Geometric Matrix Completion With Deep Conditional Random Fields.

Journal Article (Journal Article)

The problem of completing high-dimensional matrices from a limited set of observations arises in many big data applications, especially recommender systems. The existing matrix completion models generally follow either a memory- or a model-based approach, whereas geometric matrix completion (GMC) models combine the best from both approaches. Existing deep-learning-based geometric models yield good performance, but, in order to operate, they require a fixed structure graph capturing the relationships among the users and items. This graph is typically constructed by evaluating a pre-defined similarity metric on the available observations or by using side information, e.g., user profiles. In contrast, Markov-random-fields-based models do not require a fixed structure graph but rely on handcrafted features to make predictions. When no side information is available and the number of available observations becomes very low, existing solutions are pushed to their limits. In this article, we propose a GMC approach that addresses these challenges. We consider matrix completion as a structured prediction problem in a conditional random field (CRF), which is characterized by a maximum a posteriori (MAP) inference, and we propose a deep model that predicts the missing entries by solving the MAP inference problem. The proposed model simultaneously learns the similarities among matrix entries, computes the CRF potentials, and solves the inference problem. Its training is performed in an end-to-end manner, with a method to supervise the learning of entry similarities. Comprehensive experiments demonstrate the superior performance of the proposed model compared to various state-of-the-art models on popular benchmark data sets and underline its superior capacity to deal with highly incomplete matrices.

Full Text

Duke Authors

Cited Authors

  • Nguyen, DM; Calderbank, R; Deligiannis, N

Published Date

  • September 2020

Published In

Volume / Issue

  • 31 / 9

Start / End Page

  • 3579 - 3593

PubMed ID

  • 31689219

Electronic International Standard Serial Number (EISSN)

  • 2162-2388

International Standard Serial Number (ISSN)

  • 2162-237X

Digital Object Identifier (DOI)

  • 10.1109/tnnls.2019.2945111


  • eng