Adaptive Matrix Completion for the Users and the Items in Tail

Recommender systems are widely used to recommend the most appealing items to users. These recommendations can be generated by applying collaborative filtering methods. The low-rank matrix completion method is the state-of-the-art collaborative filtering method. In this work, we show that the skewed distribution of ratings in the user-item rating matrix of real-world datasets affects the accuracy of matrix-completion-based approaches. Also, we show that the number of ratings that an item or a user has positively correlates with the ability of low-rank matrix-completion-based approaches to predict the ratings for the item or the user accurately. Furthermore, we use these insights to develop four matrix completion-based approaches, i.e., Frequency Adaptive Rating Prediction (FARP), Truncated Matrix Factorization (TMF), Truncated Matrix Factorization with Dropout (TMF + Dropout) and Inverse Frequency Weighted Matrix Factorization (IFWMF), that outperforms traditional matrix-completion-based approaches for the users and the items with few ratings in the user-item rating matrix.Comment: 7 pages, 3 figures, ACM WWW'1

Individualized Rank Aggregation using Nuclear Norm Regularization

In recent years rank aggregation has received significant attention from the machine learning community. The goal of such a problem is to combine the (partially revealed) preferences over objects of a large population into a single, relatively consistent ordering of those objects. However, in many cases, we might not want a single ranking and instead opt for individual rankings. We study a version of the problem known as collaborative ranking. In this problem we assume that individual users provide us with pairwise preferences (for example purchasing one item over another). From those preferences we wish to obtain rankings on items that the users have not had an opportunity to explore. The results here have a very interesting connection to the standard matrix completion problem. We provide a theoretical justification for a nuclear norm regularized optimization procedure, and provide high-dimensional scaling results that show how the error in estimating user preferences behaves as the number of observations increase

Content-boosted Matrix Factorization Techniques for Recommender Systems

Many businesses are using recommender systems for marketing outreach. Recommendation algorithms can be either based on content or driven by collaborative filtering. We study different ways to incorporate content information directly into the matrix factorization approach of collaborative filtering. These content-boosted matrix factorization algorithms not only improve recommendation accuracy, but also provide useful insights about the contents, as well as make recommendations more easily interpretable

Bayesian Matrix Completion via Adaptive Relaxed Spectral Regularization

Bayesian matrix completion has been studied based on a low-rank matrix factorization formulation with promising results. However, little work has been done on Bayesian matrix completion based on the more direct spectral regularization formulation. We fill this gap by presenting a novel Bayesian matrix completion method based on spectral regularization. In order to circumvent the difficulties of dealing with the orthonormality constraints of singular vectors, we derive a new equivalent form with relaxed constraints, which then leads us to design an adaptive version of spectral regularization feasible for Bayesian inference. Our Bayesian method requires no parameter tuning and can infer the number of latent factors automatically. Experiments on synthetic and real datasets demonstrate encouraging results on rank recovery and collaborative filtering, with notably good results for very sparse matrices.Comment: Accepted to AAAI 201

Interaction Embeddings for Prediction and Explanation in Knowledge Graphs

Knowledge graph embedding aims to learn distributed representations for entities and relations, and is proven to be effective in many applications. Crossover interactions --- bi-directional effects between entities and relations --- help select related information when predicting a new triple, but haven't been formally discussed before. In this paper, we propose CrossE, a novel knowledge graph embedding which explicitly simulates crossover interactions. It not only learns one general embedding for each entity and relation as most previous methods do, but also generates multiple triple specific embeddings for both of them, named interaction embeddings. We evaluate embeddings on typical link prediction tasks and find that CrossE achieves state-of-the-art results on complex and more challenging datasets. Furthermore, we evaluate embeddings from a new perspective --- giving explanations for predicted triples, which is important for real applications. In this work, an explanation for a triple is regarded as a reliable closed-path between the head and the tail entity. Compared to other baselines, we show experimentally that CrossE, benefiting from interaction embeddings, is more capable of generating reliable explanations to support its predictions.Comment: This paper is accepted by WSDM201

Regret Bounds and Regimes of Optimality for User-User and Item-Item Collaborative Filtering

We consider an online model for recommendation systems, with each user being recommended an item at each time-step and providing 'like' or 'dislike' feedback. Each user may be recommended a given item at most once. A latent variable model specifies the user preferences: both users and items are clustered into types. All users of a given type have identical preferences for the items, and similarly, items of a given type are either all liked or all disliked by a given user. We assume that the matrix encoding the preferences of each user type for each item type is randomly generated; in this way, the model captures structure in both the item and user spaces, the amount of structure depending on the number of each of the types. The measure of performance of the recommendation system is the expected number of disliked recommendations per user, defined as expected regret. We propose two algorithms inspired by user-user and item-item collaborative filtering (CF), modified to explicitly make exploratory recommendations, and prove performance guarantees in terms of their expected regret. For two regimes of model parameters, with structure only in item space or only in user space, we prove information-theoretic lower bounds on regret that match our upper bounds up to logarithmic factors. Our analysis elucidates system operating regimes in which existing CF algorithms are nearly optimal.Comment: 51 page