A practical support vector regression algorithm and kernel function for attritional general insurance loss estimation

2020 ◽  
pp. 1-25
Author(s):  
Shadrack Kwasa ◽  
Daniel Jones
Keyword(s):  
Support Vector Regression ◽  
Kernel Function ◽  
Learning Task ◽  
Loss Estimation ◽  
Support Vector ◽  
Learning Method ◽  
Statistical Features ◽  
General Insurance ◽  
Loss Data ◽  
Chain Ladder Method

Abstract The aim of the paper is to derive a simple, implementable machine learning method for general insurance losses. An algorithm for learning a general insurance loss triangle is developed and justified. An argument is made for applying support vector regression (SVR) to this learning task (in order to facilitate transparency of the learning method as compared to more “black-box” methods such as deep neural networks), and SVR methodology derived is specifically applied to this learning task. A further argument for preserving the statistical features of the loss data in the SVR machine is made. A bespoke kernel function that preserves the statistical features of the loss data is derived from first principles and called the exponential dispersion family (EDF) kernel. Features of the EDF kernel are explored, and the kernel is applied to an insurance loss estimation exercise for homogeneous risk of three different insurers. Results of the cumulative losses and ultimate losses predicted by the EDF kernel are compared to losses predicted by the radial basis function kernel and the chain-ladder method. A backtest of the developed method is performed. A discussion of the results and their implications follows.

scholarly journals 24-hour cloud cover calculation using ground-based imager with machine learning

2021 ◽  
Author(s):  
Bu-Yo Kim ◽  
Joo Wan Cha ◽  
Ki-Ho Chang
Keyword(s):  
Machine Learning ◽  
Support Vector Regression ◽  
Cloud Cover ◽  
Image Data ◽  
Support Vector ◽  
Machine Learning Method ◽  
Learning Method ◽  
Learning Methods ◽  
Human Eye ◽  
Machine Learning Methods

Abstract. In this study, image data features and machine learning methods were used to calculate 24-h continuous cloud cover from image data obtained by a camera-based imager on the ground. The image data features were the time (Julian day and hour), solar zenith angle, and statistical characteristics of the red-blue ratio, blue–red difference, and luminance. These features were determined from the red, green, and blue brightness of images subjected to a pre-processing process involving masking removal and distortion correction. The collected image data were divided into training, validation, and test sets and were used to optimize and evaluate the accuracy of each machine learning method. The cloud cover calculated by each machine learning method was verified with human-eye observation data from a manned observatory. Supervised machine learning models suitable for nowcasting, namely, support vector regression, random forest, gradient boosting machine, k-nearest neighbor, artificial neural network, and multiple linear regression methods, were employed and their results were compared. The best learning results were obtained by the support vector regression model, which had an accuracy, recall, and precision of 0.94, 0.70, and 0.76, respectively. Further, bias, root mean square error, and correlation coefficient values of 0.04 tenth, 1.45 tenths, and 0.93, respectively, were obtained for the cloud cover calculated using the test set. When the difference between the calculated and observed cloud cover was allowed to range between 0, 1, and 2 tenths, high agreement of approximately 42 %, 79 %, and 91 %, respectively, were obtained. The proposed system involving a ground-based imager and machine learning methods is expected to be suitable for application as an automated system to replace human-eye observations.

scholarly journals Initial Optimal Parameters of Artificial Neural Network and Support Vector Regression

2018 ◽  
Vol 8 (5) ◽  
pp. 3341 ◽  
Author(s):  
Edy Fradinata ◽  
Sakesun Suthummanon ◽  
Wannarat Suntiamorntut
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Support Vector Regression ◽  
Kernel Function ◽  
Activation Function ◽  
Support Vector ◽  
Optimal Parameters ◽  
Artificial Neural ◽  
Hidden Layer ◽  
Linear Loss

This paper presents architecture of backpropagation Artificial Neural Network (ANN) and Support Vector Regression (SVR) models in supervised learning process for cement demand dataset. This study aims to identify the effectiveness of each parameter of mean square error (MSE) indicators for time series dataset. The study varies different random sample in each demand parameter in the network of ANN and support vector function as well. The variations of percent datasets from activation function, learning rate of sigmoid and purelin, hidden layer, neurons, and training function should be applied for ANN. Furthermore, SVR is varied in kernel function, lost function and insensitivity to obtain the best result from its simulation. The best results of this study for ANN activation function is Sigmoid. The amount of data input is 100% or 96 of data, 150 learning rates, one hidden layer, trinlm training function, 15 neurons and 3 total layers. The best results for SVR are six variables that run in optimal condition, kernel function is linear, loss function is ౬-insensitive, and insensitivity was 1. The better results for both methods are six variables. The contribution of this study is to obtain the optimal parameters for specific variables of ANN and SVR.

