Multi-dimensional Function Approximation and Regression Estimation

نویسندگان

  • Fernando Pérez-Cruz
  • Gustavo Camps-Valls
  • Emilio Soria-Olivas
  • Juan José Pérez-Ruixo
  • Aníbal R. Figueiras-Vidal
  • Antonio Artés-Rodríguez
چکیده

In this communication, we generalize the Support Vector Machines (SVM) for regression estimation and function approximation to multi-dimensional problems. We propose a multi-dimensional Support Vector Regressor (MSVR) that uses a cost function with a hyperspherical insensitive zone, capable of obtaining better predictions than using an SVM independently for each dimension. The resolution of the MSVR is achieved by an iterative procedure over the Karush-KuhnTucker conditions. The proposed algorithm is illustrated by computers experiments.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Estimation of the cost function of a two-echelon inventory system with lost sales using regression

Multi-echelon inventory systems are one of the most important and attractive areas in modelling supply chain management so that several researches and studies have been done about. In this paper, the total cost function of a two-echelon inventory system with central warehouse and many identical retailers controlled by continuous review inventory policy is estimated. We have assumed the demand i...

متن کامل

Simultaneous robust estimation of multi-response surfaces in the presence of outliers

A robust approach should be considered when estimating regression coefficients in multi-response problems. Many models are derived from the least squares method. Because the presence of outlier data is unavoidable in most real cases and because the least squares method is sensitive to these types of points, robust regression approaches appear to be a more reliable and suitable method for addres...

متن کامل

The modified degenerate kernel method for the multi-dimensional Fredholm integral equations of the second kind

In this paper, to investigate the multi-dimensional Fredholm integral equations of the second kind a modified degenerate kernel method is used. To construct the mentioned modified,  the source function is approximated by the same method which  employed to obtain a degenerate approximation of the kernel.  The Lagrange interpolation method is used to make the needed approximations. The error and ...

متن کامل

Support Vector Regression for the simultaneous learning of a multivariate function and its derivatives

In this paper, the problem of simultaneously approximating a function and its derivatives is formulated within the Support Vector Machine (SVM) framework. First, the problem is solved for a one-dimensional input space by using the εinsensitive loss function and introducing additional constraints in the approximation of the derivative. Then, we extend the method to multi-dimensional input spaces...

متن کامل

Shape-Constrained Estimation in High Dimensions

Shape-constrained estimation techniques such as convex regression or log-concave density estimation offer attractive alternatives to traditional nonparametric methods. Shape-constrained estimation often has an easyto-optimize likelihood, no tuning parameter, and an adaptivity property where the sample complexity adapts to the complexity of the underlying functions. In this dissertation, we posi...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002