Fast Function to Function Regression

Junier Oliva, William Neiswanger, Barnabas Poczos, Eric Xing, Hy Trac, Shirley Ho, Jeff Schneider
Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, PMLR 38:717-725, 2015.

Abstract

We analyze the problem of regression when both input covariates and output responses are functions from a nonparametric function class. Function to function regression (FFR) covers a large range of interesting applications including time-series prediction problems, and also more general tasks like studying a mapping between two separate types of distributions. However, previous nonparametric estimators for FFR type problems scale badly computationally with the number of input/output pairs in a data-set. Given the complexity of a mapping between general functions it may be necessary to consider large data-sets in order to achieve a low estimation risk. To address this issue, we develop a novel scalable nonparametric estimator, the Triple-Basis Estimator (3BE), which is capable of operating over datasets with many instances. To the best of our knowledge, the 3BE is the first nonparametric FFR estimator that can scale to massive data-sets. We analyze the 3BE’s risk and derive an upperbound rate. Furthermore, we show an improvement of several orders of magnitude in terms of prediction speed and a reduction in error over previous estimators in various real-world data-sets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v38-oliva15, title = {{Fast Function to Function Regression}}, author = {Oliva, Junier and Neiswanger, William and Poczos, Barnabas and Xing, Eric and Trac, Hy and Ho, Shirley and Schneider, Jeff}, booktitle = {Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics}, pages = {717--725}, year = {2015}, editor = {Lebanon, Guy and Vishwanathan, S. V. N.}, volume = {38}, series = {Proceedings of Machine Learning Research}, address = {San Diego, California, USA}, month = {09--12 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v38/oliva15.pdf}, url = {https://proceedings.mlr.press/v38/oliva15.html}, abstract = {We analyze the problem of regression when both input covariates and output responses are functions from a nonparametric function class. Function to function regression (FFR) covers a large range of interesting applications including time-series prediction problems, and also more general tasks like studying a mapping between two separate types of distributions. However, previous nonparametric estimators for FFR type problems scale badly computationally with the number of input/output pairs in a data-set. Given the complexity of a mapping between general functions it may be necessary to consider large data-sets in order to achieve a low estimation risk. To address this issue, we develop a novel scalable nonparametric estimator, the Triple-Basis Estimator (3BE), which is capable of operating over datasets with many instances. To the best of our knowledge, the 3BE is the first nonparametric FFR estimator that can scale to massive data-sets. We analyze the 3BE’s risk and derive an upperbound rate. Furthermore, we show an improvement of several orders of magnitude in terms of prediction speed and a reduction in error over previous estimators in various real-world data-sets.} }
Endnote
%0 Conference Paper %T Fast Function to Function Regression %A Junier Oliva %A William Neiswanger %A Barnabas Poczos %A Eric Xing %A Hy Trac %A Shirley Ho %A Jeff Schneider %B Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2015 %E Guy Lebanon %E S. V. N. Vishwanathan %F pmlr-v38-oliva15 %I PMLR %P 717--725 %U https://proceedings.mlr.press/v38/oliva15.html %V 38 %X We analyze the problem of regression when both input covariates and output responses are functions from a nonparametric function class. Function to function regression (FFR) covers a large range of interesting applications including time-series prediction problems, and also more general tasks like studying a mapping between two separate types of distributions. However, previous nonparametric estimators for FFR type problems scale badly computationally with the number of input/output pairs in a data-set. Given the complexity of a mapping between general functions it may be necessary to consider large data-sets in order to achieve a low estimation risk. To address this issue, we develop a novel scalable nonparametric estimator, the Triple-Basis Estimator (3BE), which is capable of operating over datasets with many instances. To the best of our knowledge, the 3BE is the first nonparametric FFR estimator that can scale to massive data-sets. We analyze the 3BE’s risk and derive an upperbound rate. Furthermore, we show an improvement of several orders of magnitude in terms of prediction speed and a reduction in error over previous estimators in various real-world data-sets.
RIS
TY - CPAPER TI - Fast Function to Function Regression AU - Junier Oliva AU - William Neiswanger AU - Barnabas Poczos AU - Eric Xing AU - Hy Trac AU - Shirley Ho AU - Jeff Schneider BT - Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics DA - 2015/02/21 ED - Guy Lebanon ED - S. V. N. Vishwanathan ID - pmlr-v38-oliva15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 38 SP - 717 EP - 725 L1 - http://proceedings.mlr.press/v38/oliva15.pdf UR - https://proceedings.mlr.press/v38/oliva15.html AB - We analyze the problem of regression when both input covariates and output responses are functions from a nonparametric function class. Function to function regression (FFR) covers a large range of interesting applications including time-series prediction problems, and also more general tasks like studying a mapping between two separate types of distributions. However, previous nonparametric estimators for FFR type problems scale badly computationally with the number of input/output pairs in a data-set. Given the complexity of a mapping between general functions it may be necessary to consider large data-sets in order to achieve a low estimation risk. To address this issue, we develop a novel scalable nonparametric estimator, the Triple-Basis Estimator (3BE), which is capable of operating over datasets with many instances. To the best of our knowledge, the 3BE is the first nonparametric FFR estimator that can scale to massive data-sets. We analyze the 3BE’s risk and derive an upperbound rate. Furthermore, we show an improvement of several orders of magnitude in terms of prediction speed and a reduction in error over previous estimators in various real-world data-sets. ER -
APA
Oliva, J., Neiswanger, W., Poczos, B., Xing, E., Trac, H., Ho, S. & Schneider, J.. (2015). Fast Function to Function Regression. Proceedings of the Eighteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 38:717-725 Available from https://proceedings.mlr.press/v38/oliva15.html.

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