Linear Regression-based Models Research Articles

Using Kalman Filtering to Forecast Disease Trajectory for Patients With Normal Tension Glaucoma

To determine whether a machine learning technique called Kalman filtering (KF) can accurately forecast future values of mean deviation (MD), pattern standard deviation, and intraocular pressure for patients with normal tension glaucoma (NTG). Development and testing of a forecasting model for glaucoma progression. We parameterized and validated a KF (KF-NTG) to forecast MD, pattern standard deviation, and intraocular pressure at 24months into the future using 263 eyes of 263 Japanese patients with NTG. We determined the proportion of patients with MD forecasts within 0.5, 1.0, and 2.5 dBs of the actual values and calculated the root mean squared error (RMSE) for each forecast. We compared KF-NTG with a previously published KF model calibrated using patients with high-tension open-angle glaucoma (KF-HTG) and to 3 conventional forecasting algorithms. The 263 patients with NTG had mean ± standard deviation age of 63.4 ± 10.5 years. KF-NTG forecasted MD values 24months ahead within 0.5, 1.0, and 2.5 dBs of the actual value for 78 eyes (32.2%), 122 eyes (50.4%), and 211 eyes (87.2%), respectively. The proportion of eyes with MD values forecasted within 2.5 dB of the actual value for the KF-NTG (87.2%) were similar to KF-HTG (86.0%) and the null model (86.4%), and much better than the 2 linear regression-based models (72.7-74.0%; P < .001). When forecasting MD, KF-NTG (RMSE= 2.71) and KF-HTG (RMSE= 2.68) achieved lower RMSE than the other 3 forecasting models (RMSE= 2.81-3.90), indicating better performance. As observed previously for patients with HTG, KF can also effectively forecast disease trajectory for many patients with NTG.

Autonomous power management in mobile devices using dynamic frequency scaling and reinforcement learning for energy minimization

Embedded systems execute applications that execute hardware differently depending on the computation task, generating time-varying workloads. Energy minimization can be reached by using the low-power central processing unit (CPU) frequency for each workload. We propose an autonomous and online approach, capable of reducing energy consumption from adaptation to workload variations even in an unknown environment. In this approach, we improved the AEWMA algorithm into a new algorithm called AEWMA-MSE, adding new functionality to detect workload changes and demonstrating why it is better to use statistical analysis for real user cases in a mobile environment. Also, a new power model for mobile devices based on k-NN algorithm for regression was proposed and validated proving to have a better trade-off between execution time and precision than neural networks and linear regression-based models. AEWMA-MSE and the proposed power model are integrated into a novel algorithm for energy management based on reinforcement learning that suitably selects the appropriate CPU frequency based on workload predictions to minimize energy consumption. The proposed approach is validated through simulation by using real smartphone data from an ARM Cortex A7 processor used in a commercial smartphone. Our proposal proved to have an improvement in the Q-learning cost function and can effectively minimize the average energy consumption by 21% and up to 29% when compared to the already existing approaches.

Multiple linear regression-based physical fitness prediction models for Turkish secondary school students

Physical fitness is a necessary component for daily activities. Measurement of physical activity is essential for determining physical fitness rate. This study aims to develop new prediction models for predicting the physical fitness of Turkish secondary school students by using multiple linear regression (MLR). The datasets comprise data of various number of subjects according to the target variables including the test scores of the 30m speed, 20m stage run, balance and hand-grip (right/left). The predictor variables used to develop the prediction models are gender, age, body mass index (BMI), body fat, number of curl-up and push-ups in 30 seconds. Eight physical fitness prediction models for each target have been created with the predictor variables listed above. The performance of the prediction models has been calculated by using standard error of estimate (SEE). The results show that MLR-based prediction models can be safely used to predict the physical fitness of Turkish secondary school students.Keywords: Physical fitness, multiple linear regression, machine learning, validation.

