Use of input deformations with brownian motion filters for discontinuous regression

Authors:
Ramūnas Girdziušas;Jorma Laaksonen
Affiliations:
Laboratory of Computer and Information Science, Helsinki University of Technology, Espoo, Finland;Laboratory of Computer and Information Science, Helsinki University of Technology, Espoo, Finland
Venue:
ICAPR'05 Proceedings of the Third international conference on Advances in Pattern Recognition - Volume Part I
Year:
2005

Citing 4
Cited 0

Finite difference, finite element and finite volume methods applied to two-point boundary value problems

Journal of Computational and Applied Mathematics
Evaluation of gaussian processes and other methods for non-linear regression

Evaluation of gaussian processes and other methods for non-linear regression
Efficient and reliable schemes for nonlinear diffusion filtering

IEEE Transactions on Image Processing
Regularization networks: fast weight calculation via Kalman filtering

IEEE Transactions on Neural Networks

Quantified Score

Hi-index	0.00

Visualization

Abstract

Bayesian Gaussian processes are known as ‘smoothing devices' and in the case of n data points they require O(n2)... O(n3) number of multiplications in order to perform a regression analysis. In this work we consider one-dimensional regression with Wiener-Lévy (Brownian motion) covariance functions. We indicate that they require only O(n) number of multiplications and show how one can utilize input deformations in order to define a much broader class of efficient covariance functions suitable for discontinuity-preserving filtering. An example of the selective smoothing is presented which shows that regression with Brownian motion filters outperforms or improves nonlinear diffusion filtering especially when observations are contaminated with noise of larger variance.