Structure Learning of Latent Factors via Clique Search on Correlation Thresholded Graphs

Dale Kim, Qing Zhou
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:16978-16996, 2023.

Abstract

Despite the widespread application of latent factor analysis, existing methods suffer from the following weaknesses: requiring the number of factors to be known, lack of theoretical guarantees for learning the model structure, and nonidentifiability of the parameters due to rotation invariance properties of the likelihood. We address these concerns by proposing a fast correlation thresholding (CT) algorithm that simultaneously learns the number of latent factors and a rotationally identifiable model structure. Our novel approach translates this structure learning problem into the search for so-called independent maximal cliques in a thresholded correlation graph that can be easily constructed from the observed data. Our clique analysis technique scales well up to thousands of variables, while competing methods are not applicable in a reasonable amount of running time. We establish a finite-sample error bound and high-dimensional consistency for the structure learning of our method. Through a series of simulation studies and a real data example, we show that the CT algorithm is an accurate method for learning the structure of factor analysis models and is robust to violations of its assumptions.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-kim23aa, title = {Structure Learning of Latent Factors via Clique Search on Correlation Thresholded Graphs}, author = {Kim, Dale and Zhou, Qing}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {16978--16996}, 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/kim23aa/kim23aa.pdf}, url = {https://proceedings.mlr.press/v202/kim23aa.html}, abstract = {Despite the widespread application of latent factor analysis, existing methods suffer from the following weaknesses: requiring the number of factors to be known, lack of theoretical guarantees for learning the model structure, and nonidentifiability of the parameters due to rotation invariance properties of the likelihood. We address these concerns by proposing a fast correlation thresholding (CT) algorithm that simultaneously learns the number of latent factors and a rotationally identifiable model structure. Our novel approach translates this structure learning problem into the search for so-called independent maximal cliques in a thresholded correlation graph that can be easily constructed from the observed data. Our clique analysis technique scales well up to thousands of variables, while competing methods are not applicable in a reasonable amount of running time. We establish a finite-sample error bound and high-dimensional consistency for the structure learning of our method. Through a series of simulation studies and a real data example, we show that the CT algorithm is an accurate method for learning the structure of factor analysis models and is robust to violations of its assumptions.} }
Endnote
%0 Conference Paper %T Structure Learning of Latent Factors via Clique Search on Correlation Thresholded Graphs %A Dale Kim %A Qing Zhou %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-kim23aa %I PMLR %P 16978--16996 %U https://proceedings.mlr.press/v202/kim23aa.html %V 202 %X Despite the widespread application of latent factor analysis, existing methods suffer from the following weaknesses: requiring the number of factors to be known, lack of theoretical guarantees for learning the model structure, and nonidentifiability of the parameters due to rotation invariance properties of the likelihood. We address these concerns by proposing a fast correlation thresholding (CT) algorithm that simultaneously learns the number of latent factors and a rotationally identifiable model structure. Our novel approach translates this structure learning problem into the search for so-called independent maximal cliques in a thresholded correlation graph that can be easily constructed from the observed data. Our clique analysis technique scales well up to thousands of variables, while competing methods are not applicable in a reasonable amount of running time. We establish a finite-sample error bound and high-dimensional consistency for the structure learning of our method. Through a series of simulation studies and a real data example, we show that the CT algorithm is an accurate method for learning the structure of factor analysis models and is robust to violations of its assumptions.
APA
Kim, D. & Zhou, Q.. (2023). Structure Learning of Latent Factors via Clique Search on Correlation Thresholded Graphs. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:16978-16996 Available from https://proceedings.mlr.press/v202/kim23aa.html.

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