Paris West University Nanterre La Défense

About: Paris West University Nanterre La Défense is a education organization based out in Paris, France. It is known for research contribution in the topics: Computer science & Politics. The organization has 895 authors who have published 1430 publications receiving 21712 citations.

Collective Matrix Completion

Abstract: Matrix completion aims to reconstruct a data matrix based on observations of a small number of its entries. Usually in matrix completion a single matrix is considered, which can be, for example, a rating matrix in recommendation system. However, in practical situations, data is often obtained from multiple sources which results in a collection of matrices rather than a single one. In this work, we consider the problem of collective matrix completion with multiple and heterogeneous matrices, which can be count, binary, continuous, etc. We first investigate the setting where, for each source, the matrix entries are sampled from an exponential family distribution. Then, we relax the assumption of exponential family distribution for the noise and we investigate the distribution-free case. In this setting, we do not assume any specific model for the observations. The estimation procedures are based on minimizing the sum of a goodness-of-fit term and the nuclear norm penalization of the whole collective matrix. We prove that the proposed estimators achieve fast rates of convergence under the two considered settings and we corroborate our results with numerical experiments.

Valuing patents using renewal data: an inquiry into the feasability of an automated patent scoring method

Abstract: In this paper, we address the problem of patent valuation. With this aim in view, we focus on the feasibility of a patent rating system. This leads us to develop a structural model of patent renewal decisions based on real options that links patent renewals and patent value and to estimate it on micro level data. Results for a sample of European patents show that unobserved heterogeneity is too high to efficiently discriminate among patents and cast some doubt on the possibility to develop a reliable rating system based only on patent metrics.