Development of multiple linear regression-based models for fatigue life evaluation of automotive coil springs

Abstract This paper discusses the establishment of multiple linear regression (MLR)-based spring durability models for predicting the fatigue life of automotive coil springs based on the vertical vibrations of the vehicle and natural frequencies of the vehicle suspension system. These models were developed in order to simplify the design and development process of vehicle suspension systems, which is both time-intensive and cost-intensive. The simulated force-time histories were processed to obtain the fatigue life of the automotive coil spring based on the strain-life models whereas the acceleration-time histories were weighted according to the ISO-2631-1:1997 standard to determine the vertical vibrations of the vehicle. MLR was used to establish the spring durability models and the goodness of fit, linearity, normality, and homoscedasticity of the models were assessed. The highest coefficient of determination at 0.8820 was obtained for the Morrow MLR-based spring durability model, with the mean square error of 0.5855. The models were validated by comparing the fatigue life values predicted by the models with those predicted from strain measurements. The results show a good agreement between the predicted and experimental values, indicating the suitability of these models in predicting the fatigue life of automotive coil springs.

Multiple Linear Regression Modeling To Predict the Stability of Polymer-Drug Solid Dispersions: Comparison of the Effects of Polymers and Manufacturing Methods on Solid Dispersion Stability.

Solid dispersions can be a successful way to enhance the bioavailability of poorly soluble drugs. Here 60 solid dispersion formulations were produced using ten chemically diverse, neutral, poorly soluble drugs, three commonly used polymers, and two manufacturing techniques, spray-drying and melt extrusion. Each formulation underwent a six-month stability study at accelerated conditions, 40 °C and 75% relative humidity (RH). Significant differences in times to crystallization (onset of crystallization) were observed between both the different polymers and the two processing methods. Stability from zero days to over one year was observed. The extensive experimental data set obtained from this stability study was used to build multiple linear regression models to correlate physicochemical properties of the active pharmaceutical ingredients (API) with the stability data. The purpose of these models is to indicate which combination of processing method and polymer carrier is most likely to give a stable solid dispersion. Six quantitative mathematical multiple linear regression-based models were produced based on selection of the most influential independent physical and chemical parameters from a set of 33 possible factors, one model for each combination of polymer and processing method, with good predictability of stability. Three general rules are proposed from these models for the formulation development of suitably stable solid dispersions. Namely, increased stability is correlated with increased glass transition temperature ( Tg) of solid dispersions, as well as decreased number of H-bond donors and increased molecular flexibility (such as rotatable bonds and ring count) of the drug molecule.

Patterns of Estimated Glomerular Filtration Rate Decline Leading to End-Stage Renal Disease in Type 1 Diabetes.

The patterns of estimated glomerular filtration rate (eGFR) decline to end-stage renal disease (ESRD) in patients with type 1 diabetes has not been conclusively described. Decline could be linearly progressive to ESRD but with a variable rate. Conversely, decline may be linear but interrupted by periods of plateaus or improvements. This observational study included 364 patients with type 1 diabetes attending the Joslin Clinic who developed ESRD between 1991 and 2013. We retrieved serum creatinine measurements from clinic visits or research examinations up to 24 years (median 6.7 years) preceding the onset of ESRD. Using serial measurements of serum creatinine to estimate renal function (eGFR), we used regression-based spline methods and a data smoothing approach to characterize individual trajectories of eGFR over time for the 257 patients with five or more data points. The rate of eGFR decline per year ranged widely, from -72 to -2 mL/min/1.73 m2 (median -8.5). The trajectories, as characterized with linear regression-based spline models, were linear or nearly so for 87% of patients, accelerating for 6%, and decelerating for 7%. Smoothed trajectories evaluated by a Bayesian approach did not significantly depart from a linear fit in 76%. The decline of eGFR in type 1 diabetes is predominantly linear. Deviations from linearity are small, with little effect on the expected time of ESRD. A single disease process most likely underlies renal decline from its initiation and continues with the same intensity to ESRD. Linearity of renal decline suggests using slope reduction as the measure of effectiveness of interventions to postpone ESRD.

