TenIPS: Inverse Propensity Sampling for Tensor Completion

Chengrun Yang, Lijun Ding, Ziyang Wu, Madeleine Udell
Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, PMLR 130:3160-3168, 2021.

Abstract

Tensors are widely used to represent multiway arrays of data. The recovery of missing entries in a tensor has been extensively studied, generally under the assumption that entries are missing completely at random (MCAR). However, in most practical settings, observations are missing not at random (MNAR): the probability that a given entry is observed (also called the propensity) may depend on other entries in the tensor or even on the value of the missing entry. In this paper, we study the problem of completing a partially observed tensor with MNAR observations, without prior information about the propensities. To complete the tensor, we assume that both the original tensor and the tensor of propensities have low multilinear rank. The algorithm first estimates the propensities using a convex relaxation and then predicts missing values using a higher-order SVD approach, reweighting the observed tensor by the inverse propensities. We provide finite-sample error bounds on the resulting complete tensor. Numerical experiments demonstrate the effectiveness of our approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v130-yang21d, title = { TenIPS: Inverse Propensity Sampling for Tensor Completion }, author = {Yang, Chengrun and Ding, Lijun and Wu, Ziyang and Udell, Madeleine}, booktitle = {Proceedings of The 24th International Conference on Artificial Intelligence and Statistics}, pages = {3160--3168}, year = {2021}, editor = {Banerjee, Arindam and Fukumizu, Kenji}, volume = {130}, series = {Proceedings of Machine Learning Research}, month = {13--15 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v130/yang21d/yang21d.pdf}, url = {https://proceedings.mlr.press/v130/yang21d.html}, abstract = { Tensors are widely used to represent multiway arrays of data. The recovery of missing entries in a tensor has been extensively studied, generally under the assumption that entries are missing completely at random (MCAR). However, in most practical settings, observations are missing not at random (MNAR): the probability that a given entry is observed (also called the propensity) may depend on other entries in the tensor or even on the value of the missing entry. In this paper, we study the problem of completing a partially observed tensor with MNAR observations, without prior information about the propensities. To complete the tensor, we assume that both the original tensor and the tensor of propensities have low multilinear rank. The algorithm first estimates the propensities using a convex relaxation and then predicts missing values using a higher-order SVD approach, reweighting the observed tensor by the inverse propensities. We provide finite-sample error bounds on the resulting complete tensor. Numerical experiments demonstrate the effectiveness of our approach. } }
Endnote
%0 Conference Paper %T TenIPS: Inverse Propensity Sampling for Tensor Completion %A Chengrun Yang %A Lijun Ding %A Ziyang Wu %A Madeleine Udell %B Proceedings of The 24th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2021 %E Arindam Banerjee %E Kenji Fukumizu %F pmlr-v130-yang21d %I PMLR %P 3160--3168 %U https://proceedings.mlr.press/v130/yang21d.html %V 130 %X Tensors are widely used to represent multiway arrays of data. The recovery of missing entries in a tensor has been extensively studied, generally under the assumption that entries are missing completely at random (MCAR). However, in most practical settings, observations are missing not at random (MNAR): the probability that a given entry is observed (also called the propensity) may depend on other entries in the tensor or even on the value of the missing entry. In this paper, we study the problem of completing a partially observed tensor with MNAR observations, without prior information about the propensities. To complete the tensor, we assume that both the original tensor and the tensor of propensities have low multilinear rank. The algorithm first estimates the propensities using a convex relaxation and then predicts missing values using a higher-order SVD approach, reweighting the observed tensor by the inverse propensities. We provide finite-sample error bounds on the resulting complete tensor. Numerical experiments demonstrate the effectiveness of our approach.
APA
Yang, C., Ding, L., Wu, Z. & Udell, M.. (2021). TenIPS: Inverse Propensity Sampling for Tensor Completion . Proceedings of The 24th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 130:3160-3168 Available from https://proceedings.mlr.press/v130/yang21d.html.

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