Using Hyperbolic Cross Approximation to measure and compensate Covariate Shift

Thomas Vanck, Jochen Garcke
Proceedings of the 5th Asian Conference on Machine Learning, PMLR 29:435-450, 2013.

Abstract

The concept of covariate shift in supervised data analysis describes a difference between the training and test distribution while the conditional distribution remains the same. To improve the prediction performance one can address such a change by using individual weights for each training datapoint, which emphasizes the training points close to the test data set so that these get a higher significance. We propose a new method for calculating such weights by minimizing a Fourier series approximation of distance measures, in particular we consider the total variation distance, the Euclidean distance and Kullback-Leibler divergence. To be able to use the Fourier approach for higher dimensional data, we employ the so-called hyperbolic cross approximation. Results show that the new approach can compete with the latest methods and that on real life data an improved performance can be obtained.

Cite this Paper

BibTeX
@InProceedings{pmlr-v29-Vanck13, title = {Using Hyperbolic Cross Approximation to measure and compensate Covariate Shift}, author = {Vanck, Thomas and Garcke, Jochen}, booktitle = {Proceedings of the 5th Asian Conference on Machine Learning}, pages = {435--450}, year = {2013}, editor = {Ong, Cheng Soon and Ho, Tu Bao}, volume = {29}, series = {Proceedings of Machine Learning Research}, address = {Australian National University, Canberra, Australia}, month = {13--15 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v29/Vanck13.pdf}, url = {https://proceedings.mlr.press/v29/Vanck13.html}, abstract = {The concept of covariate shift in supervised data analysis describes a difference between the training and test distribution while the conditional distribution remains the same. To improve the prediction performance one can address such a change by using individual weights for each training datapoint, which emphasizes the training points close to the test data set so that these get a higher significance. We propose a new method for calculating such weights by minimizing a Fourier series approximation of distance measures, in particular we consider the total variation distance, the Euclidean distance and Kullback-Leibler divergence. To be able to use the Fourier approach for higher dimensional data, we employ the so-called hyperbolic cross approximation. Results show that the new approach can compete with the latest methods and that on real life data an improved performance can be obtained.} }
Endnote
%0 Conference Paper %T Using Hyperbolic Cross Approximation to measure and compensate Covariate Shift %A Thomas Vanck %A Jochen Garcke %B Proceedings of the 5th Asian Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Cheng Soon Ong %E Tu Bao Ho %F pmlr-v29-Vanck13 %I PMLR %P 435--450 %U https://proceedings.mlr.press/v29/Vanck13.html %V 29 %X The concept of covariate shift in supervised data analysis describes a difference between the training and test distribution while the conditional distribution remains the same. To improve the prediction performance one can address such a change by using individual weights for each training datapoint, which emphasizes the training points close to the test data set so that these get a higher significance. We propose a new method for calculating such weights by minimizing a Fourier series approximation of distance measures, in particular we consider the total variation distance, the Euclidean distance and Kullback-Leibler divergence. To be able to use the Fourier approach for higher dimensional data, we employ the so-called hyperbolic cross approximation. Results show that the new approach can compete with the latest methods and that on real life data an improved performance can be obtained.
RIS
TY - CPAPER TI - Using Hyperbolic Cross Approximation to measure and compensate Covariate Shift AU - Thomas Vanck AU - Jochen Garcke BT - Proceedings of the 5th Asian Conference on Machine Learning DA - 2013/10/21 ED - Cheng Soon Ong ED - Tu Bao Ho ID - pmlr-v29-Vanck13 PB - PMLR DP - Proceedings of Machine Learning Research VL - 29 SP - 435 EP - 450 L1 - http://proceedings.mlr.press/v29/Vanck13.pdf UR - https://proceedings.mlr.press/v29/Vanck13.html AB - The concept of covariate shift in supervised data analysis describes a difference between the training and test distribution while the conditional distribution remains the same. To improve the prediction performance one can address such a change by using individual weights for each training datapoint, which emphasizes the training points close to the test data set so that these get a higher significance. We propose a new method for calculating such weights by minimizing a Fourier series approximation of distance measures, in particular we consider the total variation distance, the Euclidean distance and Kullback-Leibler divergence. To be able to use the Fourier approach for higher dimensional data, we employ the so-called hyperbolic cross approximation. Results show that the new approach can compete with the latest methods and that on real life data an improved performance can be obtained. ER -
APA
Vanck, T. & Garcke, J.. (2013). Using Hyperbolic Cross Approximation to measure and compensate Covariate Shift. Proceedings of the 5th Asian Conference on Machine Learning, in Proceedings of Machine Learning Research 29:435-450 Available from https://proceedings.mlr.press/v29/Vanck13.html.

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