A New Convex Relaxation for Tensor Completion

author: Bernardino Romera-Paredes, Department of Engineering Science, University of Oxford
published: Nov. 7, 2013,   recorded: September 2013,   views: 2618


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Tensor factorization has received a lot of interest recently in the collaborative filtering field, as a natural extension of matrix completion. That is due to the capability of tensors to model the relationships between more than two entities, such as users, products, aspects, and time. In my research, I study the case where contextual information is available about the products (as in conjoint analysis). This scenario is modeled as a multitask learning problem where the input data are products descriptions so that tasks are learned for all combinations of the remaining entities, that is, in the previous example, a task will be learned to predict how each aspect of a product is valued by each user at a given time. Multilinear algebra concepts are used to describe the resultant problem. I will discuss different approaches to solve it and the challenges that they pose when managing large data sets.

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