crossmapy 0.0.1

causal inference under dynamical causality framework

crossmapy

crossmapy implements several causal inference algorithms based on dynamical causality (DC) framework, including Granger causality (GC), Transfer entropy(TE), Convergent Cross Mapping(CCM), Partial Cross Mapping(PCM), Cross-Mapping Cardinality(CMC) and Cross-Mapping Entropy(CME).

Install

pip install crossmapy

Examples

1. 3-variable logistic system

we use the following cascade case

the corresponding dynamical equations is

where 伪_x = 3.68, 伪_y= 3.72 and 伪_z= 3.68

1.1 import packages

import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns
sns.set(context='notebook', style='white', font_scale=1.2)

import crossmapy as cmp # import our package

1.2 simlate 3-variable logistic system using crossmapy

c = 0.4 # coupling efficient between variables
b_xy = 0
b_yx = c
b_yz = c
b_zy = 0
b_xz = 0
b_zx = c
n_trial = 1 # number of trials
n_iter = 1000 # length of time series
noise = 0.002 # noise strength
seed = 0 # random number seed

xyz = cmp.mul_logistic_3v(b_xy=b_xy, b_yx=b_yx, b_yz=b_yz, b_zy=b_zy, b_xz=b_xz, b_zx=b_zx, 
                          n_trail=n_trial, n_iter=n_iter, seed=seed, noise=noise)

show partial simulated data

fig, ax = plt.subplots(3, 1, figsize=(10, 6), sharex=True, sharey=True)
for i, l in enumerate(['x', 'y', 'z']):
    ax[i].plot(xyz[0][500:600, i])
    ax[i].set_ylabel(l)
plt.tight_layout()

1.3 calculate the causal strength by six algorithms

# show the ground truth of the system
truth = np.array([[0, b_yx, b_yz],
                  [b_xy, 0, b_zy],
                  [b_xz, b_yz, 0]])

truth_mat = cmp.discretize_score(truth, c/2)
truth_mat[np.diag_indices(3)] = np.nan

fig, ax = plt.subplots(figsize=(3, 3))
cmp.plot_score_matrix(truth_mat, labels=['x', 'y', 'z'], ax=ax, annot=False,
                      diag_line=True, cbar=False, annot_kws={'fontsize': 12})
ax.set_title('Truth')
ax.set_xlabel('Effect')
ax.set_ylabel('Cause')
plt.tight_layout()

# API for algorithms 
embed_dim = 3 # embedding dimension
GC = cmp.GrangerCausality(embed_dim=embed_dim)
TE = cmp.TransferEntropy(embed_dim=embed_dim)
CCM = cmp.ConvergeCrossMapping(embed_dim=embed_dim)
PCM = cmp.PartialCrossMapping(embed_dim=embed_dim)
CMC = cmp.CrossMappingCardinality(embed_dim=embed_dim)
DCMC = cmp.DirectCrossMappingCardinality(embed_dim=embed_dim)
models = [GC, TE, CCM, PCM, CMC, DCMC]

scores = []
for model in models:
    model.fit(xyz[0]) # .fit(data) perform the calculation
    scores.append(model.scores) # model.scores stores the causal strength matrix

compare the predict networks to the ground truth

# show the predict networks, false positive (negtive) results are marked by red solid (dashed) squares. 
thr = 0.5
labels = ['GC', 'TE', 'CCM', 'PCM', 'CMC', 'DCMC']
fig, ax = plt.subplots(2, 3, figsize=(8, 6))
ax = ax.flatten()
for i, label in enumerate(labels):
    mat = cmp.discretize_score(scores[i], thr)
    mat[np.diag_indices(3)] = np.nan
    false_pos = np.where((mat==1)&(truth_mat==0))
    false_neg = np.where((mat==0)&(truth_mat==1))

    _ = cmp.plot_score_matrix(mat, labels=['x', 'y', 'z'], annot=False, ax=ax[i], vmin=0, vmax=1,
                               diag_line=True, cbar=False, annot_kws={'fontsize': 12})
    ax[i].set_title(label)
    _ = cmp.plot_annot_square(false_pos, lw=2, c='r', ls='-', ax=ax[i])
    _ = cmp.plot_annot_square(false_neg, lw=2, c='r', ls='--', ax=ax[i])
plt.tight_layout()

2. reproduce the results in our work

check the notebook files in paper_examples.

License

MIT License