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Issue with biased estimates from QR decomposition

See original GitHub issue

Hi again 😃

See issue: https://github.com/google-research/google-research/issues/436 that I posted on the main repository. Using the QR incorrectly produces results with significantly higher variance. There is quite an easy fix by simply doing

 q, r = torch.qr(flattened)
 # Make Q uniform according to https://arxiv.org/pdf/math-ph/0609050.pdf
 d = torch.diag(r, 0)
 ph = d.sign()
 q *= ph

Issue Analytics

State:
Created 3 years ago
Comments:9 (5 by maintainers)

Top GitHub Comments

1reaction

Parskattcommented, Oct 27, 2020

Haha they are doing about the same as the random matrices I would say. Haven’t had any great success with either variant yet though 😃 Im working on a completely unrelated task to nlp with them, so its a bit of work to adapt stuff.

1reaction

Parskattcommented, Oct 27, 2020

Im working more on the theoretical side at the moment. I just realised when I generated these matrices that I got a biased estimate (in 2d i literally got no samples in the 4th quadrant but maybe that was someting wrong on my end). Anyway, for those experiments I reduced the variance with about ~50%.

In the practical experiments Im running myself im still using learnable matrices.

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