Incorporating Lasso Regression to Physics-Informed Neural Network for Inverse PDE Problem

Partial Differential Equation(PDE)is among the most fundamental tools employed to model dynamic systems.Existing PDE modeling methods are typically derived from established knowledge and known phenomena,which are time-consuming and labor-intensive.Recently,discovering governing PDEs from collected actual data via Physics Informed Neural Networks(PINNs)provides a more efficient way to analyze fresh dynamic systems and establish PEDmodels.This study proposes Sequentially Threshold Least Squares-Lasso(STLasso),a module constructed by incorporating Lasso regression into the Sequentially Threshold Least Squares(STLS)algorithm,which can complete sparse regression of PDE coefficients with the constraints of l0 norm.It further introduces PINN-STLasso,a physics informed neural network combined with Lasso sparse regression,able to find underlying PDEs from data with reduced data requirements and better interpretability.In addition,this research conducts experiments on canonical inverse PDE problems and compares the results to several recent methods.The results demonstrated that the proposed PINN-STLasso outperforms other methods,achieving lower error rates even with less data.

Smart Healthcare Activity Recognition Using Statistical Regression and Intelligent Learning

In this present time,Human Activity Recognition(HAR)has been of considerable aid in the case of health monitoring and recovery.The exploitation of machine learning with an intelligent agent in the area of health informatics gathered using HAR augments the decision-making quality and significance.Although many research works conducted on Smart Healthcare Monitoring,there remain a certain number of pitfalls such as time,overhead,and falsification involved during analysis.Therefore,this paper proposes a Statistical Partial Regression and Support Vector Intelligent Agent Learning(SPR-SVIAL)for Smart Healthcare Monitoring.At first,the Statistical Partial Regression Feature Extraction model is used for data preprocessing along with the dimensionality-reduced features extraction process.Here,the input dataset the continuous beat-to-beat heart data,triaxial accelerometer data,and psychological characteristics were acquired from IoT wearable devices.To attain highly accurate Smart Healthcare Monitoring with less time,Partial Least Square helps extract the dimensionality-reduced features.After that,with these resulting features,SVIAL is proposed for Smart Healthcare Monitoring with the help of Machine Learning and Intelligent Agents to minimize both analysis falsification and overhead.Experimental evaluation is carried out for factors such as time,overhead,and false positive rate accuracy concerning several instances.The quantitatively analyzed results indicate the better performance of our proposed SPR-SVIAL method when compared with two state-of-the-art methods.

Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Characterizing and estimating rice brown spot disease severity using stepwise regression,principal component regression and partial least-square regression

Detecting plant health conditions plays a key role in farm pest management and crop protection. In this study, measurement of hyperspectral leaf reflectance in rice crop (Oryzasativa L.) was conducted on groups of healthy and infected leaves by the fungus Bipolaris oryzae (Helminthosporium oryzae Breda. de Hann) through the wavelength range from 350 to 2 500 nm. The percentage of leaf surface lesions was estimated and defined as the disease severity. Statistical methods like multiple stepwise regression, principal component analysis and partial least-square regression were utilized to calculate and estimate the disease severity of rice brown spot at the leaf level. Our results revealed that multiple stepwise linear regressions could efficiently estimate disease severity with three wavebands in seven steps. The root mean square errors (RMSEs) for training (n=210) and testing (n=53) dataset were 6.5% and 5.8%, respectively. Principal component analysis showed that the first principal component could explain approximately 80% of the variance of the original hyperspectral reflectance. The regression model with the first two principal components predicted a disease severity with RMSEs of 16.3% and 13.9% for the training and testing dataset, respec-tively. Partial least-square regression with seven extracted factors could most effectively predict disease severity compared with other statistical methods with RMSEs of 4.1% and 2.0% for the training and testing dataset, respectively. Our research demon-strates that it is feasible to estimate the disease severity of rice brown spot using hyperspectral reflectance data at the leaf level.

