How Powerful Can Any Regression Learning Procedure Be?

Yuhong Yang
Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, PMLR 2:636-643, 2007.

Abstract

Efforts have been directed at obtaining flexible learning procedures that optimally adapt to various possible characteristics of the data generating mechanism. A question that addresses the issue of how far one can go in this direction is: Given a regression procedure, however sophisticated it is, how many regression functions are estimated accurately? In this work, for a given sequence of prescribed estimation accuracy (in sample size), we give an upper bound (in terms of metric entropy) on the number of regression functions for which the accuracy is achieved. Interesting consequences on adaptive and sparse estimations are also given.

Cite this Paper

BibTeX
@InProceedings{pmlr-v2-yang07a, title = {How Powerful Can Any Regression Learning Procedure Be?}, author = {Yang, Yuhong}, booktitle = {Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics}, pages = {636--643}, year = {2007}, editor = {Meila, Marina and Shen, Xiaotong}, volume = {2}, series = {Proceedings of Machine Learning Research}, address = {San Juan, Puerto Rico}, month = {21--24 Mar}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v2/yang07a/yang07a.pdf}, url = {https://proceedings.mlr.press/v2/yang07a.html}, abstract = {Efforts have been directed at obtaining flexible learning procedures that optimally adapt to various possible characteristics of the data generating mechanism. A question that addresses the issue of how far one can go in this direction is: Given a regression procedure, however sophisticated it is, how many regression functions are estimated accurately? In this work, for a given sequence of prescribed estimation accuracy (in sample size), we give an upper bound (in terms of metric entropy) on the number of regression functions for which the accuracy is achieved. Interesting consequences on adaptive and sparse estimations are also given.} }
Endnote
%0 Conference Paper %T How Powerful Can Any Regression Learning Procedure Be? %A Yuhong Yang %B Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2007 %E Marina Meila %E Xiaotong Shen %F pmlr-v2-yang07a %I PMLR %P 636--643 %U https://proceedings.mlr.press/v2/yang07a.html %V 2 %X Efforts have been directed at obtaining flexible learning procedures that optimally adapt to various possible characteristics of the data generating mechanism. A question that addresses the issue of how far one can go in this direction is: Given a regression procedure, however sophisticated it is, how many regression functions are estimated accurately? In this work, for a given sequence of prescribed estimation accuracy (in sample size), we give an upper bound (in terms of metric entropy) on the number of regression functions for which the accuracy is achieved. Interesting consequences on adaptive and sparse estimations are also given.
RIS
TY - CPAPER TI - How Powerful Can Any Regression Learning Procedure Be? AU - Yuhong Yang BT - Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics DA - 2007/03/11 ED - Marina Meila ED - Xiaotong Shen ID - pmlr-v2-yang07a PB - PMLR DP - Proceedings of Machine Learning Research VL - 2 SP - 636 EP - 643 L1 - http://proceedings.mlr.press/v2/yang07a/yang07a.pdf UR - https://proceedings.mlr.press/v2/yang07a.html AB - Efforts have been directed at obtaining flexible learning procedures that optimally adapt to various possible characteristics of the data generating mechanism. A question that addresses the issue of how far one can go in this direction is: Given a regression procedure, however sophisticated it is, how many regression functions are estimated accurately? In this work, for a given sequence of prescribed estimation accuracy (in sample size), we give an upper bound (in terms of metric entropy) on the number of regression functions for which the accuracy is achieved. Interesting consequences on adaptive and sparse estimations are also given. ER -
APA
Yang, Y.. (2007). How Powerful Can Any Regression Learning Procedure Be?. Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 2:636-643 Available from https://proceedings.mlr.press/v2/yang07a.html.

Related Material