scholarly journals A Meta-Learning Method to Select the Kernel Width in Support Vector Regression

2004 ◽  
Vol 54 (3) ◽  
pp. 195-209 ◽  
Author(s):  
Carlos Soares ◽  
Pavel B. Brazdil ◽  
Petr Kuba
Keyword(s):  
Support Vector Regression ◽  
Support Vector ◽  
Learning Method ◽  
Kernel Width ◽  
Meta Learning

Parameter Estimation for Weibull Distribution Using Support Vector Regression

2007 ◽  
Author(s):  
Dan Ling ◽  
Hong-Zhong Huang ◽  
Qiang Miao ◽  
Bo Yang
Keyword(s):  
Weibull Distribution ◽  
Support Vector Regression ◽  
Statistical Learning ◽  
Support Vector ◽  
System Failure ◽  
Machine Learning Method ◽  
Learning Method ◽  
Weibull Analysis ◽  
Numerical Examples ◽  
Failure Data

The Weibull distribution is widely used in life testing and reliability studies. Weibull analysis is the process of discovering the trends in product or system failure data, and using them to predict future failures in similar situations. Support Vector Regression is a machine learning method based on statistical learning theory, which has been applied successfully to solve forecasting problems in many fields. In this paper, support vector regression is used to build a parameter estimating model for Weibull distribution. Numerical examples are presented to show good performance of this method.

scholarly journals Parameter Selection Method for Support Vector Regression Based on Adaptive Fusion of the Mixed Kernel Function

2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Hailun Wang ◽  
Daxing Xu
Keyword(s):  
Kalman Filter ◽  
Support Vector Regression ◽  
Kernel Function ◽  
Unscented Kalman Filter ◽  
Selection Method ◽  
Parameter Selection ◽  
Support Vector ◽  
Regression Parameters ◽  
Cubature Kalman Filter ◽  
Adaptive Fusion

Support vector regression algorithm is widely used in fault diagnosis of rolling bearing. A new model parameter selection method for support vector regression based on adaptive fusion of the mixed kernel function is proposed in this paper. We choose the mixed kernel function as the kernel function of support vector regression. The mixed kernel function of the fusion coefficients, kernel function parameters, and regression parameters are combined together as the parameters of the state vector. Thus, the model selection problem is transformed into a nonlinear system state estimation problem. We use a 5th-degree cubature Kalman filter to estimate the parameters. In this way, we realize the adaptive selection of mixed kernel function weighted coefficients and the kernel parameters, the regression parameters. Compared with a single kernel function, unscented Kalman filter (UKF) support vector regression algorithms, and genetic algorithms, the decision regression function obtained by the proposed method has better generalization ability and higher prediction accuracy.

scholarly journals Prior-knowledge based Green's kernel for support vector regression

2021 ◽  
Author(s):  
Tahir Farooq
Keyword(s):  
Support Vector Regression ◽  
Prior Knowledge ◽  
Kernel Function ◽  
Real World ◽  
Matched Filter ◽  
Kernel Functions ◽  
Support Vector ◽  
Mathematical Framework ◽  
Knowledge Based ◽  
Model Complex

This thesis presents a novel prior knowledge based Green's kernel for support vector regression (SVR) and provides an empirical investigation of SVM's (support vector machines) ability to model complex real world problems using a real dataset. After reviewing the theoretical background such as theory SVM, the correspondence between kernels functions used in SVM and regularization operators used in regularization networks as well as the use of Green's function of their corresponding regularization operators to construct kernel functions for SVM, a mathematical framework is presented to obtain the domain knowledge about the magnitude of the Fourier transform of the function to be predicted and design a prior knowledge based Green's kernel that exhibits optimal regularization properties by using the concept of matched filters. The matched filter behavior of the proposed kernel function provides the optimal regularization and also makes it suitable for signals corrupted with noise that includes many real world systems. Several experiments, mostly using benchmark datasets ranging from simple regression models to non-linear and high dimensional chaotic time series, have been conducted in order to compare the performance of the proposed technique with the results already published in the literature for other existing support vector kernels over a variety of settings including different noise levels, noise models, loss functions and SVM variations. The proposed kernel function improves the best known results by 18.6% and 24.4% on a benchmark dataset for two different experimental settings.

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