A Nonparametric Kernel Approach to Interval-Valued Data Analysis

Ecological data are often complex. The explanatory and the response variables may be categorical variables or numerical variables. The ecological relationships that need to be defined are often nonlinear and involve high-order interactions between explanatory variables. Missing values for both response and predictor variables are very common,and outliers almost always exist. Random forest( RF),a novel machine learning technique,is ideally suited for the analysis ofcomplex ecological data. RF predictors are a ensemble-learning approach based on regression or classification trees. Instead of building one classification tree( classifier),the RF algorithm builds multiple classifiers using randomly selected subsets of the observations and random subsets of the predictor variables. The predictions from the ensemble of trees are then averaged in the case of regression trees,or tallied using a voting system for classification trees. RF is efficient to support flexible modelling strategies. RF is capable of detecting and making use of more complex relationships among the variables. RF is unexcelled in accuracy among current algorithms and does not overfit. It also generates an internal unbiased estimate of the generalization error as the forest building progresses. Potential applications of RF to ecology include: classification and regression analysis,survival analysis,variable importance estimate and data proximities. Proximities can be used for clustering,detecting outliers,multi-dimensional scaling,and unsupervised classification. RF can interpolate missing value and maintain high accuracy even when a large proportion of the data are missing. RF can handle thousands of input variables without variable exclusion. It runs efficiently on large data bases. RF can also handle a spectrum of response types, including categorical,numeric,ratings,and survival data. Another advantage of the RF is that it requires only two userdefined parameters( The number of trees and the number of randomly selected predictive variables used to split the nodes) to be defined. These two parameters should be optimized in order to improve predictive accuracy. In recent years,RF has been widely used by ecologists to model complex ecological relationships because they are easy to implement and easy to interpret. To understand and use the RF,further information about how they are computed is useful. Here,we summarized the basic principle of RF and showed how RF handle complex data by modelling the geographical distribution of Yunan Pine( Pinus yunnanensis) in China. RF is a robust and widely used technique in the field of species distribution modelling( SDM),since it meets the basic needs of SDM: simulating species distribution and identifying the main drivers of species distribution. In this work,RF showed a high predictive performance in simulating the distribution of Yunan Pine,which was consistent with the multi-dimensional scaling plot that showed it was possible to separate the presences from the absences. We also estimated the relative importance of predictor variables and produced the partial dependence plots for selected predictor variables for random forest predictions of the presences of Yunan Pine. The main aim of the article is to familiarize the reader with the general concepts,terminology and basic principle behind RF. We believe RF will get more applications and development in ecology.

Regression analysis is one method in statistics that used to know the pattern of functional relationships between response variables and predictor variables. Combination of parametric and nonparametric regression is semi parametric regression. The most popular estimator for nonparametric or semi parametric regression is spline truncated estimator. Problems in everyday life often using regression modeling with longitudinal data. Longitudinal data is a combination of cross-section data and time-series data. In longitudinal data, between subjects are independent of each other but between observations in the subject are dependent. One of the most important parts of statistical inference is interval estimation. Interval estimation aims to determine predictor variables that have a significant effect on the response variable. This study aims to obtain the form of interval estimation for parameters of semi parametric regression models using spline truncated estimator in longitudinal data. To solve this problem, the Weighted Least Square method and a pivotal quantity method were used for unknown population variance cases. The result of the theoretical study was that pivotal quantity distributed student-t. The shortest parameter interval estimation of semi parametric spline truncated regression model was obtained through the optimization process using the method of Lagrange.Regression analysis is one method in statistics that used to know the pattern of functional relationships between response variables and predictor variables. Combination of parametric and nonparametric regression is semi parametric regression. The most popular estimator for nonparametric or semi parametric regression is spline truncated estimator. Problems in everyday life often using regression modeling with longitudinal data. Longitudinal data is a combination of cross-section data and time-series data. In longitudinal data, between subjects are independent of each other but between observations in the subject are dependent. One of the most important parts of statistical inference is interval estimation. Interval estimation aims to determine predictor variables that have a significant effect on the response variable. This study aims to obtain the form of interval estimation for parameters of semi parametric regression models using spline truncated estimator in longitudinal data. To solve this problem, t...

