forecasting performance of the QGAM than the PLAQR or AQR models. However, in situations of probabilistic forecasting metric preferences, each model can be prioritised to be applied to the metric where it performed slightly the best. The three models performed differently in different locations, but the location was not a significant factor in their performances. In contrast, forecasting horizon and sample size influenced model performance differently in the three additive models. The performance variations also depended on the metric being evaluated. Therefore, the study has established the best forecasting horizons and sample sizes for the different metrics. It was finally concluded that a 20% forecasting horizon and a minimum sample size of 10000 data points are ideal when modelling additive effects of solar irradiation using non-parametric QR.

Stock market prices and Dividends in the US: Bubbles or Long-run equilibria relationships?

This paper presents a novel approach to identifying potential bubbles in the US stock market by employing alternative time series methods based on long memory, including fractional integration and cointegration, as well as duration dependence non-parametric models. To test for duration dependence, the paper employs a unique non-parametric hazard function estimation method, using monotonic P-splines, which enables the estimation of a coherent and sophisticated Bayesian confidence interval for the function. By analyzing historical data of real US stock index from January 1871 to November 2022, the results reveal strong evidence of bubbles in the US stock market. It is worth noting that this is the first time a fractional integration approach and a novel non-parametric hazard function have been utilized to test for rational speculative bubbles in the US stock market, making this paper a significant contribution to the field.

Enhancing healthcare decision support through explainable AI models for risk prediction

Electronic health records (EHRs) are a valuable source of information that can aid in understanding a patient’s health condition and making informed healthcare decisions. However, modelling longitudinal EHRs with heterogeneous information is a challenging task. Although recurrent neural networks (RNNs) are frequently utilized in artificial intelligence (AI) models for capturing longitudinal data, their explanatory capabilities are limited. Predictive clustering stands as the most recent advancement within this domain, offering interpretable indications at the cluster level for predicting disease risk. Nonetheless, the challenge of determining the optimal number of clusters has put a brake on the widespread application of predictive clustering for disease risk prediction. In this paper, we introduce a novel non-parametric predictive clustering-based risk prediction model that integrates the Dirichlet Process Mixture Model (DPMM) with predictive clustering via neural networks. To enhance the model’s interpretability, we integrate attention mechanisms that enable the capture of local-level evidence in addition to the cluster-level evidence provided by predictive clustering. The outcome of this research is the development of a multi-level explainable artificial intelligence (AI) model. We evaluated the proposed model on two real-world datasets and demonstrated its effectiveness in capturing longitudinal EHR information for disease risk prediction. Moreover, the model successfully produced interpretable evidence to bolster its predictions.

Partially fixed bayesian additive regression trees

Bayesian Additive Regression Trees (BART) is a widely popular nonparametric regression model known for its accurate prediction capabilities. In certain situations, there is knowledge suggesting the existence of certain dominant variables. However, the BART model fails to fully utilize the knowledge. To tackle this problem, the paper introduces a modification to BART known as the Partially Fixed BART model. By fixing a portion of the trees' structure, this model enables more efficient utilization of prior knowledge, resulting in enhanced estimation accuracy. Moreover, the Partially Fixed BART model can offer more precise estimates and valuable insights for future analysis even when such prior knowledge is absent. Empirical results substantiate the enhancement of the proposed model in comparison to the original BART.

Leveraging Transformer-Based Non-Parametric Probabilistic Prediction Model for Distributed Energy Storage System Dispatch

In low-voltage distribution networks, distributed energy storage systems (DESSs) are widely used to manage load uncertainty and voltage stability. Accurate modeling and estimation of voltage fluctuations are crucial to informed DESS dispatch decisions. However, existing parametric probabilistic approaches have limitations in handling complex uncertainties, since they always rely on predefined distributions and complex inference processes. To address this, we integrate the patch time series Transformer model with the non-parametric Huberized composite quantile regression method to reliably predict voltage fluctuation without distribution assumptions. Comparative simulations on the IEEE 33-bus distribution network show that the proposed model reduces the DESS dispatch cost by 6.23% compared to state-of-the-art parametric models.