A partial least-squares regression approach to land use studies in the Suzhou-Wuxi-Changzhou region

In several LUCC studies, statistical methods are being used to analyze land use data. A problem using conventional statistical methods in land use analysis is that these methods assume the data to be statistically independent. But in fact, they have the tendency to be dependent, a phenomenon known as multicollinearity, especially in the cases of few observations. In this paper, a Partial Least-Squares （PLS） regression approach is developed to study relationships between land use and its influencing factors through a case study of the Suzhou-Wuxi-Changzhou region in China. Multicollinearity exists in the dataset and the number of variables is high compared to the number of observations. Four PLS factors are selected through a preliminary analysis. The correlation analyses between land use and influencing factors demonstrate the land use character of rural industrialization and urbanization in the Suzhou-Wuxi-Changzhou region, meanwhile illustrate that the first PLS factor has enough ability to best describe land use patterns quantitatively, and most of the statistical relations derived from it accord with the fact. By the decreasing capacity of the PLS factors, the reliability of model outcome decreases correspondingly.

PARTIAL LEAST-SQUARES(PLS)REGRESSION AND SPECTROPHOTOMETRY AS APPLIED TO THE ANALYSIS OF MULTICOMPONENT MIXTURES

The UV absorption spectra of o-naphthol,α-naphthylamine,2,7-dihydroxy naphthalene,2,4-dimethoxy ben- zaldehyde and methyl salicylate,overlap severely;therefore it is impossible to determine them in mixtures by traditional spectrophotometric methods.In this paper,the partial least-squares(PLS)regression is applied to the simultaneous determination of these compounds in mixtures by UV spectrophtometry without any pretreatment of the samples.Ten synthetic mixture samples are analyzed by the proposed method.The mean recoveries are 99.4%,996%,100.2%,99.3% and 99.1%,and the relative standard deviations(RSD) are 1.87%,1.98%,1.94%,0.960% and 0.672%,respectively.

Based on Partial Least-squares Regression to Build up and Analyze the Model of Rice Evapotranspiration

During the course of calculating the rice evapotranspiration using weather factors,we often find that some independent variables have multiple correlation.The phenomena can lead to the traditional multivariate regression model which based on least square method distortion.And the stability of the model will be lost.The model will be built based on partial least square regression in the paper,through applying the idea of main component analyze and typical correlation analyze,the writer picks up some component from original material.Thus,the writer builds up the model of rice evapotranspiration to solve the multiple correlation among the independent variables (some weather factors).At last,the writer analyses the model in some parts,and gains the satisfied result.

Partial least squares regression for predicting economic loss of vegetables caused by acid rain

To predict the economic loss of crops caused by acid rain,we used partial least squares(PLS) regression to build a model of single dependent variable -the economic loss calculated with the decrease in yield related to the pH value and levels of Ca2+,NH4+,Na+,K+,Mg2+,SO42-,NO3-,and Cl-in acid rain. We selected vegetables which were sensitive to acid rain as the sample crops,and collected 12 groups of data,of which 8 groups were used for modeling and 4 groups for testing. Using the cross validation method to evaluate the performace of this prediction model indicates that the optimum number of principal components was 3,determined by the minimum of prediction residual error sum of squares,and the prediction error of the regression equation ranges from -2.25% to 4.32%. The model predicted that the economic loss of vegetables from acid rain is negatively corrrelated to pH and the concentrations of NH4+,SO42-,NO3-,and Cl-in the rain,and positively correlated to the concentrations of Ca2+,Na+,K+ and Mg2+. The precision of the model may be improved if the non-linearity of original data is addressed.

