Residual Square Error Research Articles

Deep Neural Networks Guided Ensemble Learning for Point Estimation

In modern statistics, interests shift from pursuing the uniformly minimum variance unbiased estimator to reducing mean squared error (MSE) or residual squared error. Shrinkage-based estimation and regression methods offer better prediction accuracy and improved interpretation. However, the characterization of such optimal statistics in terms of minimizing MSE remains open and challenging in many problems, for example, estimating the treatment effect in adaptive clinical trials with pre-planned modifications to design aspects based on accumulated data. From an alternative perspective, we propose a deep neural network based automatic method to construct an improved estimator from existing ones. Theoretical properties are studied to provide guidance on applicability of our estimator to seek potential improvement. Simulation studies demonstrate that the proposed method has considerable finite-sample efficiency gain compared to several common estimators. In the Adaptive COVID-19 Treatment Trial (ACTT) as a motivating example, our ensemble estimator essentially contributes to a more ethical and efficient adaptive clinical trial with fewer patients enrolled. The proposed framework can be generally applied to various statistical problems, and can serve as a reference measure to guide statistical research.

Cross-sectional Ct distributions from qPCR tests can provide an early warning signal for the spread of COVID-19 in communities.

SARS-CoV-2 PCR testing data has been widely used for COVID-19 surveillance. Existing COVID-19 forecasting models mainly rely on case counts obtained from qPCR results, even though the binary PCR results provide a limited picture of the pandemic trajectory. Most forecasting models have failed to accurately predict the COVID-19 waves before they occur. Recently a model utilizing cross-sectional population cycle threshold (Ct-the number of cycles required for the fluorescent signal to cross the background threshold) values obtained from PCR tests (Ct-based model) was developed to overcome the limitations of using only binary PCR results. In this study, we aimed to improve on COVID-19 forecasting models using features derived from the Ct-based model, to detect epidemic waves earlier than case-based trajectories. PCR data was collected weekly at Northeastern University (NU) between August 2020 and January 2022. Campus and county epidemic trajectories were generated from case counts. A novel forecasting approach was developed by enhancing a recent deep learning model with Ct-based features and applied in Suffolk County and NU campus. For this, cross-sectional Ct values from PCR data were used to generate Ct-based epidemic trajectories, including effective reproductive rate (Rt) and incidence. The improvement in forecasting performance was compared using absolute errors and residual squared errors with respect to actual observed cases at the 7-day and 14-day forecasting horizons. The model was also tested prospectively over the period January 2022 to April 2022. Rt curves estimated from the Ct-based model indicated epidemic waves 12 to 14 days earlier than Rt curves from NU campus and Suffolk County cases, with a correlation of 0.57. Enhancing the forecasting models with Ct-based information significantly decreased absolute error (decrease of 49.4 and 221.5 for the 7 and 14-day forecasting horizons) and residual squared error (40.6 and 217.1 for the 7 and 14-day forecasting horizons) compared to the original model without Ct features. Ct-based epidemic trajectories can herald an earlier signal for impending epidemic waves in the community and forecast transmission peaks. Moreover, COVID-19 forecasting models can be enhanced using these Ct features to improve their forecasting accuracy. In this study, we make the case that public health agencies should publish Ct values along with the binary positive/negative PCR results. Early and accurate forecasting of epidemic waves can inform public health policies and countermeasures which can mitigate spread.

Complexity reduction of ordinary kriging algorithm for 3D REM design

This work has investigated the feasibility of using cluster ordinary kriging (OK) interpolation to speed up indoor three-dimensional (3D) radio environment map (REM) generation time than the conventional OK-based REM generation time in two-dimensional (2D) and 3D ways mainly. The REM has been generated on the real-time received signal strength (RSS) dataset of an ultra-high frequency active television (TV) channel to explore TV grey space (TVGS) volume for cognitive access inside a six-storied office building. It can support future home networks for high-speed data-based applications. The optimal number of clusters has been found at K=4 on both 3D and 2D ways through distortion % deviation analysis. The maximum distortion % deviation = 88.74%, has been found at K=4. The exponential semivariogram model has been selected as the best-fit model after a thorough cross-validated comparative analysis of the clustered and non-clustered OK algorithms separately on residual squared error (RSE), root mean square error (RMSE) and the ratio of expected variance (EV) and kriging variance (KV) results. The RSE and RMSE are minimum, and the EV: KV ratio is in between 0.95 to 1.05 for the exponential model. Significant observation of the analysis of the results shows that cluster OK algorithms outperform conventional OK algorithms of corresponding domains on time complexity. A comparative study on RMSE, correlation coefficient (CC), and relative recovery error (RRE) show that cluster OK improves the accuracy. Cluster 2D and 3D OK-based detected TVGS volume is 13450 m3, 5.634% of the whole building volume.

