EigenGame: PCA as a Nash Equilibrium

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1. Overview (basic ideas)

• PCA can be seen as a differentiable game.

2. Novelty

• Formulation of PCA as finding the Nash equilibrium of a suitable game
• Decentralized version that is competitive with modern streaming k~PCA
• Demonstration by computing top-32 PCs of the matrix of ResNet200 activations with imagenet.

3. Method (Technical details)

Todo

4. Results

5. links to papers, codes, etc.

• Arxiv : https://arxiv.org/abs/2010.00554
• OpenReiview: https://openreview.net/forum?id=NzTU59SYbNq
• Deepmind: https://deepmind.com/research/publications/EigenGame-PCA-as-a-Nash-Equilibrium
• GoodNotes:

6. Thoughts, Comments

I just thought the title was cool. But it turns out that this formulation could allow PCA to work faster on GPUs/TPUs and so it might be useful for subspace computation.

7. bibtex

@misc{gemp2020eigengame,
title={EigenGame: PCA as a Nash Equilibrium},
author={Ian Gemp and Brian McWilliams and Claire Vernade and Thore Graepel},
year={2020},
eprint={2010.00554},
archivePrefix={arXiv},
primaryClass={cs.LG}
}

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