A thread for questions and discussion about W3D3 (causality day).
For exercise 3 of W3D3 Tutorial 4, not very clear that why use Z value at time t+1 instead of using Z value at time t
I agree with you, it’s not explained why it should be regressed on the future timestep
We want instrument at time t affecting the neuron at time t or, in this case, t+1 at time t+1:
x⃗ _{t+1}= σ(Ax⃗_t+ηz⃗_{t+1})
is the same as
x⃗ _{t}=σ(Ax⃗_{t-1}+ηz⃗_{t})
This was a notation choice on our part to align with the previous equations from the earlier tutorials, but a couple others have noted this was confusing as well so sorry about that!
Regarding the regression, we again want to make sure that the first stage regression has Z and X aligned on the same time step, hence the same slice is being made here (Tutorial 4 Section 2.1):
stage1.fit(Z[:, :-1].transpose(), X[:, :-1].transpose())
X_hat = stage1.predict(Z[:, :-1].transpose())
Thank you! Your explanation is very clear, I understand now.