Simple Prediction of an Ecosystem-Specific Water Quality Index and the Water Quality Classification of a Highly Polluted River through Supervised Machine Learning

Water quality indices (WQIs) are used for the simple assessment and classification of the water quality of surface water sources. However, considerable time, financial resources, and effort are required to measure the parameters used for their calculation. Prediction of WQIs through supervised machine learning is a useful and simple approach to reduce the cost of the analysis through the development of predictive models with a reduced number of water quality parameters. In this study, regression and classification machine-learning models were developed to estimate the ecosystem-specific WQI previously developed for the Santiago-Guadalajara River (SGR-WQI), which involves the measurement of 17 water quality parameters. The best subset selection method was employed to reduce the number of significant parameters required for the SGR-WQI prediction. The multiple linear regression model using 12 parameters displayed a residual square error (RSE) of 3.262, similar to that of the multiple linear regression model using 17 parameters (RSE = 3.255), which translates into significant savings for WQI estimation. Additionally, the generalized additive model not only displayed an adjusted R2 of 0.9992, which is the best fit of all the models evaluated, but also fitted the rating curves of each parameter developed for the original algorithm for the SGR-WQI calculation with great accuracy. Regarding the classification models, an overall proportion of 93% and 86% of data were correctly classified using the logistic regression model with 17 and 12 parameters, respectively, while the linear discriminant functions using 12 parameters correctly classified an overall proportion of 84%. The models evaluated were found to be efficient in predicting the SGR-WQI with a reduced number of parameters as complementary tools to extend the current water quality monitoring program of the Santiago-Guadalajara River.

Deep Learning-based Quantification of Abdominal Subcutaneous and Visceral Fat Volume on CT Images

Develop a deep learning-based algorithm using the U-Net architecture to measure abdominal fat on computed tomography (CT) images. Sequential CT images spanning the abdominal region of seven subjects were manually segmented to calculate subcutaneous fat (SAT) and visceral fat (VAT). The resulting segmentation maps of SAT and VAT were augmented using a template-based data augmentation approach to create a large dataset for neural network training. Neural network performance was evaluated on both sequential CT slices from three subjects and randomly selected CT images from the upper, central, and lower abdominal regions of 100 subjects. Both subcutaneous and abdominal cavity segmentation images created by the two methods were highly comparable with an overall Dice similarity coefficient of 0.94. Pearson's correlation coefficients between the subcutaneous and visceral fat volumes quantified using the two methods were 0.99 and 0.99 and the overall percent residual squared error were 5.5% and 8.5%. Manual segmentation of SAT and VAT on the 555 CT slices used for testing took approximately 46 hours while automated segmentation took approximately 1 minute. Our data demonstrates that deep learning methods utilizing a template-based data augmentation strategy can be employed to accurately and rapidly quantify total abdominal SAT and VAT with a small number of training images.

Método de perturbación con transformada de Laplace para resolver problemas no lineales de múltiples soluciones, con condiciones a la frontera mixtas y Neumann

El campo de las ecuaciones diferenciales ha cobrado auge en la actualidad por el desarrollo científico y tecnológico. Por esta situación, el estudio de nuevas metodologías para solucionarlas se ha vuelto importante. A partir de la combinación del método de Laplace Transform (LT) y el método de perturbación (PM) este trabajo presenta el método LT-PM, y su motivación se encuentra en la aplicación conocida de la LT a ecuaciones diferenciales ordinarias lineales. El objetivo de este trabajo fue presentar una modificación del método de perturbación (PM), el método de perturbación con transformada de Laplace (LT-PM), con el fin de resolver problemas perturbativos no lineales, con condiciones a la frontera definidas en intervalos finitos. La metodología consistió en aplicar LT a la ecuación diferencial por resolver y después de asumir que la solución de la misma se puede expresar como una serie de potencias de un parámetro perturbativo, se obtiene la solución del problema aplicando sistemáticamente la transformada inversa de Laplace. Los principales resultados de este trabajo se muestran a partir de dos casos de estudio presentados, donde se observa que LT-PM es potencialmente útil para encontrar soluciones múltiples de problemas no lineales. Además, LT-PM mejora la aplicabilidad del método de perturbación en algunos casos de condiciones a la frontera mixtas y de Neumann, donde PM simplemente no funciona. Con el fin de verificar la exactitud de los resultados obtenidos, se calculó su error residual cuadrático (SRE), el cual resultó muy bajo, de donde se dedujo su precisión y la potencialidad de LT-PM. Se concluye que si bien el método propuesto resulta eficiente en los casos particulares presentados, se espera que sea una herramienta potencialmente eficiente y útil para otros casos de estudio, particularmente, en aquellos relacionados con aplicaciones prácticas en ciencias e ingeniería.

