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

• URL: http://arxiv.org/abs/2210.03505v3
• Date: Wed, 6 Sep 2023 00:35:30 GMT
• Title: Sample-Efficient Personalization: Modeling User Parameters as Low Rank Plus Sparse Components
• Authors: Soumyabrata Pal, Prateek Varshney, Prateek Jain, Abhradeep Guha Thakurta, Gagan Madan, Gaurav Aggarwal, Pradeep Shenoy and Gaurav Srivastava
• Abstract summary: Personalization of machine learning (ML) predictions for individual users/domains/enterprises is critical for practical recommendation systems. We propose a novel meta-learning style approach that models network weights as a sum of low-rank and sparse components. We show that AMHT-LRS solves the problem efficiently with nearly optimal sample complexity.
• Score: 30.32486162748558
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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.

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