Relative error prediction via kernel regression smoothers

Relative error prediction via kernel regression smoothers

In this article, we introduce and study local constant and our preferred local linear nonparametric regression estimators when it is appropriate to assess performance in terms of mean squared relative error of prediction. We give asymptotic results for both boundary and non-boundary cases. These are special cases of more general asymptotic results that we provide concerning the estimation of th...

Estimating Explanatory Power in a Simple Regression Model Via Smoothers

Kernel Ridge Regression via Partitioning

In this paper, we investigate a divide and conquer approach to Kernel Ridge Regression (KRR). Given n samples, the division step involves separating the points based on some underlying disjoint partition of the input space (possibly via clustering), and then computing a KRR estimate for each partition. The conquering step is simple: for each partition, we only consider its own local estimate fo...

Error Analysis of Generalized Nyström Kernel Regression

Nyström method has been successfully used to improve the computational efficiency of kernel ridge regression (KRR). Recently, theoretical analysis of Nyström KRR, including generalization bound and convergence rate, has been established based on reproducing kernel Hilbert space (RKHS) associated with the symmetric positive semi-definite kernel. However, in real world applications, RKHS is not a...

Kernel regression for fMRI pattern prediction

This paper introduces two kernel-based regression schemes to decode or predict brain states from functional brain scans as part of the Pittsburgh Brain Activity Interpretation Competition (PBAIC) 2007, in which our team was awarded first place. Our procedure involved image realignment, spatial smoothing, detrending of low-frequency drifts, and application of multivariate linear and non-linear k...