Empirical Error Research Articles

Unsupervised Learning‐Guided Accelerated Discovery of Alkaline Anion Exchange Membranes for Fuel Cells

AbstractWithout insight into the correlation between the structure and properties, anion exchange membranes (AEMs) for fuel cells are developed usually using the empirical trial and error method or simulation methods. Here, a virtual module compound enumeration screening (V‐MCES) approach, which does not require the establishment of expensive training databases and can search the chemical space containing more than 4.2×105 candidates was proposed. The accuracy of the V‐MCES model was considerably improved when the model was combined with supervised learning for the feature selection of molecular descriptors. Techniques from V‐MCES, correlating the molecular structures of the AEMs with the predicted chemical stability, generated a ranking list of potential high stability AEMs. Under the guidance of V‐MCES, highly stable AEMs were synthesized. With understanding of AEM structure and performance by machine learning, AEM science may enter a new era of unprecedented levels of architectural design.

Homogeneity Test of Many-to-One Relative Risk Ratios in Unilateral and Bilateral Data with Multiple Groups

In medical clinical studies, we often encounter paired organs’ unilateral or bilateral data. For bilateral data, there exists an intraclass correlation between paired organs. Under an intraclass correlation model, this paper proposes asymptotic statistics for testing the equality of many-to-one relative risk ratios in combined unilateral and bilateral data. Furthermore, we calculate the explicit expressions of these statistics. Moreover, these procedures are adequate to solve the hypothesis problems of unilateral or bilateral data. Through comparison, the simulation results show that the score test has a robust empirical type-I error rate and sufficient power. We provide a clinical trial of acute otitis media to illustrate our proposed methods.

Joint Frailty Model of Recurrent and Terminal Events in the Presence of Cure Fraction using a Bayesian Approach

Introduction: Recurrent event data are common in many longitudinal studies. Often, a terminating event such as death can be correlated with the recurrent event process. A shared frailty model applied to account for the association between recurrent and terminal events. In some situations, a fraction of subjects experience neither recurrent events nor death; these subjects are cured.
 Methods: In this paper, we discussed the Bayesian approach of a joint frailty model for recurrent and terminal events in the presence of cure fraction. We compared estimates of parameters in the Frequentist and Bayesian approaches via simulation studies in various sample sizes; we applied the joint frailty model in the presence of cure fraction with Frequentist and Bayesian approaches for breast cancer.
 Results: In small sample size Bayesian approach compared to Frequentist approach had a smaller standard error and mean square error, and the coverage probabilities close to nominal level of 95%. Also, in Bayesian approach, the sampling means of the estimated standard errors were close to the empirical standard error.
 Conclusion: The simulation results suggested that when sample size was small, the use of Bayesian joint frailty model in the presence of cure fraction led to more efficiency in parameter estimation and statistical inference.

Intraday Periodic Volatility Curves

The volatility of financial asset returns displays pronounced variation over the trading day. Our goal is nonparametric inference for the average intraday volatility pattern, viewed as a function of time-of-day. The functional inference is based on a long span of high-frequency return data. Our setup allows for general forms of volatility dynamics, including time-variation in the intraday pattern. The estimation is based on forming local volatility estimates from the high-frequency returns over overlapping blocks of asymptotically shrinking size, and then averaging these estimates across days in the sample. The block-based estimation of volatility renders the error in the estimation due to the martingale return innovation asymptotically negligible. As a result, the centered and scaled calendar volatility effect estimator converges to a Gaussian process determined by the empirical process error associated with estimating average volatility across the trading day. Feasible inference is obtained by consistently estimating the limiting covariance operator. Simulation results corroborate our theoretical findings. In an application to S&P 500 futures data, we find evidence for a shift in the intraday volatility pattern over time, including a more pronounced role for volatility outside U.S. trading hours in the latter part of the sample. Supplementary materials for this article are available online.