Predicting Performance

PURPOSE: Due to recent external biases shown to have influenced the ability of a nonlinear regression model to predict Olympic performance, the purpose of this study was to employ additional statistical analytics as a means to characterize the progression of performances at future Olympic swim competitions. METHODS: Nonlinear regression models were fit for each swimming event for men (m) and women (w) at the Olympic Games (n=26) from 1948 to 2012. From these, and based upon predicted and observed performances, a ‘best fit’ model including 7 Olympic Games from 1988 to 2012 was selected. To predict future performances (2016), 1454 championship finals swim performances from this time frame were utilized. The mean time of the 8 swimmers in each final was used as the dependent variable to fit the model [time = a x yearb]. A 95% percent confidence interval was calculated using a Monte Carlo simulation method. Residual squared error (RSE), r-squared (r2), confidence interval (CI) length, and absolute difference between observed and predicted of each regression model were compared. RESULTS: Average RSEm (1.24 ± 1.25), RSEw (1.39 ± 1.15). Average r2m (0.76 ± 0.09), r2w (0.72 ± 0.12). There were no statistically significance differences in average RSE (p=0.35) or average r2 (p=0.35) between sex models. Average length of the 95% CIm (3.07 ± 3.13), CIw (3.44 ± 2.86). No difference existed between length of CI between sex (p=0.76). Absolute difference in time between observed and predicted for men (0.79 ± 0.73 s), women (1.56 ± 1.89 s). No differences existed between the absolute difference in observed and predicted between the men and women models (p=0.19). 92.3% (n=12) of observed men and 69.2% (n=9) observed women mean performances for 2016 fell within the 95% confidence interval of the predicted model value. CONCLUSIONS: In general, the nonlinear regression prediction models produce a valid and accurate approximation of Olympic performance progression as reflected by the 2016 Games. However, it is unclear why there is a different accuracy of ‘fit’ for the men and women predictions. Further study is needed to evaluate the potential factors apparently allowing the women to out-perform the ‘best fit’ model.

Laplace transform–homotopy perturbation method with arbitrary initial approximation and residual error cancelation

This paper presents a modified Laplace transform homotopy perturbation method with finite boundary conditions (MLT–HPM) designed to improve the accuracy of the approximate solutions obtained by LT–HPM and other methods. To this purpose, a suitable initial approximation will be introduced, in addition, the residual error in several points of the interest interval (RECP) will be canceled. In order to prove the efficiency of the proposed method a couple of nonlinear ordinary differential equations with mixed boundary conditions, indeed, difficult to approximate, are proposed. The square residual error (S.R.E) of the proposed solutions will result to be of hundredths and tenths, requiring only a first order approximation of MLT–HPM, unlike LT–HPM, which will require more iterations for the same cases study.

Estimation of growth curve characteristics of Hemsin male and female sheep

In the present study, we examined the suitability of seven asymptotic nonlinear models to describe body weight growth of Hemsin male and female sheep from birth to 36 months of age and, using the selected functions, to provide a biological interpretation for this growth. The weight–age data for this study were obtained from records of 108 Hemsin female and male sheep held in variety breeder flocks of Artvin province in Turkey. The sheep records were collected between 2008 and 2010 with measurements taken at birth, 2nd, 3rd, 6th, 12th, 18th, 24th, and 36th months of age. Body weight–age data from Hemsin sheep were used to obtain a growth pattern for sheep, with the use of Negative exponential, Brody, Gompertz, Logistic, Bertalanffy, Richards, and Janoschek nonlinear functions. Comparisons between these functions were based on coefficients of determination and residual squared error. The R2 values of the models ranged from 0.971 to 0.989 for males and from 0.951 to 0.991 for males. In both sexes, the Brody, Richards, and Janoschek models, with equal R2 as 0.99, were superior to the others. However, the Brody was precise on its parameters and easy to interpret than Richards and Janoschek functions.

Estimating bioenergetics model parameters for fish with incomplete recapture histories

Traditional methods for modeling growth of free-ranging fish are often limited by missing recapture observations that prevent individual growth estimates for a given time interval. Our purpose is to present a method for modeling growth rates of juvenile steelhead ( Oncorhynchus mykiss ) that addresses this limitation. Age-1 juvenile steelhead were individually marked with passive integrated transponder (PIT) tags, released in a Michigan, USA, watershed, and sampled monthly (May–November) with barge electrofishing. Individual growth was modeled using daily water temperature and observed fish sizes as inputs and by determining the proportion of maximum consumption parameter (P) for the bioenergetics equation that provided a minimum residual squared error. Results demonstrate that individual steelhead growth can be accurately modeled using water temperature and a temporally specific P shared by all individuals. Advantages of using this method to model fish growth include the ability to bridge data gaps where observations are lacking in individual length histories, rigorously test for differences in P across time periods, and estimate variability of P among fish within a given stream reach.

