Exploiting Observation Bias to Improve Matrix Completion

• URL: http://arxiv.org/abs/2306.04775v2
• Date: Mon, 5 Feb 2024 00:25:10 GMT
• Title: Exploiting Observation Bias to Improve Matrix Completion
• Authors: Yassir Jedra, Sean Mann, Charlotte Park, Devavrat Shah
• Abstract summary: We consider a variant of matrix completion where entries are revealed in a biased manner. The goal is to exploit the shared information between the bias and the outcome of interest to improve predictions. We find that with this two-stage algorithm, the estimates have 30x smaller mean squared error compared to traditional matrix completion methods.
• Score: 16.57405742112833
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a variant of matrix completion where entries are revealed in a biased manner, adopting a model akin to that introduced by Ma and Chen. Instead of treating this observation bias as a disadvantage, as is typically the case, the goal is to exploit the shared information between the bias and the outcome of interest to improve predictions. Towards this, we consider a natural model where the observation pattern and outcome of interest are driven by the same set of underlying latent or unobserved factors. This leads to a two stage matrix completion algorithm: first, recover (distances between) the latent factors by utilizing matrix completion for the fully observed noisy binary matrix corresponding to the observation pattern; second, utilize the recovered latent factors as features and sparsely observed noisy outcomes as labels to perform non-parametric supervised learning. The finite-sample error rates analysis suggests that, ignoring logarithmic factors, this approach is competitive with the corresponding supervised learning parametric rates. This implies the two-stage method has performance that is comparable to having access to the unobserved latent factors through exploiting the shared information between the bias and outcomes. Through empirical evaluation using a real-world dataset, we find that with this two-stage algorithm, the estimates have 30x smaller mean squared error compared to traditional matrix completion methods, suggesting the utility of the model and the method proposed in this work.

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