Update PNL

[ErdunGAO]

Updates

• Change the gradient descent training method to stochastic gradient descent (For acceleration).
• Delete the dele_abnormal function, which is useless since our new implementation is robust.
• Add the testing results of our method on the real data and an additional simulation case simulation_dataset_3.

Description

• Files in data folder TestData/
  • Reduce the number of samples in the two previous simulation datasets from $1000$ to $200$, to make the test faster. (Actually, $200$ is enough for finding the causal direction of two variables.)
  • Add one more simulation dataset.
• TestPNL.py file
  • Increase the p-value threshold from $0.1$ to $0.5$.
  • Update the stored results since the previous datasets are changed.
  • Add the test functions for the third simulation dataset and the real data.
• PNL.py file
  • Add a PairDataset(Dataset) function (for batch training).
  • Reduce the total epochs from $100000$ to $3000$.
  • Codes in lines $96-107$ are cleaned. Actually, the code logic is not changed.
  • Change the learning rate from $1e-5$ to $1e-4$.
  • Delete the loss recording variables named loss_all, loss_pdf_all, and loss_jacob_all.
  • Variables $y1$, $y2$ are deleted. $y1$ is useless and $y2$ is actually the estimated noise. We use $e$ to replace $y2$ and $e_estimated$ to name the estimated noise.
  • zero_grad() of G1 and G2 is replaced by optimizer.zero_grad().
  • The dele_abnormal function is deleted.

Notes

• Please kindly note that the p_value_threshold is set to $0.5$ in TestPNL.py. This is because the p_value_backward (0.394) on real data is high, which may caused by the model misspecification on real data.
• Please try to normalize your testing data if it was collected from the real world.

Test plan
python -m unittest tests.TestPNL # should pass

[tofuwen]

this is the only concern I have.

Do we have enough evidence to claim something if we compare with threshold 0.5? This basically means you can have false positive error as large as 0.5?

[tofuwen]

cc @kunwuz to merge