Stochastic Gradient Descent Meets Distribution Regression

Nicole Muecke
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:2143-2151, 2021.

Abstract

Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from probability measures to real-valued responses. Secondly, we sample bags from these distributions for utilizing them to solve the overall regression problem. Recently, DR has been tackled by applying kernel ridge regression and the learning properties of this approach are well understood. However, nothing is known about the learning properties of SGD for two stage sampling problems. We fill this gap and provide theoretical guarantees for the performance of SGD for DR. Our bounds are optimal in a mini-max sense under standard assumptions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-muecke21a, title = { Stochastic Gradient Descent Meets Distribution Regression }, author = {Muecke, Nicole}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {2143--2151}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/muecke21a/muecke21a.pdf}, url = {https://proceedings.mlr.press/v130/muecke21a.html}, abstract = { Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from probability measures to real-valued responses. Secondly, we sample bags from these distributions for utilizing them to solve the overall regression problem. Recently, DR has been tackled by applying kernel ridge regression and the learning properties of this approach are well understood. However, nothing is known about the learning properties of SGD for two stage sampling problems. We fill this gap and provide theoretical guarantees for the performance of SGD for DR. Our bounds are optimal in a mini-max sense under standard assumptions. } }
Endnote
%0 Conference Paper %T Stochastic Gradient Descent Meets Distribution Regression %A Nicole Muecke %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-muecke21a %I PMLR %P 2143--2151 %U https://proceedings.mlr.press/v130/muecke21a.html %V 130 %X Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from probability measures to real-valued responses. Secondly, we sample bags from these distributions for utilizing them to solve the overall regression problem. Recently, DR has been tackled by applying kernel ridge regression and the learning properties of this approach are well understood. However, nothing is known about the learning properties of SGD for two stage sampling problems. We fill this gap and provide theoretical guarantees for the performance of SGD for DR. Our bounds are optimal in a mini-max sense under standard assumptions.
APA
Muecke, N.. (2021). Stochastic Gradient Descent Meets Distribution Regression . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:2143-2151 Available from https://proceedings.mlr.press/v130/muecke21a.html.

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