TestPC: added simple simulation for discrete and kci test

[MarkDana]

Updated files:

• tests/TestPC.py: test_pc_simulate_linear_nongaussian_with_kci and test_pc_simulate_discrete_with_chisq.
• tests/utils_simulate_data.py: some utils for simulation. Now contains forward sampling (for discrete variables) and linear SEM (for continuous variables).

What this update can do:

• Ensure PC's correctness on simple simulated data:
  • Last time we had tests for PC over loaded dataset and over data simulated from specific graphs.
  • For the latter one, we expect that PC will return totally correct CPDAG when the given graph is simple.
  • So except for the linear Gaussian case (using fisherZ) last time, now we added discrete case (using chisq) and linear nonGaussian (exponential) case (using kci).
  • The simple example graph used are all same: a 5 nodes 7 edges graph.
• Some utils for data simulation from DAG [and TODOs, with lower priority]:
  • simulate_linear_continuous_data: Simulate data by linear mixing of exogenous noises. TODOs:
    • Now noises are of the same distribution (and variance).
    • Only support noise components of Gaussian and exponential.
    • And the parameters to noise generators are fixed.
  • simulate_discrete_data: Use pgmpy's forward sampling for discrete case. TODOs:
    • Now the max cardinalities product is fixed (for speed).
    • Alpha parameters for Dirichlet sampling is also fixed.
  • Overall TODOs:
    • Check with existed simulations in Tetrad to see whether parameters here are reasonable.
    • Also incorporate nonlinear SEM.

Test plan:

python -m unittest TestPC.TestPC.test_pc_simulate_linear_nongaussian_with_kci 
# should pass, but in ~17mins (for 5 nodes, samplesize=2500)
# if you reduce the samplesize (e.g., to 2000) for speed consideration, the returned graph will not be totally correct.

# if you need to run forward sampling, please install pgmpy
pip install pgmpy
python -m unittest TestPC.TestPC.test_pc_simulate_discrete_with_chisq  # should pass within one second

[tofuwen]

Thanks @MarkDana for your awesome work!! :)

This is great!!

BTW, I think we can add some PC benchmarked results (for speed and scale) in our doc now, as PC is currently best tested method :) (thanks to you!)

cc @kunwuz to merge this PR

[MarkDana]

@tofuwen Thanks! I will work on the PC benchmarks soon.

And @kunwuz this is ready to go. Thx :))