Measurement error introduced by mismatches of scale and location between response and predictor variables is one of the major sources of error in forest structure mapping. It affects the evaluation of analytical models, compromises the results of accuracy assessments, and reduces the accuracy of mapping products. Using forest structure attributes measured in a specifically-designed ground plot system, we isolated the measurement error from the total mapping errors that are related to multiple factors, and examined the distribution and magnitude of this error caused by a scale mismatch between a relatively larger forest unit and a relatively smaller forest unit, as well as location mismatch of a specific distance between two forest units of the same size. We demonstrated the effects of measurement error on the analytical models and resulting maps for three common mapping scenarios linking ground data with remote sensing imagery. Our results indicated that this scale- and location-related error can be analyzed using the Classical and Berkson error models in most practical mapping exercises involving data measured on-ground and remotely-sensed imagery, and that the distinct error pattern of each type of measurement error can be used to identify the major error source. Based on this analysis, we can adjust the plot design or adjust the resolution of imagery, and select the optimal analytical method to achieve the best mapping result.

In this paper, we propose a Spatial Robust Mixture Regression model to investigate the relationship between a response variable and a set of explanatory variables over the spatial domain, assuming that the relationships may exhibit complex spatially dynamic patterns that cannot be captured by constant regression coefficients. Our method integrates the robust finite mixture Gaussian regression model with spatial constraints, to simultaneously handle the spatial non-stationarity, local homogeneity, and outlier contaminations. Compared with existing spatial regression models, our proposed model assumes the existence a few distinct regression models that are estimated based on observations that exhibit similar response-predictor relationships. As such, the proposed model not only accounts for non-stationarity in the spatial trend, but also clusters observations into a few distinct and homogenous groups. This provides an advantage on interpretation with a few stationary sub-processes identified that capture the predominant relationships between response and predictor variables. Moreover, the proposed method incorporates robust procedures to handle contaminations from both regression outliers and spatial outliers. By doing so, we robustly segment the spatial domain into distinct local regions with similar regression coefficients, and sporadic locations that are purely outliers. Rigorous statistical hypothesis testing procedure has been designed to test the significance of such segmentation. Experimental results on many synthetic and real-world datasets demonstrate the robustness, accuracy, and effectiveness of our proposed method, compared with other robust finite mixture regression, spatial regression and spatial segmentation methods.

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Helida Nurcahayani, I. Nyoman Budiantara, Ismaini Zain; The curve estimation of bi-response nonparametric regression using truncated spline on East Java SDGs achievement. AIP Conference Proceedings 25 January 2023; 2554 (1): 030007. https://doi.org/10.1063/5.0106527 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search

We consider the problem of nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support using polynomial splines. We provide a general computational framework that treats these estimation problems in a unified manner, without the limitations of the existing methods. Applications of our approach include computing optimal spline estimators for regression, density estimation, and arrival rate estimation problems in the presence of various shape constraints. Our approach can also handle multiple simultaneous shape constraints. The approach is based on a characterization of nonnegative polynomials that leads to semidefinite programming (SDP) and second-order cone programming (SOCP) formulations of the problems. These formulations extend and generalize a number of previous approaches in the literature, including those with piecewise linear and B-spline estimators. We also consider a simpler approach in which nonnegative splines are approximated by splines whose pieces are polynomials with nonnegative coefficients in a nonnegative basis. A condition is presented to test whether a given nonnegative basis gives rise to a spline cone that is dense in the space of nonnegative continuous functions. The optimization models formulated in the article are solvable with minimal running time using off-the-shelf software. We provide numerical illustrations for density estimation and regression problems. These examples show that the proposed approach requires minimal computational time, and that the estimators obtained using our approach often match and frequently outperform kernel methods and spline smoothing without shape constraints. Supplementary materials for this article are provided online.

Machine learning for Big Data analytics in plants.

