Interpretable Matrix Completion

Powerful recommender system that gives detailed explanations for each suggestion

State-of-the-art recommender systems are black boxes

Companies such as Amazon, Netflix, and Airbnb rely on recommender systems to suggest items that users are more likely to interact with, hence increasing user engagement and consequently revenue. The most commonly-used recommender system is collaborative filtering, which learns user preferences from historical interactions. It is often solved by a low-rank matrix factorization process.

A main disadvantage of this approach is that it assumes users and items are described by some unseen "latent factors", despite the fact that specific attributes of users and items are known. As a result, the system does not use any side information even when it is valuable. Furthermore, when the system makes a recommendation, it provides very little explanation.
User Movie 1 Movie 2 Movie 3
A 1 5 ?
B ? ? 4
C 2 ? ?
D ? ? 5

Example matrix completion problem for recommender systems

Interpretable Matrix Completion offers simple explanation while achieving higher accuracy

With the power of modern optimization, Interpretable Matrix Completion finds the exact solution to the problem while additionally incorporating side information. It learns to select the most relevant sparse subset of features given the interactions, hence providing concise and contextual reasoning behind the recommendation.

Because Interpretable Matrix Completions solves the problem exactly, in addition to being interpretable, it also achieves superior performance compared to classical matrix completion algorithms. In large scale experiments, it achieves lower mean absolute percentage error (MAPE) compared to a state-of-the-art method, SoftImpute.

Interpretable Matrix Completion achieves lower error than SoftImpute as the number of items increases

Extremely fast and scalable

Interpretable Matrix Completion is offered in two flavors: the exact method as well as a stochastic approach. Both scale well to large datasets as a result of progress made in modern optimization over the past decades.

In particular, the stochastic version of the algorithm scales to solving massive datasets with millions of users and millions of items in under an hour.

Comparison of computation time showing both exact and stochastic versions of Interpretable Matrix Completion are significantly faster than SoftImpute.

Extension to multiple slices of noisy data to further boost performance

Traditional recommender system solutions are designed for 2-dimensional matrices. If we have multiple dimensions of data (e.g. interactions over time or multiple types of interactions), it can be advantageous for the model to leverage these many slices of the data simultaneously.

An extension of our Interpretable Matrix Completion algorithm allows it to incorporate these additional slices of data. Addressing this limitation allows us to gain more insights and make more holistic recommendations.

Completion problem with multiple slices

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