2026-09-18T19:09:48Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1563122024-08-22T03:40:17Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Shah, Devavrat
Park, Charlotte
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2024-08-21T18:55:53Z
2024-08-21T18:55:53Z
2024-05
2024-07-10T12:59:48.772Z
https://hdl.handle.net/1721.1/156312
We consider a variant of matrix completion where entries are revealed in a biased manner, adopting a model akin to that introduced by Ma & Chen (2019) [1]. 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 f inite-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.
S.M.
Massachusetts Institute of Technology
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Exploiting Observation Bias to Improve Matrix Completion
Thesis
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Master
Master of Science in Electrical Engineering and Computer Science
Publication
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<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 & Chen (2019) [1]. 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 f inite-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.</Abstract>
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