Discrimination of Transgenic Rice Based on Near Infrared Reflectance Spectroscopy and Partial Least Squares Regression Discriminant Analysis

Near infrared reflectance spectroscopy （NIRS）, a non-destructive measurement technique, was combined with partial least squares regression discrimiant analysis （PLS-DA） to discriminate the transgenic （TCTP and mi166） and wild type （Zhonghua 11） rice. Furthermore, rice lines transformed with protein gene （OsTCTP） and regulation gene （Osmi166） were also discriminated by the NIRS method. The performances of PLS-DA in spectral ranges of 4 000-8 000 cm-1 and 4 000-10 000 cm-1 were compared to obtain the optimal spectral range. As a result, the transgenic and wild type rice were distinguished from each other in the range of 4 000-10 000 cm-1, and the correct classification rate was 100.0% in the validation test. The transgenic rice TCTP and mi166 were also distinguished from each other in the range of 4 000-10 000 cm-1, and the correct classification rate was also 100.0%. In conclusion, NIRS combined with PLS-DA can be used for the discrimination of transgenic rice.

Estimating Wheat Grain Protein Content Using Multi-Temporal Remote Sensing Data Based on Partial Least Squares Regression

Estimating wheat grain protein content by remote sensing is important for assessing wheat quality at maturity and making grains harvest and purchase policies. However, spatial variability of soil condition, temperature, and precipitation will affect grain protein contents and these factors usually cannot be monitored accurately by remote sensing data from single image. In this research, the relationships between wheat protein content at maturity and wheat agronomic parameters at different growing stages were analyzed and multi-temporal images of Landsat TM were used to estimate grain protein content by partial least squares regression. Experiment data were acquired in the suburb of Beijing during a 2-yr experiment in the period from 2003 to 2004. Determination coefficient, average deviation of self-modeling, and deviation of cross- validation were employed to assess the estimation accuracy of wheat grain protein content. Their values were 0.88, 1.30%, 3.81% and 0.72, 5.22%, 12.36% for 2003 and 2004, respectively. The research laid an agronomic foundation for GPC （grain protein content） estimation by multi-temporal remote sensing. The results showed that it is feasible to estimate GPC of wheat from multi-temporal remote sensing data in large area.

Comparison of dimension reduction-based logistic regression models for case-control genome-wide association study:principal components analysis vs.partial least squares

With recent advances in biotechnology, genome-wide association study （GWAS） has been widely used to identify genetic variants that underlie human complex diseases and traits. In case-control GWAS, typical statistical strategy is traditional logistical regression （LR） based on single-locus analysis. However, such a single-locus analysis leads to the well-known multiplicity problem, with a risk of inflating type I error and reducing power. Dimension reduction-based techniques, such as principal component-based logistic regression （PC-LR）, partial least squares-based logistic regression （PLS-LR）, have recently gained much attention in the analysis of high dimensional genomic data. However, the perfor- mance of these methods is still not clear, especially in GWAS. We conducted simulations and real data application to compare the type I error and power of PC-LR, PLS-LR and LR applicable to GWAS within a defined single nucleotide polymorphism （SNP） set region. We found that PC-LR and PLS can reasonably control type I error under null hypothesis. On contrast, LR, which is corrected by Bonferroni method, was more conserved in all simulation settings. In particular, we found that PC-LR and PLS-LR had comparable power and they both outperformed LR, especially when the causal SNP was in high linkage disequilibrium with genotyped ones and with a small effective size in simulation. Based on SNP set analysis, we applied all three methods to analyze non-small cell lung cancer GWAS data.

Simultaneous Spectrophotometric Determination of Three Components Including Deoxyschizandrin by Partial Least Squares Regression

The computer auxiliary partial least squares is introduced to simultaneously determine the contents of Deoxyschizandin, Schisandrin, r-Schisandrin in the extracted solution of wuweizi. Regression analysis of the experimental results shows that the average recovery of each component is all in the range from 98.9% to 110.3% , which means the partial least squares regression spectrophotometry can circumvent the overlappirtg of absorption spectrums of mlulti-components, so that sctisfactory results can be obtained without any scrapple pre-separation.

Double-Penalized Quantile Regression in Partially Linear Models

In this paper, we propose the double-penalized quantile regression estimators in partially linear models. An iterative algorithm is proposed for solving the proposed optimization problem. Some numerical examples illustrate that the finite sample performances of proposed method perform better than the least squares based method with regard to the non-causal selection rate (NSR) and the median of model error (MME) when the error distribution is heavy-tail. Finally, we apply the proposed methodology to analyze the ragweed pollen level dataset.