Poisson regression analysis shows the relationship between predictor variables and response variables that follow the Poisson distribution which has equal dispersion and average values (λ), a situation called equidispersion. However, the variance can also be greater than the average value, called overdispersion. This can be caused by excess opportunities for the emergence of zero values in the response variable or zero excess. The parameter of the overdispersed data analysis can be underestimated so that the results become biased. This bias issue can be, hopefully, overcome by the Zero Inflated Negative Binomial (ZINB) regression analysis. In the 2016 Maternal Mortality Rate data in Bojonegoro District, overdipersion was overcome by ZINB regression even though there was no significant predictor variable found affecting the response variable. ZINB regression analysis can also be applied to generated data (simulation). We had the data with average λ = (0.2, 0.4, 0.6, 0.8, 1.0, 5.0) proportion of zeros p = (0.4, 0.6, 0.8), and the number of observationsn = (200,500, 800), with each setting was repeated 100 times. From the simulation study it was found that all overdispersion events were always accompanied by zero excess events but not vice versa. The greater the value of λ then the greater the dispersion coefficient. The ZINB regression is proven to be able to overcome overdispersion in various conditions of different values of λ, p, n which can be seen from the value τ (dispersion coefficient) after ZINB regression is less than 1 in all conditions.

The response variable of the regression analysis has a linear relationship with one of the variable predictors, however the unknown relationship pattern with the other predictor variables. Consequently, it can be approached by using semiparametric regression model. The predictor variable that has a linear relationship with the response variable can be approached by using linear parametric curve called parametric component. Meanwhile, the unknown relationship between the response variable with another predictor variable can be approached by using nonparametric curve called nonparametric component. If the predictor variable in nonparametric component is more than one, then it can be approached by using a different nonparametric curve named combined or mixed estimator. In this research, nonparametric component is approached using mixed estimator of multivariable linear truncated spline and multivariable kernel. The objective of this research is to estimate the model of semiparametric regression curve with mixed estimator of multivariable truncated spline and multivariable kernel. Estimation of this mixed model using ordinary least square method.

This experiment was conducted to evaluate the association between risk factors and the risk of culling in Iranian Holstein cows. The data consisted of 329,772 lactation records obtained from the Animal Breeding Center of Iran (2003 - 2012) and logistic regression was applied to investigate the associations between the predictor and response variables. The response variable in this experiment was the risk of culling and predictor variables were included calving season, parity, birth type, calving ease, standardized 305-d milk yield, age at the first calving, region and the number of calving cows in the herd. Risk factors analysis showed that the risk of culling significantly (P< 0.001) increased with parity and twinning. The odds ratio of cows leaving the herd were 1.32, 1.55, 1.62, 1.67 and 1.88 for parities 2 to 6, respectively and 1.09 for twinnings. Also, the OR increased with increasing in calving difficulty score except for farmer assistant cow. The OR were 1.12, 1.36 and 1.23 for herds with 26 to 53, 54 to 125 and ≥126 calving cows and risk of culling was increased with increase in number of calving cows in the herd. Calving in hot season increased the risk of culling and cows calved in cool seasons had lower risk of culling. The OR were 0.87, 0.79 and .077 for summer, fall and winter respectively. The analysis showed that region had a significant effect (P< 0.001) on culling risk and cows in warm and dry and warm and semi-arid regions had a higher risk of culling compared the cows in temperate or cold and wet region. Risk of culling significantly (P< 0.001) decreased with increasing in standardized 305-d milk yield so that cows with higher milk yield had the lower risk of culling. Cows at the age first calving about 24 months had the lower risk of culling and with increasing the age at first calving, the risk of culling increased. In general, the obtained results showed that the evaluated risk factors can significantly affected the risk of culling in dairy farms and farmers can control and manage dairy cattle according to these factors.

In this study, an elastic net (EN) regression model based on the empirical mode decomposition (EMD) algorithm is used in two applications, namely, numerical experiment and actual time series data. EMD is used to analyze a nonstationary and nonlinear signal dataset, which includes a set of orthogonal intrinsic mode functions (IMFs) and residual components. EN regression is used to select the most significant predictor variables influencing response variables and can address the multicollinearity problem between predictor variables. The main objective of this study is to apply the proposed method, EMD-EN, by using two variables for selecting important orthogonal IMFs and the residual components of predictor variables with significant effects on response variables. Moreover, this study uses the EMD-EN method in two different applications involving nonstationary and nonlinear problems. Results show that the proposed method outperforms other competitive methods in the numerical experiment and applications.

