Conditional Linear Regression for Heterogeneous Covariances

Leda Liang, Brendan Juba
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:6182-6199, 2022.

Abstract

Often machine learning and statistical models will attempt to describe the majority of the data. However, there may be situations where only a fraction of the data can be fit well by a linear regression model. Here, we are interested in a case where such inliers can be identified by a Disjunctive Normal Form (DNF) formula. We give a polynomial time algorithm for the conditional linear regression task, which identifies a DNF condition together with the linear predictor on the corresponding portion of the data. In this work, we improve on previous algorithms by removing a requirement that the covariances of the data satisfying each of the terms of the condition have to all be very similar in spectral norm to the covariance of the overall condition.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-liang22a, title = { Conditional Linear Regression for Heterogeneous Covariances }, author = {Liang, Leda and Juba, Brendan}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {6182--6199}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/liang22a/liang22a.pdf}, url = {https://proceedings.mlr.press/v151/liang22a.html}, abstract = { Often machine learning and statistical models will attempt to describe the majority of the data. However, there may be situations where only a fraction of the data can be fit well by a linear regression model. Here, we are interested in a case where such inliers can be identified by a Disjunctive Normal Form (DNF) formula. We give a polynomial time algorithm for the conditional linear regression task, which identifies a DNF condition together with the linear predictor on the corresponding portion of the data. In this work, we improve on previous algorithms by removing a requirement that the covariances of the data satisfying each of the terms of the condition have to all be very similar in spectral norm to the covariance of the overall condition. } }
Endnote
%0 Conference Paper %T Conditional Linear Regression for Heterogeneous Covariances %A Leda Liang %A Brendan Juba %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-liang22a %I PMLR %P 6182--6199 %U https://proceedings.mlr.press/v151/liang22a.html %V 151 %X Often machine learning and statistical models will attempt to describe the majority of the data. However, there may be situations where only a fraction of the data can be fit well by a linear regression model. Here, we are interested in a case where such inliers can be identified by a Disjunctive Normal Form (DNF) formula. We give a polynomial time algorithm for the conditional linear regression task, which identifies a DNF condition together with the linear predictor on the corresponding portion of the data. In this work, we improve on previous algorithms by removing a requirement that the covariances of the data satisfying each of the terms of the condition have to all be very similar in spectral norm to the covariance of the overall condition.
APA
Liang, L. & Juba, B.. (2022). Conditional Linear Regression for Heterogeneous Covariances . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:6182-6199 Available from https://proceedings.mlr.press/v151/liang22a.html.

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