# Matrix Completion for the Independence Model

• Kaie Kubjas Aalto University
• Zvi Rosen University of Pennsylvania
Keywords: matrix completion, independence model, weighted graphs, tensor completion, real algebraic geometry, optimal completions

### Abstract

We investigate the problem of completing partial matrices to rank-one matrices in the standard simplex $\Delta^{mn-1}$. The motivation for studying this problem comes from statistics: A lack of eligible completion can provide a falsification test for partial observations to come from the independence model. For each pattern of specified entries, we give equations and inequalities which are satisfied if and only if an eligible completion exists. We also describe the set of valid completions, and we optimize over this set.

### Author Biographies

Kaie Kubjas, Aalto University
Aalto Science Institute, postdoctoral researcher
Zvi Rosen, University of Pennsylvania
postdoctoral researcher
Published
2017-02-08
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Articles