Non-negative least square regression (NLS) is a constrained least squares problem where the coefficients are restricted to be non-negative. It is useful for modeling non-negative responses such as time measurements, count data, histograms and so on. Existing NLS solvers are designed for cases where the predictor variables and response variables have linear relationships, and do not consider interactions among predictor variables. In this paper, we solve NLS in the complete space of power sets of variables. Such an extension is particularly useful in biology, for modeling genetic associations. Our new algorithms solve NLS problems exactly while decreasing computational burden by using an active set method. The algorithm proceeds in an iterative fashion, such that an optimal interaction term is searched by a branch-and-bound subroutine, and added to the solution set one another. The resulting large search space is efficiently restricted by novel pruning conditions and two kinds of sparsity promoting regularization; <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$l_{1}$ </tex-math></inline-formula> norm and non-negativity constraints. In computational experiments using HIV-1 datasets, 99% of the search space was safely pruned without losing the optimal variables. In mutagenicity datasets, the proposed method could identify long and accurate patterns compared to the original NLS. Codes are available from <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/afiveithree/inlars</uri> .

There exists a large literature on univariate density estimation by various methods, for example, the method of kernels first considered by Rosenblatt (1956) [see Whittle (1958), Parzen (1962), and Watson and Leadbetter (1963)] and the method of orthogonal series introduced by Cencov (1962) [see Schwartz (1967), Watson (1969), Walter (1977), and Wahba (1981)]; also see Wahba (1975). The methods were extended to vector-variate density estimation by, e.g., Cacoullos (1966), Epanechnikov (1969), and Scott (1992); see also the books by Prakasa Rao (1983) and Silverman (1986). Hall, Watson, and Cabrera (1987) considered kernel density estimation on the hypersphere V1, m .

Visible and near infrared (Vis-NIR) spectroscopy is a non-destructive analytical method that can be used to complement, enhance or potentially replace conventional methods of soil analysis. The aim of this research was to predict the particle size distribution (PSD) of soils using a Vis-NIR) spectrophotometry in one irrigate field having a vertisol clay texture in the Karacabey district of Bursa Province, Turkey. A total of 86 soil samples collected from the study area were subjected to optical scanning in the laboratory with a portable, fiber-type Vis&amp;ndash;NIR spectrophotometer (AgroSpec, tec5 Technology for Spectroscopy, Germany). Before the partial least square regression (PLSR) analysis, the entire reflectance spectra were randomly split into calibration (80%) and validation (20%) sets. A leave-one-out cross-validation PLSR analysis was carried out using the calibration set with Unscrambler&amp;reg; software, whereas the model prediction ability was tested using the validation (prediction) set. Models developed were used to predict sand and clay content using on-line collected spectra from the field. Results showed an &amp;ldquo;excellent&amp;rdquo; laboratory prediction performance for both sand (R2= 0.81, RMSEP = 3.84% and RPD = 2.32 in cross-validation; R2= 0.90, RMSEP = 2.91% and RPD = 2.99 in the prediction set) and clay (R2= 0.86, RMSEP = 3.4% and RPD = 2.66 in cross validation; R2= 0.92, RMSEP = 2.67% and RPD = 3.14 in the prediction set). Modelling of silt did not result in any meaningful correlations. Less accurate on-line predictions were recorded compared to the laboratory results, although the on-line predictions were very good (RPD = 2.24-2.31). On-line predicted maps showed reasonable spatial similarity to corresponding laboratory measured maps. This study proved that soil sand and clay content can be successfully measured and mapped using Vis-NIR spectroscopy under both laboratory and on-line scanning conditions.

Introduction: Achievement of specified qualitative indicators in machine learning solutions depends not only on the efficiency of algorithms, but also on data properties. One of the lines for the development of classification and regression models is the specification of local properties of data. Purpose: To improve the qualitative predictors when solving classification and regression problems based on the adaptive selection of various machine learning models on separate local segments of data sample. Results: We propose a method that uses a combination of different models and machine learning algorithms on subsamples in regression and classification problems. The method is based on the calculation of qualitative predictors and the selection of the best models on the local segments of data sample. The finding of transformations of data and time series allows to create sample sets, with the data having different properties (for example, variance, sampling fraction, data range, etc.). We consider the data segmentation based on the change point detection algorithm in time series trends and on analytical information. On the example of the real dataset, we show the experimental values of the loss function for the proposed method with different classifiers on separate segments and on the whole sample. Practical relevance: The results can be used in classification and regression problems for the development of machine learning models and methods. The proposed method allows to improve classification and regression qualitative predictors by assigning models that have the best performance on separate segments.