River Flow Model Using Artificial Neural Networks

The use of artificial neural networks (ANNs) is becoming increasingly common in the analysis of hydrology and water resources problems. In this research, an ANN was developed and used to model the rainfall-runoff relationship, in a catchment located in a semiarid and Mediterranean climate in Algeria. The performance of the developed neural network-based model was compared against multiple linear regression-based models using the same observed data. It was found that the neural network model consistently gives superior predictions. Based on the results of this research, artificial neural network modeling appears to be a promising technique for the prediction of flow for catchments in semi-arid and Mediterranean regions. Accordingly, the neural network method can be applied to various hydrological systems where other models may be inappropriate.

Identifying the discriminative predictors of upper body power of cross-country skiers using support vector machines combined with feature selection

Upper body power (UBP) is a major parameter in cross-country skiing that strongly influences the performance of skiers during races. Although the direct measurement of UBP in laboratory environment provides the most accurate assessment, practical difficulties such as the need of sophisticated and expensive testing equipment and trained stuff have given rise to the necessity of predicting and identifying the relevant predictors of UBP. This study aims to develop feature selection-based prediction models to predict 10-s UBP (UBP10) and 60-s UBP (UBP60) of cross-country skiers with the help of support vector machines (SVMs) using different kernel functions. For model testing, tenfold cross-validation has been carried out, and the performance of the models has been assessed by computing their standard error of estimates (SEEs) and multiple correlation coefficients (Rs). With respect to the obtained results, the lowest SEEs (27.81 and 18.73 W) and the highest Rs (0.92 and 0.94) for the most accurate UBP10 and UBP60 prediction models have been obtained by SVM using the radial basis function kernel (SVM-RBF), respectively. The predictor variables gender and age have been found to be the most important variables in predicting the UBP10 and UBP60 of cross-country skiers. Also, the results have been compared to those of multilayer perceptron and multiple linear regression-based prediction models. Prediction models based on SVM-RBF exhibit much lower SEEs and higher Rs than the prediction models developed by other regression methods and can be safely utilized in making UBP predictions within acceptable limits of accuracy.

Initial stage clustering when estimating accounting quality measures with self-organizing maps

This study introduces self-organizing maps as a clustering approach for several measures in accounting that rely on local linear regression-based estimation models with an initial and essential clustering phase. Clustering by industry is the most frequently used approach in prior literature when estimating measures such as real activities manipulation or accruals quality. However, this approach has been subject to criticism due to its association with sample attrition and biased outcome measures. The purpose of our study is to develop and evaluate the performance of a self-organizing map (SOM) local regression-based estimation model for several measures of accounting quality. The SOM is built by utilizing general firm characteristics such as regular balance sheet items as cluster variables instead of model specific variables. According to the results, our SOM local regression models outperform previously suggested clustering methods. Simulation tests show that estimation models based on SOM clustering with general firm characteristics detect abnormality in the accounting quality measures much better than previously used clustering methods. By utilizing the SOM approach, the estimation process of the measures is significantly improved which results in more accurate outcome measures that can be used in various contexts including expert systems designed for auditors and investors.

The relation between reinforcement learning parameters and the influence of reinforcement history on choice behavior

Reinforcement learning (RL) models have been widely used to analyze the choice behavior of humans and other animals in a broad range of fields, including psychology and neuroscience. Linear regression-based models that explicitly represent how reward and choice history influences future choices have also been used to model choice behavior. While both approaches have been used independently, the relation between the two models has not been explicitly described. The aim of the present study is to describe this relation and investigate how the parameters in the RL model mediate the effects of reward and choice history on future choices. To achieve these aims, we performed analytical calculations and numerical simulations. First, we describe a special case in which the RL and regression models can provide equivalent predictions of future choices. The general properties of the RL model are discussed as a departure from this special case. We clarify the role of the RL-model parameters, specifically, the learning rate, inverse temperature, and outcome value (also referred to as the reward value, reward sensitivity, or motivational value), in the formation of history dependence.

