Under-Counted Tensor Completion with Neural Incorporation of Attributes

Shahana Ibrahim, Xiao Fu, Rebecca Hutchinson, Eugene Seo
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:14283-14315, 2023.

Abstract

Systematic under-counting effects are observed in data collected across many disciplines, e.g., epidemiology and ecology. Under-counted tensor completion (UC-TC) is well-motivated for many data analytics tasks, e.g., inferring the case numbers of infectious diseases at unobserved locations from under-counted case numbers in neighboring regions. However, existing methods for similar problems often lack supports in theory, making it hard to understand the underlying principles and conditions beyond empirical successes. In this work, a low-rank Poisson tensor model with an expressive unknown nonlinear side information extractor is proposed for under-counted multi-aspect data. A joint low-rank tensor completion and neural network learning algorithm is designed to recover the model. Moreover, the UC-TC formulation is supported by theoretical analysis showing that the fully counted entries of the tensor and each entry’s under-counting probability can be provably recovered from partial observations—under reasonable conditions. To our best knowledge, the result is the first to offer theoretical supports for under-counted multi-aspect data completion. Simulations and real-data experiments corroborate the theoretical claims.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-ibrahim23a, title = {Under-Counted Tensor Completion with Neural Incorporation of Attributes}, author = {Ibrahim, Shahana and Fu, Xiao and Hutchinson, Rebecca and Seo, Eugene}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {14283--14315}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/ibrahim23a/ibrahim23a.pdf}, url = {https://proceedings.mlr.press/v202/ibrahim23a.html}, abstract = {Systematic under-counting effects are observed in data collected across many disciplines, e.g., epidemiology and ecology. Under-counted tensor completion (UC-TC) is well-motivated for many data analytics tasks, e.g., inferring the case numbers of infectious diseases at unobserved locations from under-counted case numbers in neighboring regions. However, existing methods for similar problems often lack supports in theory, making it hard to understand the underlying principles and conditions beyond empirical successes. In this work, a low-rank Poisson tensor model with an expressive unknown nonlinear side information extractor is proposed for under-counted multi-aspect data. A joint low-rank tensor completion and neural network learning algorithm is designed to recover the model. Moreover, the UC-TC formulation is supported by theoretical analysis showing that the fully counted entries of the tensor and each entry’s under-counting probability can be provably recovered from partial observations—under reasonable conditions. To our best knowledge, the result is the first to offer theoretical supports for under-counted multi-aspect data completion. Simulations and real-data experiments corroborate the theoretical claims.} }
Endnote
%0 Conference Paper %T Under-Counted Tensor Completion with Neural Incorporation of Attributes %A Shahana Ibrahim %A Xiao Fu %A Rebecca Hutchinson %A Eugene Seo %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-ibrahim23a %I PMLR %P 14283--14315 %U https://proceedings.mlr.press/v202/ibrahim23a.html %V 202 %X Systematic under-counting effects are observed in data collected across many disciplines, e.g., epidemiology and ecology. Under-counted tensor completion (UC-TC) is well-motivated for many data analytics tasks, e.g., inferring the case numbers of infectious diseases at unobserved locations from under-counted case numbers in neighboring regions. However, existing methods for similar problems often lack supports in theory, making it hard to understand the underlying principles and conditions beyond empirical successes. In this work, a low-rank Poisson tensor model with an expressive unknown nonlinear side information extractor is proposed for under-counted multi-aspect data. A joint low-rank tensor completion and neural network learning algorithm is designed to recover the model. Moreover, the UC-TC formulation is supported by theoretical analysis showing that the fully counted entries of the tensor and each entry’s under-counting probability can be provably recovered from partial observations—under reasonable conditions. To our best knowledge, the result is the first to offer theoretical supports for under-counted multi-aspect data completion. Simulations and real-data experiments corroborate the theoretical claims.
APA
Ibrahim, S., Fu, X., Hutchinson, R. & Seo, E.. (2023). Under-Counted Tensor Completion with Neural Incorporation of Attributes. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:14283-14315 Available from https://proceedings.mlr.press/v202/ibrahim23a.html.

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