Personalized Social Recommendations – Accurate or Private?

PVLDB 2011 (Invited to VLDB Journal Special Issue)
Personalized Social Recommendations – Accurate or Private?
Atish Das Sarma, Ashwin Machanavajjhala, Aleksandra Korolova

With the recent surge of social networks such as Facebook, new forms of recommendations have become possible -- recommendations that rely on one's social connections in order to make personalized recommendations of ads, content, products, and people. Since recommendations may use sensitive information, it is speculated that these recommendations are associated with privacy risks. The main contribution of this work is in formalizing trade-offs between accuracy and privacy of personalized social recommendations.

We study whether "social recommendations", or recommendations that are solely based on a user's social network, can be made without disclosing sensitive links in the social graph. More precisely, we quantify the loss in utility when existing recommendation algorithms are modified to satisfy a strong notion of privacy, called differential privacy. We prove lower bounds on the minimum loss in utility for any recommendation algorithm that is differentially private.

We then adapt two privacy preserving algorithms from the differential privacy literature to the problem of social recommendations, and analyze their performance in comparison to our lower bounds, both analytically and experimentally.

We show that good private social recommendations are feasible only for a small subset of the users in the social network or for a lenient setting of privacy parameters.

Another publication from the same category: Machine Learning and Data Science

IEEE Computing Conference 2018, London, UK

Regularization of the Kernel Matrix via Covariance Matrix Shrinkage Estimation

The kernel trick concept, formulated as an inner product in a feature space, facilitates powerful extensions to many well-known algorithms. While the kernel matrix involves inner products in the feature space, the sample covariance matrix of the data requires outer products. Therefore, their spectral properties are tightly connected. This allows us to examine the kernel matrix through the sample covariance matrix in the feature space and vice versa. The use of kernels often involves a large number of features, compared to the number of observations. In this scenario, the sample covariance matrix is not well-conditioned nor is it necessarily invertible, mandating a solution to the problem of estimating high-dimensional covariance matrices under small sample size conditions. We tackle this problem through the use of a shrinkage estimator that offers a compromise between the sample covariance matrix and a well-conditioned matrix (also known as the "target") with the aim of minimizing the mean-squared error (MSE). We propose a distribution-free kernel matrix regularization approach that is tuned directly from the kernel matrix, avoiding the need to address the feature space explicitly. Numerical simulations demonstrate that the proposed regularization is effective in classification tasks.