Hold-out estimates of prediction models for Markov processes

We consider the selection of prediction models for Markovian time series. For this purpose, we study the theoretical properties of the hold-out method. In the econometrics literature, the hold-out method is called ‘out-of-sample’ and is the main method to select a suitable time series model. This method consists of estimating models on a learning set and picking up the model with minimal empirical error on a validation set of future observations. Hold-out estimates are well studied in the independent case, but, as far as we know, this is not the case when the validation set is not independent of the learning set. In this paper, assuming uniform ergodicity of the Markov chain, we state generalization bounds and oracle inequalities for such method; in particular, we show that the ‘out-of-sample’ selection method is adaptive to noise condition.

Abstract P599: Should Regression Calibration or Multiple Imputation Be Used When Calibrating Different Devices in a Longitudinal Study?

Objective: In longitudinal studies, devices used to measure exposures, like pulse wave velocity (PWV), can change from visit to visit. Calibration studies, where a subset of participants receive measurements from both devices at follow-up, are often used to assess differences in the device measurements. Regression calibration and multiple imputation are common statistical methods to correct for those differences, but no study yet exists to compare the two when the quantity of interest is change in the exposure over time. We compared both methods in a hypothetical study of change in PWV and its association with total brain volume. Methods: We simulated true values of PWV at baseline and follow up, as well as imperfect measurements of PWV using an “old” device and “new” device. Two statistical methods were compared: regression calibration , which calibrates the new device measurements at follow up to the old device using linear regression in a calibration study; and multiple imputation , which imputes the (mostly) missing old device measurements at follow up.We varied the bias and measurement error of each device and for each scenario simulated 1,000 datasets of size n=2,500. Two percent of participants in each iteration were chosen to participate in the calibration study, and thus had measurements on the old and new devices at follow up. We used 200 bootstrap replicates to calculate the standard errors for the regression calibration method and 50 imputed datasets for the multiple imputation method. To compare the methods we used bias of the estimated association and how well the standard errors approximated the empirical standard errors. Results: Regression calibration was virtually unbiased for the association between change in PWV and total brain volume when the old device had larger measurement error than the new device. The maximum bias for regression calibration across all scenarios was still small (6%). When the old device had more measurement error or the two devices had equal measurement error, multiple imputation underestimated the association by more than 10%. This underestimation was reduced to approximately 2% when the new device had a larger measurement error than the old device. In all scenarios, regression calibration underestimated the empirical standard error by approximately 35%, while multiple imputation underestimated it by only 2-5%. Conclusions: In analyses of change in PWV and total brain volume, when unbiased estimation is the main objective, regression calibration is favorable to multiple imputation. When null hypothesis significance testing is the main objective, multiple imputation may be favorable in order to not underestimate the standard errors. We expect these conclusions to apply to other change in exposure and outcome relationships with similar ratios between the association’s magnitude and the amount of measurement error.

Data-driven risk-averse newsvendor problems: developing the CVaR criteria and support vector machines

Incorporating decision-makers' risk preferences into data-driven newsvendor models and developing machine learning methods to solve the models are the challenging problems addressed in this study. To consider different distributions and decision-makers' different risk preferences for the two losses of the total cost newsvendor model, the symmetrical, the partial symmetrical and the asymmetrical CVaR criteria are introduced. The regularisation, the primal-dual approach and the kernels in support vector machines are used to transform the data-driven risk-averse newsvendor problems under the CVaR criterion into the convex quadratic programming problems with good theoretical properties. Computational experiments are conducted on a real-world dataset. The models under the partial symmetrical and the asymmetrical CVaR criteria obtained good performances, but that under the symmetrical CVaR criterion suffered the underfitting problem. Two factors including the degrees of risk aversion for the two losses in the total cost newsvendor model and the empirical errors of data-driven models affect order decisions. The degrees of risk aversion for the two losses have anti-directional effects on order quantities. The introduction of asymmetrical CVaR criterion paves a new way to reveal the effects of different risk references for different losses on order decisions, and has the potential to improve newsvendor decisions.

Estimation in discrete time coarsened multivariate longitudinal models.

