Faster Maximum Inner Product Search in High Dimensions

Mo Tiwari, Ryan Kang, Jaeyong Lee, Donghyun Lee, Christopher J Piech, Sebastian Thrun, Ilan Shomorony, Martin Jinye Zhang
Proceedings of the 41st International Conference on Machine Learning, PMLR 235:48344-48361, 2024.

Abstract

Maximum Inner Product Search (MIPS) is a ubiquitous task in machine learning applications. Given a query vector and $n$ other vectors in $d$ dimensions, the MIPS problem is to find the atom that has the highest inner product with the query vector. Existing MIPS algorithms scale at least as $O(\sqrt{d})$ with respect to $d$, which becomes computationally prohibitive in high-dimensional settings. In this work, we present BanditMIPS, a novel randomized algorithm that provably improves the state-of-the-art complexity from $O(\sqrt{d})$ to $O(1)$ with respect to $d$. We validate the scaling of BanditMIPS and demonstrate that BanditMIPS outperforms prior state-of-the-art MIPS algorithms in sample complexity, wall-clock time, and precision/speedup tradeoff across a variety of experimental settings. Furthermore, we propose a variant of our algorithm, named BanditMIPS-$\alpha$, which improves upon BanditMIPS by employing non-uniform sampling across coordinates. We also demonstrate the usefulness of BanditMIPS in problems for which MIPS is a subroutine, including Matching Pursuit and Fourier analysis. Finally, we demonstrate that BanditMIPS can be used in conjunction with preprocessing techniques to improve its complexity with respect to $n$. All of our experimental results are reproducible via a 1-line script at github.com/ThrunGroup/BanditMIPS.

Cite this Paper

BibTeX
@InProceedings{pmlr-v235-tiwari24a, title = {Faster Maximum Inner Product Search in High Dimensions}, author = {Tiwari, Mo and Kang, Ryan and Lee, Jaeyong and Lee, Donghyun and Piech, Christopher J and Thrun, Sebastian and Shomorony, Ilan and Zhang, Martin Jinye}, booktitle = {Proceedings of the 41st International Conference on Machine Learning}, pages = {48344--48361}, year = {2024}, editor = {Salakhutdinov, Ruslan and Kolter, Zico and Heller, Katherine and Weller, Adrian and Oliver, Nuria and Scarlett, Jonathan and Berkenkamp, Felix}, volume = {235}, series = {Proceedings of Machine Learning Research}, month = {21--27 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v235/main/assets/tiwari24a/tiwari24a.pdf}, url = {https://proceedings.mlr.press/v235/tiwari24a.html}, abstract = {Maximum Inner Product Search (MIPS) is a ubiquitous task in machine learning applications. Given a query vector and $n$ other vectors in $d$ dimensions, the MIPS problem is to find the atom that has the highest inner product with the query vector. Existing MIPS algorithms scale at least as $O(\sqrt{d})$ with respect to $d$, which becomes computationally prohibitive in high-dimensional settings. In this work, we present BanditMIPS, a novel randomized algorithm that provably improves the state-of-the-art complexity from $O(\sqrt{d})$ to $O(1)$ with respect to $d$. We validate the scaling of BanditMIPS and demonstrate that BanditMIPS outperforms prior state-of-the-art MIPS algorithms in sample complexity, wall-clock time, and precision/speedup tradeoff across a variety of experimental settings. Furthermore, we propose a variant of our algorithm, named BanditMIPS-$\alpha$, which improves upon BanditMIPS by employing non-uniform sampling across coordinates. We also demonstrate the usefulness of BanditMIPS in problems for which MIPS is a subroutine, including Matching Pursuit and Fourier analysis. Finally, we demonstrate that BanditMIPS can be used in conjunction with preprocessing techniques to improve its complexity with respect to $n$. All of our experimental results are reproducible via a 1-line script at github.com/ThrunGroup/BanditMIPS.} }
Endnote
%0 Conference Paper %T Faster Maximum Inner Product Search in High Dimensions %A Mo Tiwari %A Ryan Kang %A Jaeyong Lee %A Donghyun Lee %A Christopher J Piech %A Sebastian Thrun %A Ilan Shomorony %A Martin Jinye Zhang %B Proceedings of the 41st International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2024 %E Ruslan Salakhutdinov %E Zico Kolter %E Katherine Heller %E Adrian Weller %E Nuria Oliver %E Jonathan Scarlett %E Felix Berkenkamp %F pmlr-v235-tiwari24a %I PMLR %P 48344--48361 %U https://proceedings.mlr.press/v235/tiwari24a.html %V 235 %X Maximum Inner Product Search (MIPS) is a ubiquitous task in machine learning applications. Given a query vector and $n$ other vectors in $d$ dimensions, the MIPS problem is to find the atom that has the highest inner product with the query vector. Existing MIPS algorithms scale at least as $O(\sqrt{d})$ with respect to $d$, which becomes computationally prohibitive in high-dimensional settings. In this work, we present BanditMIPS, a novel randomized algorithm that provably improves the state-of-the-art complexity from $O(\sqrt{d})$ to $O(1)$ with respect to $d$. We validate the scaling of BanditMIPS and demonstrate that BanditMIPS outperforms prior state-of-the-art MIPS algorithms in sample complexity, wall-clock time, and precision/speedup tradeoff across a variety of experimental settings. Furthermore, we propose a variant of our algorithm, named BanditMIPS-$\alpha$, which improves upon BanditMIPS by employing non-uniform sampling across coordinates. We also demonstrate the usefulness of BanditMIPS in problems for which MIPS is a subroutine, including Matching Pursuit and Fourier analysis. Finally, we demonstrate that BanditMIPS can be used in conjunction with preprocessing techniques to improve its complexity with respect to $n$. All of our experimental results are reproducible via a 1-line script at github.com/ThrunGroup/BanditMIPS.
APA
Tiwari, M., Kang, R., Lee, J., Lee, D., Piech, C.J., Thrun, S., Shomorony, I. & Zhang, M.J.. (2024). Faster Maximum Inner Product Search in High Dimensions. Proceedings of the 41st International Conference on Machine Learning, in Proceedings of Machine Learning Research 235:48344-48361 Available from https://proceedings.mlr.press/v235/tiwari24a.html.

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