Paper ID: 2210.03505

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

Soumyabrata Pal, Prateek Varshney, Prateek Jain, Abhradeep Guha Thakurta, Gagan Madan, Gaurav Aggarwal, Pradeep Shenoy, Gaurav Srivastava

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.

Submitted: Oct 7, 2022