We consider the analysis of longitudinal data of multiple types of events where some of the events are observed on a coarser level (e.g. grouped) at some time points during the follow-up, for example, when certain events, such as disease progression, are only observable during parts of follow-up for some subjects, causing gaps in the data, or when the time of death is observed but the cause of death is unknown. In this case, there is missing data in key characteristics of the event history such as onset, time in state, and number of events. We derive the likelihood function, score and observed information under independent and non-informative coarsening, and conduct a simulation study where we compare bias, empirical standard errors, and confidence interval coverage of estimators based on direct maximum likelihood, Monte Carlo Expectation Maximisation, ignoring the coarsening thus acting as if no event occurred, and artificial right censoring at the first time of coarsening. Longitudinal data on drug prescriptions and survival in men receiving palliative treatment for prostate cancer is used to estimate the parameters of one of the data-generating models. We demonstrate that the performance depends on several factors, including sample size and type of coarsening.

The adhesive energies between Poly(3‐hexylthiophene) and Polyvinylpyrrolidone for organic electronic devices: Hybrid‐exchange density‐functional‐theory studies

AbstractStudying the building blocks for organic electronics—molecules—is important for achieving a great performance for organic electronic devices. Poly(3‐hexylthiophene) (P3HT) and povidone (PVP) are common molecules chosen for the semiconducting and dielectric layers of organic electronic devices, respectively. Here, we have applied the hybrid‐exchange density‐functional theory, taking into account empirical dispersion forces and basis set superposition errors, to study the adhesive energies and optimal geometries when integrating the two types of molecules. To ease the analysis of the molecular structures, we have simplified the polymer chain structure to the monomer, dimer and trimer for the P3HT and PVP. By using B3LYP and BLYP functionals in combination with dispersion forces, we have found that the optimal inter‐molecular vertical distances between P3HT and PVP are approximately 3.6, 6 and 5 Å for monomer, dimer and trimer, respectively, with the lowest adsorption energy of ~−0.35, −0.15 and −0.45 eV. However, the sliding effect for the molecular combination is relatively small. These computational results can be potentially compared with the relevant experiments on the molecular crystal structure. The molecular orbitals of the P3HT and PVP molecules show that the charge density is mainly on the five‐member rings rather than the polymer chains, which further supports our finite‐chain approximation. Our calculations, especially the potential curves, could be useful for the optimal design of molecular structures for organic electronic devices.

AUTOMATED PARAMETER SEARCH FOR FRACTAL FUNCTIONS IN DATA FITTING PROBLEMS

Parameter optimization is an important problem in the theory of fractal interpolation functions and data fitting. In the literature, the methods for determining values of parameters in data fitting problems are developed only for affine and recurrent affine fractal interpolation functions. There is still no direct method to determine the optimum values of parameters for various types of fractal functions. The aim of this paper is to apply an automated parameter search algorithm from machine learning to the problem of parameters optimization when we use a class of fractal functions to fit a given data set. We first establish a finite set of fractal interpolation functions, and then consider three linear combinations of these functions to fit a given data set. We apply Optuna to find the optimum values of hyperparameters in our approach that minimize the given empirical error. Two examples are given to show the results. Our approach can be applied to many types of fractal functions, and even their linear combinations. The advantage of tuning hyperparameters of fractal functions by AI-based algorithms is that it is not limited to the construction methods and forms of fractal functions.

Deep-Quantile-Regression-Based Surrogate Model for Joint Chance-Constrained Optimal Power Flow With Renewable Generation

Joint chance-constrained optimal power flow (JCC-OPF) is a promising tool for managing distributed renewable generation uncertainties. However, existing works are usually based on power flow equations, which require accurate network parameters that may be unobservable in many distribution systems. To address this issue, this paper proposes a learning-based surrogate model for JCC-OPF with renewable generation. This model equivalently converts joint chance constraints into quantile-based forms. Two multi-layer perceptrons are trained based on special loss functions to predict the quantile of constraint violations and expected power loss. By reformulating these two MLPs into mixed-integer linear constraints, we can replicate the JCC-OPF without network parameters. Two pre-processing steps, i.e., data augmentation and calibration, are further developed to improve its performance. The former trains a simulator to generate more training samples for enhancing the prediction accuracy of MLPs. The latter designs a positive parameter based on empirical prediction errors to calibrate the outputs of MLPs so that feasibility can be guaranteed. Numerical experiments based on the IEEE 33- and 123-bus systems validate that the proposed model can achieve desirable feasibility and optimality simultaneously with no need for network parameters.

