Thanks a lot for the great post, really enjoyed reading it. It opens up a new horizon for looking at RNNs which is super interesting. I was wondering if you could provide references that you've mentioned in through the post.

Thanks! ]]>

1) The definition of an instrumental variable doesn't seem very clear to me. If you have variables which can predict y (in your example it was personal ability) that variable should be in the x block. It isn't an error estimator, it's a direct correlate to the y variable. I'm also unsure how it adds error to your x variable, as education and ability are different direct measurables.

In short, I don't see how this changes the simple linear regression equation. You may have variables with higher impact on y, certainly. You may also have noise in your measurements (e.g. white noise in a spectral dataset). Yet your description claws at something greater and I'm having a hard time seeing it.

2) is this math significantly different than a PCA or PLS calculation? You've pre-selected your z-variables (it seems) and then computed a y variable from this limited selection. I can't recall the math directly bur it seems quite similar.

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