Scalable Algorithms for Learning High-Dimensional Linear Mixed Models

Zilong Tan, Kimberly Roche, Xiang Zhou, Sayan Mukherjee
Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, PMLR R16:258-267, 2018.

Abstract

Linear mixed models (LMMs) are used exten- sively to model observations that are not in- dependent. Parameter estimation for LMMs can be computationally prohibitive on big data. State-of-the-art learning algorithms require computational complexity which depends at least linearly on the dimension p of the co- variates, and often use heuristics that do not offer theoretical guarantees. We present scal- able algorithms for learning high-dimensional LMMs with sublinear computational complex- ity dependence on p. Key to our approach are novel dual estimators which use only kernel functions of the data, and fast computational techniques based on the subsampled random- ized Hadamard transform. We provide theo- retical guarantees for our learning algorithms, demonstrating the robustness of parameter es- timation. Finally, we complement the theory with experiments on large synthetic and real data.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR16-tan18a, title = {Scalable Algorithms for Learning High-Dimensional Linear Mixed Models}, author = {Tan, Zilong and Roche, Kimberly and Zhou, Xiang and Mukherjee, Sayan}, booktitle = {Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence}, pages = {258--267}, year = {2018}, editor = {Globerson, Amir and Silva, Ricardo}, volume = {R16}, series = {Proceedings of Machine Learning Research}, month = {06--10 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r16/main/assets/tan18a/tan18a.pdf}, url = {https://proceedings.mlr.press/r16/tan18a.html}, abstract = {Linear mixed models (LMMs) are used exten- sively to model observations that are not in- dependent. Parameter estimation for LMMs can be computationally prohibitive on big data. State-of-the-art learning algorithms require computational complexity which depends at least linearly on the dimension p of the co- variates, and often use heuristics that do not offer theoretical guarantees. We present scal- able algorithms for learning high-dimensional LMMs with sublinear computational complex- ity dependence on p. Key to our approach are novel dual estimators which use only kernel functions of the data, and fast computational techniques based on the subsampled random- ized Hadamard transform. We provide theo- retical guarantees for our learning algorithms, demonstrating the robustness of parameter es- timation. Finally, we complement the theory with experiments on large synthetic and real data.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Scalable Algorithms for Learning High-Dimensional Linear Mixed Models %A Zilong Tan %A Kimberly Roche %A Xiang Zhou %A Sayan Mukherjee %B Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2018 %E Amir Globerson %E Ricardo Silva %F pmlr-vR16-tan18a %I PMLR %P 258--267 %U https://proceedings.mlr.press/r16/tan18a.html %V R16 %X Linear mixed models (LMMs) are used exten- sively to model observations that are not in- dependent. Parameter estimation for LMMs can be computationally prohibitive on big data. State-of-the-art learning algorithms require computational complexity which depends at least linearly on the dimension p of the co- variates, and often use heuristics that do not offer theoretical guarantees. We present scal- able algorithms for learning high-dimensional LMMs with sublinear computational complex- ity dependence on p. Key to our approach are novel dual estimators which use only kernel functions of the data, and fast computational techniques based on the subsampled random- ized Hadamard transform. We provide theo- retical guarantees for our learning algorithms, demonstrating the robustness of parameter es- timation. Finally, we complement the theory with experiments on large synthetic and real data. %Z Reissued by PMLR on 04 October 2026.
APA
Tan, Z., Roche, K., Zhou, X. & Mukherjee, S.. (2018). Scalable Algorithms for Learning High-Dimensional Linear Mixed Models. Proceedings of the 34th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R16:258-267 Available from https://proceedings.mlr.press/r16/tan18a.html. Reissued by PMLR on 04 October 2026.

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