Finding the Number of Clusters Using a Small Training Sequence

In clustering the training sequence (TS), K-means algorithm tries to find empirically optimal representative vectors that achieve the empirical minimum to inductively design optimal representative vectors yielding the true optimum for the underlying distribution. In this paper, the convergence rates on the clustering errors are first observed as functions of β <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-α</sup> , where β is the training ratio that relates the training sequence size to the number of representative vectors, and α is a non-negative constant. From the convergence rates, we can observe the training performance for a finite TS size. If the TS size is relatively small, errors occur in finding the number of clusters. In order to reduce the errors from small TS sizes, a compensation constant (1-β <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-α</sup> ) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> for the empirical errors is devised based on the rate analyses and a novel algorithm for finding the number of clusters is proposed. The compensation constant can be applied to other clustering applications especially when the TS size is relatively small.

ВИЗНАЧЕННЯ ТОВЩИНИ ПЛАЗМОН-НОСІЙНИХ ШАРІВ ФОТОМЕТРИЧНИМ МЕТОДОМ

The influence of design and technological factors, in particular, the deviation of the thickness of the plasma-carrying layer from the nominal value, introduces uncertainty into the measurement by the method of surface plasmon resonance. The effect of the thickness of nanoscale films of surface plasmon resonance sensors on the characteristics of these sensors is shown in the work using the method of numerical modeling. An experimental study of the transmission spectra and reflection characteristics of gold films of different thicknesses was conducted and consistency with theoretical calculations was established. Transmittance coefficients were used as an informative parameter for estimating the thickness of nanosized gold films of surface plasmon resonance sensors. Not only the difference in the angular positions of the resonance and the intensity of the reflected light in it, but also the different width of the resonance characteristics in the region of the minimum and the shape of the intensity graph at angles smaller than the critical one are characteristic for samples with different thicknesses. The correlation coefficient between the thickness of the studied samples and the corresponding transmission coefficients at a wavelength of 532 nm is r = - 0.943. This means that there is a correlation between the parameters, there is a linear functional dependence between them. An empirical dependence of d=1100.7712·T-0.3328 with a high degree of correlation (r = - 0.943) was established between the thickness and the corresponding transmittance coefficients of gold films for λ=532 nm. With this relative empirical error of thickness determination does not exceed 3%. The dependence of the maximum transmission spectrum Tλmax of nanosized gold films on the thickness of these films was experimentally established. At this step, the thickness determination did not exceed 1 Ǻ. The research data show the prospects of using the monochromatic photometric method to determine the thickness of plasma-carrying nanoscale layers.

Blending Sea Surface Winds from the HY-2 Satellite Scatterometers Based on a 2D-Var Method

The launch of the Haiyang-2 (HY-2) satellite constellation fosters the quick acquisition of global sea surface vector winds from the perspective of remote sensing. This study intends to develop a six-hourly mesoscale analysis of sea surface winds based on the microwave scatterometers onboard the HY-2 satellite series, with the objective of meeting the considerable demand for accurate and gap-free ocean wind forcing products. First, the accuracy of HY-2 scatterometers (HSCATs) in measuring wind is evaluated. In particular, the standard deviation (SD) errors of HSCATs data are assessed using the collocated buoy measurements with different temporal windows in order to account for the temporal representativeness errors in the blending analysis. Afterwards, a two-dimensional variational (2D-Var) method is implemented to blend the HSCATs measured winds and the European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis winds over the global ocean surface. This approach is different from existing methods in that it takes both wind error and background error correlation into account. The results show that the blended wind product is of a promising quality compared with independent wind references. Interestingly, the blended winds derived from 2D-Var in combination with an empirical background error correlation show smaller SD errors than those using a Gaussian error correlation function. Overall, the blended wind product should be valuable for forcing global ocean models or describing air-sea interaction processes on a scale close to the scatterometer measurements.