Respiratory control during air-breathing exercise in humans following an 8h exposure to hypoxia

Hypoxic exposure lasting a few hours results in an elevation of ventilation and a lowering of end-tidal that persists on return to breathing air. We sought to determine whether this increment in ventilation is fixed (hypothesis 1), or whether it increases in proportion to the rise in metabolic rate associated with exercise (hypothesis 2). Ten subjects were studied on two separate days. On 1 day, subjects were exposed to 8 h of isocapnic hypoxia (end-tidal 55 Torr) and on the other day to 8 h of euoxia as a control. Before and 30 min after each exposure, subjects undertook an incremental exercise test. The best fit of a model for the variation in with metabolic rate gave a residual squared error that was ∼20-fold less for hypothesis 2 than for hypothesis 1 (p < 0.005, F-ratio test). We conclude that the alterations in respiratory control induced during early ventilatory acclimatization to hypoxia better reflect those associated with hypothesis 2 rather than hypothesis 1.

Mesophilic Digestion Kinetics of Manure Slurry

Anaerobic digestion kinetics study of cow manure was performed at 35 degrees C in bench-scale gas-lift digesters (3.78 l working volume) at eight different volatile solids (VS) loading rates in the range of 1.11-5.87 g l-1 day-1. The digesters produced methane at the rates of 0.44-1.18 l l-1 day-1, and the methane content of the biogas was found to increase with longer hydraulic retention time (HRT). Based on the experimental observations, the ultimate methane yield and the specific methane productivity were estimated to be 0.42 l CH4 (g VS loaded)-1 and 0.45 l CH4 (g VS consumed)-1, respectively. Total and dissolved chemical oxygen demand (COD) consumptions were calculated to be 59-17% and 78-43% at 24.4-4.6 days HRTs, respectively. Maximum concentration of volatile fatty acids in the effluent was observed as 0.7 g l-1 at 4.6 days HRT, while it was below detection limit at HRTs longer than 11 days. The observed methane production rate did not compare well with the predictions of Chen and Hashimoto's [1] and Hill's [2] models using their recommended kinetic parameters. However, under the studied experimental conditions, the predictions of Chen and Hashimoto's [1] model compared better to the observed data than that of Hill's [2] model. The nonlinear regression analysis of the experimental data was performed using a derived methane production rate model, for a completely mixed anaerobic digester, involving Contois kinetics [3] with endogenous decay. The best fit values for the maximum specific growth rate (micro m) and dimensionless kinetic parameter (K) were estimated as 0.43 day-1 and 0.89, respectively. The experimental data were found to be within 95% confidence interval of the prediction of the derived methane production rate model with the sum of residual squared error as 0.02.

County child poverty rates in the US: a spatial regression approach

We apply methods of exploratory spatial data analysis (ESDA) and spatial regression analysis to examine intercounty variation in child poverty rates in the US. Such spatial analyses are important because regression models that exclude explicit specification of spatial effects, when they exist, can lead to inaccurate inferences about predictor variables. Using county-level data for 1990, we re- examine earlier published results (Friedman and Lichter (Popul Res Policy Rev 17:91-109, 1998)). We find that formal tests for spatial autocorrelation among county child poverty rates confirm and quantify what is obvious from simple maps of such rates: the risk of a child living in poverty is not (spatially) a randomly distributed risk at the county level. Explicit acknowledgment of spatial effects in an explanatory regression model improves considerably the earlier published regression results, which did not take account of spatial autocorrelation. These improvements include: (1) the shifting of ''wrong sign'' parameters in the direction originally hypothesized by the authors, (2) a reduction of residual squared error, and (3) the elimination of any substantive residual spatial autocorrelation. While not without its own problems and some remaining ambiguities, this reanalysis is a convincing demonstration of the need for demographers and other social scientists to examine spatial autocorrelation in their data and to explicitly correct for spatial externalities, if indicated, when performing multiple regression analyses on variables that are spatially referenced. Substantively, the analysis improves the estimates of the joint effects of place- influences and family-influences on child poverty.

A microprocessor-based automatic polynomial lineariser for constant-temperature anemometry systems

The paper describes a microprocessor-based lineariser module which automatically computes the coefficients, offset, and gain settings required for an integral wideband polynomial lineariser. An iterative technique is used whereby the aggregate residual-squared error between the normalised input data and the generated 4th-order polynomial converges to a minimum. Weighting factors are included to give a curve-fitting accuracy approximating to a constant percentage of reading.