Stability of matrix factorization for collaborative filtering

We study the stability vis a vis adversarial noise of matrix factorization algorithm for matrix completion. In particular, our results include: (I) we bound the gap between the solution matrix of the factorization method and the ground truth in terms of root mean square error; (II) we treat the matrix factorization as a subspace fitting problem and analyze the difference between the solution subspace and the ground truth; (III) we analyze the prediction error of individual users based on the subspace stability. We apply these results to the problem of collaborative filtering under manipulator attack, which leads to useful insights and guidelines for collaborative filtering system design.Comment: ICML201

Hybrid Collaborative Filtering with Autoencoders

Collaborative Filtering aims at exploiting the feedback of users to provide personalised recommendations. Such algorithms look for latent variables in a large sparse matrix of ratings. They can be enhanced by adding side information to tackle the well-known cold start problem. While Neu-ral Networks have tremendous success in image and speech recognition, they have received less attention in Collaborative Filtering. This is all the more surprising that Neural Networks are able to discover latent variables in large and heterogeneous datasets. In this paper, we introduce a Collaborative Filtering Neural network architecture aka CFN which computes a non-linear Matrix Factorization from sparse rating inputs and side information. We show experimentally on the MovieLens and Douban dataset that CFN outper-forms the state of the art and benefits from side information. We provide an implementation of the algorithm as a reusable plugin for Torch, a popular Neural Network framework

PrivateJobMatch: A Privacy-Oriented Deferred Multi-Match Recommender System for Stable Employment

Coordination failure reduces match quality among employers and candidates in the job market, resulting in a large number of unfilled positions and/or unstable, short-term employment. Centralized job search engines provide a platform that connects directly employers with job-seekers. However, they require users to disclose a significant amount of personal data, i.e., build a user profile, in order to provide meaningful recommendations. In this paper, we present PrivateJobMatch -- a privacy-oriented deferred multi-match recommender system -- which generates stable pairings while requiring users to provide only a partial ranking of their preferences. PrivateJobMatch explores a series of adaptations of the game-theoretic Gale-Shapley deferred-acceptance algorithm which combine the flexibility of decentralized markets with the intelligence of centralized matching. We identify the shortcomings of the original algorithm when applied to a job market and propose novel solutions that rely on machine learning techniques. Experimental results on real and synthetic data confirm the benefits of the proposed algorithms across several quality measures. Over the past year, we have implemented a PrivateJobMatch prototype and deployed it in an active job market economy. Using the gathered real-user preference data, we find that the match-recommendations are superior to a typical decentralized job market---while requiring only a partial ranking of the user preferences.Comment: 45 pages, 28 figures, RecSys 201