Sample-Efficient Personalization: Modeling User Parameters as Low Rank Plus Sparse Components

Soumyabrata Pal, Prateek Varshney, Gagan Madan, Prateek Jain, Abhradeep Thakurta, Gaurav Aggarwal, Pradeep Shenoy, Gaurav Srivastava
Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, PMLR 238:1702-1710, 2024.

Abstract

Personalization of machine learning (ML) predictions for individual users/domains/enterprises is critical for practical recommendation systems. Standard personalization approaches involve learning a user/domain specific \emph{embedding} that is fed into a fixed global model which can be limiting. On the other hand, personalizing/fine-tuning model itself for each user/domain — a.k.a meta-learning — has high storage/infrastructure cost. Moreover, rigorous theoretical studies of scalable personalization approaches have been very limited. To address the above issues, we propose a novel meta-learning style approach that models network weights as a sum of low-rank and sparse components. This captures common information from multiple individuals/users together in the low-rank part while sparse part captures user-specific idiosyncrasies. We then study the framework in the linear setting, where the problem reduces to that of estimating the sum of a rank-$r$ and a $k$-column sparse matrix using a small number of linear measurements. We propose a computationally efficient alternating minimization method with iterative hard thresholding — AMHT-LRS — to learn the low-rank and sparse part. Theoretically, for the realizable Gaussian data setting, we show that AMHT-LRS solves the problem efficiently with nearly optimal sample complexity. Finally, a significant challenge in personalization is ensuring privacy of each user’s sensitive data. We alleviate this problem by proposing a differentially private variant of our method that also is equipped with strong generalization guarantees.

Cite this Paper

BibTeX
@InProceedings{pmlr-v238-pal24a, title = { Sample-Efficient Personalization: Modeling User Parameters as Low Rank Plus Sparse Components }, author = {Pal, Soumyabrata and Varshney, Prateek and Madan, Gagan and Jain, Prateek and Thakurta, Abhradeep and Aggarwal, Gaurav and Shenoy, Pradeep and Srivastava, Gaurav}, booktitle = {Proceedings of The 27th International Conference on Artificial Intelligence and Statistics}, pages = {1702--1710}, year = {2024}, editor = {Dasgupta, Sanjoy and Mandt, Stephan and Li, Yingzhen}, volume = {238}, series = {Proceedings of Machine Learning Research}, month = {02--04 May}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v238/pal24a/pal24a.pdf}, url = {https://proceedings.mlr.press/v238/pal24a.html}, abstract = { Personalization of machine learning (ML) predictions for individual users/domains/enterprises is critical for practical recommendation systems. Standard personalization approaches involve learning a user/domain specific \emph{embedding} that is fed into a fixed global model which can be limiting. On the other hand, personalizing/fine-tuning model itself for each user/domain — a.k.a meta-learning — has high storage/infrastructure cost. Moreover, rigorous theoretical studies of scalable personalization approaches have been very limited. To address the above issues, we propose a novel meta-learning style approach that models network weights as a sum of low-rank and sparse components. This captures common information from multiple individuals/users together in the low-rank part while sparse part captures user-specific idiosyncrasies. We then study the framework in the linear setting, where the problem reduces to that of estimating the sum of a rank-$r$ and a $k$-column sparse matrix using a small number of linear measurements. We propose a computationally efficient alternating minimization method with iterative hard thresholding — AMHT-LRS — to learn the low-rank and sparse part. Theoretically, for the realizable Gaussian data setting, we show that AMHT-LRS solves the problem efficiently with nearly optimal sample complexity. Finally, a significant challenge in personalization is ensuring privacy of each user’s sensitive data. We alleviate this problem by proposing a differentially private variant of our method that also is equipped with strong generalization guarantees. } }
Endnote
%0 Conference Paper %T Sample-Efficient Personalization: Modeling User Parameters as Low Rank Plus Sparse Components %A Soumyabrata Pal %A Prateek Varshney %A Gagan Madan %A Prateek Jain %A Abhradeep Thakurta %A Gaurav Aggarwal %A Pradeep Shenoy %A Gaurav Srivastava %B Proceedings of The 27th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2024 %E Sanjoy Dasgupta %E Stephan Mandt %E Yingzhen Li %F pmlr-v238-pal24a %I PMLR %P 1702--1710 %U https://proceedings.mlr.press/v238/pal24a.html %V 238 %X Personalization of machine learning (ML) predictions for individual users/domains/enterprises is critical for practical recommendation systems. Standard personalization approaches involve learning a user/domain specific \emph{embedding} that is fed into a fixed global model which can be limiting. On the other hand, personalizing/fine-tuning model itself for each user/domain — a.k.a meta-learning — has high storage/infrastructure cost. Moreover, rigorous theoretical studies of scalable personalization approaches have been very limited. To address the above issues, we propose a novel meta-learning style approach that models network weights as a sum of low-rank and sparse components. This captures common information from multiple individuals/users together in the low-rank part while sparse part captures user-specific idiosyncrasies. We then study the framework in the linear setting, where the problem reduces to that of estimating the sum of a rank-$r$ and a $k$-column sparse matrix using a small number of linear measurements. We propose a computationally efficient alternating minimization method with iterative hard thresholding — AMHT-LRS — to learn the low-rank and sparse part. Theoretically, for the realizable Gaussian data setting, we show that AMHT-LRS solves the problem efficiently with nearly optimal sample complexity. Finally, a significant challenge in personalization is ensuring privacy of each user’s sensitive data. We alleviate this problem by proposing a differentially private variant of our method that also is equipped with strong generalization guarantees.
APA
Pal, S., Varshney, P., Madan, G., Jain, P., Thakurta, A., Aggarwal, G., Shenoy, P. & Srivastava, G.. (2024). Sample-Efficient Personalization: Modeling User Parameters as Low Rank Plus Sparse Components . Proceedings of The 27th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 238:1702-1710 Available from https://proceedings.mlr.press/v238/pal24a.html.

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