An algebraic method for constructing stable and consistent autoregressive filters

In this paper, we introduce an algebraic method to construct stable and consistent univariate autoregressive (AR) models of low order for filtering and predicting nonlinear turbulent signals with memory depth. By stable, we refer to the classical stability condition for the AR model. By consistent, we refer to the classical consistency constraints of Adams–Bashforth methods of order-two. One attractive feature of this algebraic method is that the model parameters can be obtained without directly knowing any training data set as opposed to many standard, regression-based parameterization methods. It takes only long-time average statistics as inputs. The proposed method provides a discretization time step interval which guarantees the existence of stable and consistent AR model and simultaneously produces the parameters for the AR models. In our numerical examples with two chaotic time series with different characteristics of decaying time scales, we find that the proposed AR models produce significantly more accurate short-term predictive skill and comparable filtering skill relative to the linear regression-based AR models. These encouraging results are robust across wide ranges of discretization times, observation times, and observation noise variances. Finally, we also find that the proposed model produces an improved short-time prediction relative to the linear regression-based AR-models in forecasting a data set that characterizes the variability of the Madden–Julian Oscillation, a dominant tropical atmospheric wave pattern.

Effect of occlusal vertical dimension changes on postsurgical skeletal changes in a surgery-first approach for skeletal Class III deformities

The purposes of this study were to investigate the relationship between occlusal vertical dimension (VD) changes and postsurgical skeletal changes in the surgery-first approach and to derive regression models for the final mandibular setback at B-point. This retrospective study included 40 patients (16 men, 24 women; ages, 22.6±4.0years) who had undergone a bimaxillary surgery-first approach. Using cephalograms generated from cone-beam computed tomography representing the presurgical, postsurgical, and posttreatment stages, skeletal landmarks in the maxilla and mandible were investigated to derive multivariate linear regression-based prediction models. Additionally, a patient classification based on the VD was established and verified to generate regression models for the classified groups. For the nonincreased VD group, the surgical setback of B-point was its predictor for the final mandibular setback (R(2) at 92%). Meanwhile, the final mandibular setback of the increased VD group was predicted according to the surgical upward movement of pogonion, the postsurgical horizontal position of A-point, and the postsurgical vertical position of the coronoid process (R(2) at 94%). The results of this study support the clinical observation that the more increased the vertical occlusal dimension after surgery, the less predictable the position of B-point at the posttreatment stage.

Modeling of Furfural and 5-Hydroxymethylfurfural Content of Fermented Lotus Root: Artificial Neural Networks and a Genetic Algorithm Approach

Abstract The aim of this study was to investigate the effect of different pretreatment and reducing sugar content on furfural (F) and 5-hydroxymethylfurfural (HMF) contents of fermented lotus root by vinegar. The lotus root samples were fermented using vinegar for 15 days, at different solution concentrations and temperatures. The processing conditions were considered as inputs of neural network to predict the F and HMF contents of lotus root. Genetic algorithm was applied to optimize the structure and learning parameters of ANN. The developed genetic algorithm-artificial neural network (GA-ANN) which included 23 and 17 neurons in the first and second hidden layers, respectively, gives the lowest mean squared error (MSE). The correlation coefficient of ANN was compared with multiple linear regression-based models. The GA-ANN model was found to be a more accurate prediction method for the F and HMF contents of fermented lotus root than linear regression-based models. In addition, sensitivity analysis and Pearson’s correlation coefficient were also analyzed to find out the relation between input and output variables.

Impact of data characteristics on recommender systems performance

This article investigates the impact of rating data characteristics on the performance of several popular recommendation algorithms, including user-based and item-based collaborative filtering, as well as matrix factorization. We focus on three groups of data characteristics: rating space, rating frequency distribution, and rating value distribution. A sampling procedure was employed to obtain different rating data subsamples with varying characteristics; recommendation algorithms were used to estimate the predictive accuracy for each sample; and linear regression-based models were used to uncover the relationships between data characteristics and recommendation accuracy. Experimental results on multiple rating datasets show the consistent and significant effects of several data characteristics on recommendation accuracy.