Time efficient variants of Twin Extreme Learning Machine

Twin Extreme Learning Machine models can obtain better generalization ability than the standard Extreme Learning Machine model. But, they require to solve a pair of quadratic programming problems for this. It makes them more complex and computationally expensive than the standard Extreme Learning Machine model. In this paper, we propose two novel time-efficient formulations of the Twin Extreme Learning Machine, which only require the solution of systems of linear equations for obtaining the final classifier. In this sense, they can combine the benefits of the Twin Support Vector Machine and standard Extreme Learning Machine in the true sense. We term our first formulation as ‘Least Squared Twin Extreme Learning Machine’. It minimizes the L2-norm of error variables in its optimization problem. Our second formulation ‘Weighted Linear loss Twin Extreme Learning Machine’ uses the weighted linear loss function for calculating the empirical error, which makes it insensitive towards outliers. Numerical results obtained with multiple benchmark datasets show that proposed formulations are time efficient with better generalization ability. Further, we have used the proposed formulations in the detection of phishing websites and shown that they are much more effective in the detection of phishing websites than other Extreme Learning Machine models.

Riemannian representation learning for multi-source domain adaptation

Multi-Source Domain Adaptation (MSDA) aims at training a classification model that achieves small target error, by leveraging labeled data from multiple source domains and unlabeled data from a target domain. The source and target domains are described by related but different joint distributions, which lie on a Riemannian manifold named the statistical manifold. In this paper, we characterize the joint distribution difference by the Hellinger distance, which bears strong connection to the Riemannian metric defined on the statistical manifold. We show that the target error of a neural network classification model is upper bounded by the average source error of the model and the average Hellinger distance, i.e., the average of multiple Hellinger distances between the source and target joint distributions in the network representation space. Motivated by the error bound, we introduce Riemannian Representation Learning (RRL): An approach that trains the network model by minimizing (i) the average empirical Hellinger distance with respect to the representation function, and (ii) the average empirical source error with respect to the network model. Specifically, we derive the average empirical Hellinger distance by constructing and solving unconstrained convex optimization problems whose global optimal solutions are easy to find. With the network model trained, we expect it to achieve small error in the target domain. Our experimental results on several image datasets demonstrate that the proposed RRL approach is statistically better than the comparison methods.

Simulation and Validation of Optimized PID Controller in AGV (Automated Guided Vehicles) Model Using PSO and BAS Algorithms.

Automated guided vehicles (AGVs) are popular subsets of robots that come in various shapes and sizes. The group's use in the industry ranges from applications for carrying pallets, carts, and utensils to helping the elderly or transporting medicine to hospitals. Even recently, they have been used in libraries to carry books on shelves. The main part of an AGV includes its body, motor, driver, processor, and sensors, which are more or less the same in all types of AGVs, and addons vary depending on the application and the work environment. The part that affects AGV performance is the control strategy, to which researchers have shown different approaches. Using various techniques and simulations to obtain a model is the key and can help to improve and evaluate the performance of the strategy of the robot. In this study, based on the actual design of the AGV system, all data and components are described, and the simulation is performed in MATLAB software. Then, for controlling the platform based on the PID controller tuning, four methods of Ziegler Nichols, empirical, Particle Swarm Optimization (PSO), and Beetle Antennae Searching (BAS) (optimizer) are discussed, and the results are compared in the four paths including the circle, ellipse, Spiral and 8-shaped paths by observing and testing the tuned PID parameters. Finally, a series of subsequent experiences were carried out in CoppeliaSim (VREP) as a famous robot simulator to overcome the environmental constraints for the same paths that were used in Matlab based on the extracted PID values. Based on the results, the empirical methods, PSO, and BAS errors are very close together. But in general, the BAS algorithm is the fastest, and the PSO had better performance. In general, the maximum error is linked to the path of 8 shapes and the minimum is related to circle shape one. Finally, the analysis of results in different paths in both simulators shows the same results. Therefore, concerning the limited test on the real platform and using the PID coefficients obtained from the simulation shows the model's ability for the researchers in robotic research.

