Joo-Yong Shim

Support Vector Quantile Regression with Weighted Quadratic Loss Function

Support vector quantile regression(SVQR) is capable of providing more complete description of the linear and nonlinear relationships among random variables. In this paper we propose an iterative reweighted least squares(IRWLS) procedure to solve the problem of SVQR with a weighted quadratic loss function. Furthermore, we introduce the generalized approximate cross validation function to select the hyperparameters which affect the performance of SVQR. Experimental results are then presented which illustrate the performance of the IRWLS procedure for SVQR.

Support Vector Quantile Regression Using Asymmetric e-Insensitive Loss Function

Support vector quantile regression(SVQR) is capable of providing a good description of the linear and nonlinear relationships among random variables. In this paper we propose a sparse SVQR to overcome a limitation of SVQR, nonsparsity. The asymmetric e-insensitive loss function is used to efficiently provide sparsity. The experimental results are presented to illustrate the performance of the proposed method by comparing it with nonsparse SVQR.

Kernel Ridge Regression with Randomly Right Censored Data

This paper deals with the estimations of kernel ridge regression when the responses are subject to randomly right censoring. The iterative reweighted least squares(IRWLS) procedure is employed to treat censored observations. The hyperparameters of model which affect the performance of the proposed procedure are selected by a generalized cross validation(GCV) function. Experimental results are then presented which indicate the performance of the proposed procedure.

Multiclass Classification via Least Squares Support Vector Machine Regression

In this paper we propose a new method for solving multiclass problem with least squares support vector machine(LS-SVM) regression. This method implements one-against-all scheme which is as accurate as any other approach. We also propose cross validation(CV) method to select effectively the optimal values of hyper-parameters which affect the performance of the proposed multiclass method. Experimental results are then presented which indicate the performance of the proposed multiclass method.

Hybrid Fuzzy Least Squares Support Vector Machine Regression for Crisp Input and Fuzzy Output

Hybrid fuzzy regression analysis is used for integrating randomness and fuzziness into a regression model. Least squares support vector machine(LS-SVM) has been very successful in pattern recognition and function estimation problems for crisp data. This paper proposes a new method to evaluate hybrid fuzzy linear and nonlinear regression models with crisp inputs and fuzzy output using weighted fuzzy arithmetic(WFA) and LS-SVM. LS-SVM allows us to perform fuzzy nonlinear regression analysis by constructing a fuzzy linear regression function in a high dimensional feature space. The proposed method is not computationally expensive since its solution is obtained from a simple linear equation system. In particular, this method is a very attractive approach to modeling nonlinear data, and is nonparametric method in the sense that we do not have to assume the underlying model function for fuzzy nonlinear regression model with crisp inputs and fuzzy output. Experimental results are then presented which indicate the performance of this method.

Combination of Value-at-Risk Models with Support Vector Machine

Value-at-Risk(VaR) has been used as an important tool to measure the market risk. However, the selection of the VaR models is controversial. This paper proposes VaR forecast combinations using support vector machine quantile regression instead of selecting a single model out of historical simulation and GARCH.

The Uniform Law of Large Numbers for the Baker Transformation

The baker transformation is an ergodic transformation defined on the half open unit square. This paper considers the limiting behavior of the partial sum process of a martingale sequence constructed from the baker transformation. We get the uniform law of large numbers for the baker transformation.

Estimating Variance Function with Kernel Machine

In this paper we propose a variance function estimation method based on kernel trick for replicated data or data consisted of sample variances. Newton-Raphson method is used to obtain associated parameter vector. Furthermore, the generalized approximate cross validation function is introduced to select the hyper-parameters which affect the performance of the proposed variance function estimation method. Experimental results are then presented which illustrate the performance of the proposed procedure.

Fuzzy Semiparametric Support Vector Regression for Seasonal Time Series Analysis

Fuzzy regression is used as a complement or an alternative to represent the relation between variables among the forecasting models especially when the data is insufficient to evaluate the relation. Such phenomenon often occurs in seasonal time series data which require large amount of data to describe the underlying pattern. Semiparametric model is useful tool in the case where domain knowledge exists about the function to be estimated or emphasis is put onto understandability of the model. In this paper we propose fuzzy semiparametric support vector regression so that it can provide good performance on forecasting of the seasonal time series by incorporating into fuzzy support vector regression the basis functions which indicate the seasonal variation of time series. In order to indicate the performance of this method, we present two examples of predicting the seasonal time series. Experimental results show that the proposed method is very attractive for the seasonal time series in fuzzy environments.

Sparse Multinomial Kernel Logistic Regression

Multinomial logistic regression is a well known multiclass classification method in the field of statistical learning. More recently, the development of sparse multinomial logistic regression model has found application in microarray classification, where explicit identification of the most informative observations is of value. In this paper, we propose a sparse multinomial kernel logistic regression model, in which the sparsity arises from the use of a Laplacian prior and a fast exact algorithm is derived by employing a bound optimization approach. Experimental results are then presented to indicate the performance of the proposed procedure.