Despite the variety of robust regression methods that have been developed, current regression formulations are either NP-hard, or allow unbounded response to even a single leverage point. We present a general formulation for robust regression—Variational M-estimation—that unifies a number of robust regression methods while allowing a tractable approximation strategy. We develop an estimator tha...

Locally weighted polynomial regression LWPR is a popular instance based al gorithm for learning continuous non linear mappings For more than two or three in puts and for more than a few thousand dat apoints the computational expense of pre dictions is daunting We discuss drawbacks with previous approaches to dealing with this problem and present a new algorithm based on a multiresolution search...

Modal local polynomial regression uses double kernel as the loss function to gain some robustness in the nonparametric regression. Current researches use the standard normal density function as the weight function to down-weigh the influences from the outliers. This paper extends the standard normal weight function to a general class weight functions. All the theoretical properties found by usi...

Important issues in multimedia information systems are the development of e cient storage layout models and e ective retrieval system to manage multimedia database. In multimedia information systems, the capability for interaction with video media type is still extremely limited due to a huge amount of video database. We present the Fast Polynomial Regression Transform (FPRT) based metadata sch...

We reveal the phenomenon that ”naive” multivariate local polynomial regression can adapt to local smooth lower dimensional structure in the sense that it achieves the optimal convergence rate for nonparametric estimation of regression functions belonging to a Sobolev space when the predictor variables live on or close to a lower dimensional manifold.

This paper discusses key results from the literature in the field of local polynomial regression. Local polynomial regression (LPR) is a nonparametric technique for smoothing scatter plots and modeling functions. For each point, x0, a low-order polynomial WLS regression is fit using only points in some “neighborhood” of x0. The result is a smooth function over the support of the data. LPR has g...

Perspective distortion always occurs while scanning thick, bound documents, resulting in two problems in the scanned grayscale image – (i) shade along the ‘spine’ of the book, and (ii) warping of words in the shade area. We proposed a restoration system to solve these two problems in our previous paper [1]. However the shape of the warped words was not fully restored, since we simply shifted an...

B. Seifert Th. Gasser University of Zurich Department of Biostatistics Sumatrastrasse 30 CH{8006 Z urich, Switzerland Abstract When estimating a regression function r or its th derivative, local polynomials are an attractive choice due to their exibility and asymptotic performance. Seifert & Gasser (1996) proposed local polynomial ridging to overcome problems of local polynomials with variance...