Revisiting the General Solubility Equation: In Silico Prediction of Aqueous Solubility Incorporating the Effect of Topographical Polar Surface Area

The General Solubility Equation (GSE) is a QSPR model based on the melting point and log P of a chemical substance. It is used to predict the aqueous solubility of nonionizable chemical compounds. However, its reliance on experimentally derived descriptors, particularly melting point, limits its applicability to virtual compounds. The studies presented show that the GSE is able to predict, to within 1 log unit, the experimental aqueous solubility (log S) for 81% of the compounds in a data set of 1265 diverse chemical structures (-8.48 < log S < 1.58). However, the predictive ability of the GSE is reduced to 75% when applied to a subset of the data (1160 compounds -6.00 < log S < 0.00), which discounts those compounds occupying the sparsely populated regions of data space. This highlights how sparsely populated extremities of data sets can significantly skew results for linear regression-based models. Replacing the melting point descriptor of the GSE with a descriptor which accounts for topographical polar surface area (TPSA) produces a model of comparable quality to the GSE (the solubility of 81% of compounds in the full data set predicted accurately). As such, we propose an alternative simple model for predicting aqueous solubility which replaces the melting point descriptor of the GSE with TPSA and hence can be applied to virtual compounds. In addition, incorporating TPSA into the GSE in addition to log P and melting point gives a three descriptor model that improves accurate prediction of aqueous solubility over the GSE by 5.1% for the full and 6.6% for the reduced data set, respectively.

Testing the hypothesis of market efficiency in the Taiwan-US forward exchange market since 1990

This article examines the applicability of the hypothesis of market efficiency in Taiwan's foreign exchange market using daily data. Instead of linear regression-based models, we consider the possibility that the true data generating process may come from two different distributions, and we employ the Markov Switching approach to analyse this. From the results of the two-state Markov Switching model, we define State 1 as the efficient state and State 2 as the inefficient one. Only the 30-day forward rate is able to differentiate between the two states. Based on the unconditional probabilities from the Markov switching model, we also find that the 30-day forward rate has a 70% probability in the efficient state, which indicates that 70% of all speculators fully extract information when predicting future spot rates, while 30% of all investors do not.

A Mechanistic QSAR Study on the Leishmanicidal Activity of Some 5‐Substituted‐1,3,4‐Thiadiazole Derivatives

Quantitative structure-activity relationship studies help chemist to find chemical facts about the mechanism of action and/or behavior of the system under study. In this study, quantitative structure-activity relationship was employed as a promising tool to investigate some chemical, electronic, and structural features affecting on the antileishmanial activity of 5-substituted-1,3,4-thiadiazole derivatives. A data set, consisting of 21 thiadiazole derivatives with known in vitro leishmanicidal activity, was taken and semi-empirical AM1 quantum chemical calculation was employed to find the optimum three-dimensional geometry of the molecules. Multiple linear regression-based quantitative structure-activity relationship models were obtained between the antileishmanial activity and electronic, chemical, and topological descriptors of the molecules. Model performances and predictivity were evaluated using leave-one-out cross-validation method. The resulted models had good prediction ability (0.83 > q(2) > 0.71) and thus they described the structure-activity relationships in a useful manner. It was obtained that LUMO molecular orbital energy represents significant impact on the leishmanicidal activity. This means that the molecules may act on the leishmania parasites through an electron transfer reaction. Further theoretical investigations suggested that one probable mechanism for the activity of the thiadiazole derivatives may be due to the reduction of -NO(2) substituents of the molecules to -NO.

Management Selection by Multiple-Domain Assessment: II. Utility to the Organization

The utility of a multiple-domain assessment approach to management selection was examined in detail. On the basis of concurrent validity results obtained in a recent large-scale validity study by the present authors, the issue of utility, or concrete gains, that the participating organization would realize was investigated from a number of different perspectives and through use of several different utility models. In addition, some new procedures were examined for estimating the variability of job performance, a quantity needed in the linear regression-based utility models. Empirical utility results are presented, and some methodological considerations connected with utility analysis are noted.