Partial Least Squares Regression Model to Predict Water Quality in Urban Water Distribution Systems

The water distribution system of one residential district in Tianjin is taken as an example to analyze the changes of water quality.Partial least squares(PLS) regression model,in which the turbidity and Fe are regarded as control objectives,is used to establish the statistical model.The experimental results indicate that the PLS regression model has good predicted results of water quality compared with the monitored data.The percentages of absolute relative error(below 15%,20%,30%) are 44.4%,66.7%,100%(turbidity) and 33.3%,44.4%,77.8%(Fe) on the 4th sampling point;77.8%,88.9%,88.9%(turbidity) and 44.4%,55.6%,66.7%(Fe) on the 5th sampling point.

Boosting the partial least square algorithm for regression modelling

Boosting algorithms are a class of general methods used to improve the general periormance of regression analysis. The main idea is to maintain a distribution over the train set. In order to use the given distribution directly, a modified PLS algorithm is proposed and used as the base learner to deal with the nonlinear multivariate regression problems. Experiments on gasoline octane number prediction demonstrate that boosting the modified PLS algorithm has better general performance over the PLS algorithm.

PARAMETRIC TEST IN PARTIAL LINEAR REGRESSION MODELS

Consider the regression model, n. Here the design points (xi,ti) are known and nonrandom, and ei are random errors. The family of nonparametric estimates of g() including known estimates proposed by Gasser & Muller[1] is also proposed to be a class of new nearest neighbor estimates of g(). Baed on the nonparametric regression procedures, we investigate a statistic for testing H0:g=0, and obtain some aspoptotic results about estimates.

Machine learning algorithm partially reconfigured on FPGA for an image edge detection system

Unmanned aerial vehicles(UAVs)have been widely used in military,medical,wireless communications,aerial surveillance,etc.One key topic involving UAVs is pose estimation in autonomous navigation.A standard procedure for this process is to combine inertial navigation system sensor information with the global navigation satellite system(GNSS)signal.However,some factors can interfere with the GNSS signal,such as ionospheric scintillation,jamming,or spoofing.One alternative method to avoid using the GNSS signal is to apply an image processing approach by matching UAV images with georeferenced images.But a high effort is required for image edge extraction.Here a support vector regression(SVR)model is proposed to reduce this computational load and processing time.The dynamic partial reconfiguration(DPR)of part of the SVR datapath is implemented to accelerate the process,reduce the area,and analyze its granularity by increasing the grain size of the reconfigurable region.Results show that the implementation in hardware is 68 times faster than that in software.This architecture with DPR also facilitates the low power consumption of 4 mW,leading to a reduction of 57%than that without DPR.This is also the lowest power consumption in current machine learning hardware implementations.Besides,the circuitry area is 41 times smaller.SVR with Gaussian kernel shows a success rate of 99.18%and minimum square error of 0.0146 for testing with the planning trajectory.This system is useful for adaptive applications where the user/designer can modify/reconfigure the hardware layout during its application,thus contributing to lower power consumption,smaller hardware area,and shorter execution time.

Quantum partial least squares regression algorithm for multiple correlation problem

Partial least squares(PLS) regression is an important linear regression method that efficiently addresses the multiple correlation problem by combining principal component analysis and multiple regression. In this paper, we present a quantum partial least squares(QPLS) regression algorithm. To solve the high time complexity of the PLS regression, we design a quantum eigenvector search method to speed up principal components and regression parameters construction. Meanwhile, we give a density matrix product method to avoid multiple access to quantum random access memory(QRAM)during building residual matrices. The time and space complexities of the QPLS regression are logarithmic in the independent variable dimension n, the dependent variable dimension w, and the number of variables m. This algorithm achieves exponential speed-ups over the PLS regression on n, m, and w. In addition, the QPLS regression inspires us to explore more potential quantum machine learning applications in future works.