An Interval Analysis Scheme Based on Empirical Error and MCMC to Quantify Uncertainty of Wind Speed

The widespread existence of uncertainty makes power system control and decision-making face various risks, especially the interconnection of modern large-scale power systems, which makes its influence range more extensive. In smart grid, the renewable energy prediction and uncertainty analysis methods represented by wind power generation have attracted extensive attention. In this study, an adaptive parameter selection method based on Kullback−Leibler divergence is designed to fully extract the potential information of data. The grey wolf optimization based on reverse learning is used for prediction optimization, identifying historical data, processing dynamic information, and improving the accuracy of the model. In interval prediction, an interval prediction method combining empirical error, quantile statistics, and Markov Chain Monte Carlo is creatively proposed to generate a large number of independent error cases, and form a series of interval predictions with given confidence according to the quantile of random simulation results. Taking wind speed forecasting as an example, it is verified that the method proposed in this article has good performance. Using interval analysis to quantify the volatility and randomness can provide new ideas for load forecasting in power system and renewable energy output forecasting.

Assessment of human error contribution to maritime pilot transfer operation under HFACS-PV and SLIM approach

Human factor plays an important role in sustainable maritime transportation. Human errors are the leading cause of death or injuries during maritime pilot transfer operations despite international regulations. This paper proposes a hybrid human factors analysis model, comprised of qualitative and quantitative approaches by combining Success Likelihood Index Method (SLIM) and Human Factor Analysis and Classification System (HFACS) methods, to obtain the seafarers’ errors in the pilot boarding and disembarking. Human errors in the maritime pilot transfer process are determined by examining accident reports, literature reviews and expert judgments. Accidents and near misses are often poorly reported in the maritime industry. Therefore, determining human error probability (HEP) is of paramount importance in maritime transportation. This paper conducts an empirical human error prediction for a maritime pilot transfer operation to enhance operational safety and minimize human errors, providing a methodological extension through the integration of the HFACS technique into the SLIM. Utilizing HFACS and SLIM constitutes the unique contribution of this paper by predicting the possibility of human error since it presents the first application of the maritime industry. Thus, possible loss of life and injury will be prevented, the sustainability of maritime safety will be contributed, and pilots will be provided to work in a safe environment.

Generating synthetic mixed discrete-continuous health records with mixed sum-product networks.

Privacy is a concern whenever individual patient health data is exchanged for scientific research. We propose using mixed sum-product networks (MSPNs) as private representations of data and take samples from the network to generate synthetic data that can be shared for subsequent statistical analysis. This anonymization method was evaluated with respect to privacy and information loss. Using a simulation study, information loss was quantified by assessing whether synthetic data could reproduce regression parameters obtained from the original data. Predictors variable types were varied between continuous, count, categorical, and mixed discrete-continuous. Additionally, we measured whether the MSPN approach successfully anonymizes the data by removing associations between background and sensitive information for these datasets. The synthetic data generated with MSPNs yielded regression results highly similar to those generated with original data, differing less than 5% in most simulation scenarios. Standard errors increased compared to the original data. Particularly for smaller datasets (1000 records), this resulted in a discrepancy between the estimated and empirical standard errors. Sensitive values could no longer be inferred from background information for at least 99% of tested individuals. The proposed anonymization approach yields very promising results. Further research is required to evaluate its performance with other types of data and analyses, and to predict how user parameter choices affect a bias-privacy trade-off. Generating synthetic data from MSPNs is a promising, easy-to-use approach for anonymization of sensitive individual health data that yields informative and private data.