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3_3_causal_discovery.py
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3_3_causal_discovery.py
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"""
This script uses the DirectLiNGAM algorithm from the lingam package to estimate
the causal graph for the specific datasets of the German traffic sign data.
"""
# ------------------------------------------------------------------------------
# imports
import os
import pandas as pd
import numpy as np
import networkx as nx
import matplotlib.pyplot as plt
from matplotlib.colors import Normalize
from lingam import DirectLiNGAM
# ------------------------------------------------------------------------------
def main(which_label: str, save_plots: bool = False, show_plots: bool = False,
verbose: bool = False):
MEASURE = 'pwling'
SEED = 610
SAVE_DIR = 'local/figures/causal_discovery/'
SAVE_FILE = f'{which_label}-{MEASURE}'
SHAPE_DIM = 2
COLOR_DIM = 3
SYMBOL_DIM = 15
if which_label in ['shapes', 'colors']:
NUM_LABELS = 4
elif which_label == 'isSpeedLimit':
NUM_LABELS = 1
else:
raise ValueError(f'Invalid label! Got {which_label}')
DATA_DIR = 'local/causal_data/'
if which_label in ['shapes', 'colors']:
DATA_FILE = f'trn_shapes-colors_{which_label}.csv'
NODE_COLORS = ['blue']*SHAPE_DIM + ['green']*COLOR_DIM + \
['red']*NUM_LABELS
NUM_DATA = SHAPE_DIM + COLOR_DIM
NUM_TOTAL = SHAPE_DIM + COLOR_DIM + NUM_LABELS
elif which_label == 'isSpeedLimit':
DATA_FILE = f'trn_shapes-colors-symbols_{which_label}.csv'
NODE_COLORS = ['blue']*SHAPE_DIM + ['green']*COLOR_DIM + \
['gold']*SYMBOL_DIM + ['red']
NUM_DATA = SHAPE_DIM + COLOR_DIM + SYMBOL_DIM
NUM_TOTAL = SHAPE_DIM + COLOR_DIM + SYMBOL_DIM + NUM_LABELS
else:
raise ValueError(f'Invalid label! Got {which_label}')
# --- create the figure directory if it does not exist ---
if save_plots:
if not os.path.exists(SAVE_DIR):
os.makedirs(SAVE_DIR)
# --- load the data ---
df = pd.read_csv(DATA_DIR + DATA_FILE)
array = df.to_numpy()
# --- encode prior knowledge ---
forbidden_edges = []
# no edges between task nodes
for i in range(NUM_DATA,NUM_TOTAL):
for j in range(NUM_TOTAL):
forbidden_edges.append((i,j))
# no edges between nodes of the same domain
for i in range(SHAPE_DIM):
for j in range(SHAPE_DIM):
forbidden_edges.append((i,j))
for i in range(SHAPE_DIM, SHAPE_DIM+COLOR_DIM):
for j in range(SHAPE_DIM, SHAPE_DIM+COLOR_DIM):
forbidden_edges.append((i,j))
for i in range(SHAPE_DIM+COLOR_DIM, NUM_DATA):
for j in range(SHAPE_DIM+COLOR_DIM, NUM_DATA):
forbidden_edges.append((i,j))
prior_knowledge_array = -1*np.ones((NUM_TOTAL,NUM_TOTAL))
for edge in forbidden_edges:
prior_knowledge_array[edge[0],edge[1]] = 0
if verbose:
print('\nPrior knowledge:')
print(prior_knowledge_array)
# --- convert binary labels to {-1,1} ---
if which_label == 'isSpeedLimit':
array[:,-1] = 2*array[:,-1]-1
else:
array[:,NUM_DATA:] = 2*array[:,NUM_DATA:]-1
# --- standardize the other rows ---
if verbose:
print('means:', np.mean(array[:,:NUM_DATA], axis=0))
print('stds:', np.std(array[:,:NUM_DATA], axis=0))
array[:,:NUM_DATA] = (array[:,:NUM_DATA] - np.mean(array[:,:NUM_DATA], axis=0)) / \
np.std(array[:,:NUM_DATA], axis=0)
# --- causal discovery ---
alg = DirectLiNGAM(prior_knowledge=prior_knowledge_array,
measure=MEASURE, random_state=SEED)
alg.fit(array)
pred_dag = alg.adjacency_matrix_
soft_dag = np.copy(pred_dag)
pred_dag = (np.abs(pred_dag) > 0.0).astype(int)
if verbose:
print('\nPredicted adjacency matrix:')
print(pred_dag)
print(np.round(soft_dag,2))
# --- report some interesting info ---
if verbose:
print()
cyc_mat = pred_dag.copy()
cycle_nodes = []
for i in range(2,NUM_TOTAL+1):
cyc_mat = cyc_mat @ pred_dag
for j in range(NUM_TOTAL):
if cyc_mat[j,j] and (j not in cycle_nodes):
cycle_nodes.append(j)
print(f'Cycle at node {j}! {i} steps')
if len(cycle_nodes) == 0:
print('No cycles found!')
cyc_mat = pred_dag.copy()
for i in range(2,NUM_TOTAL):
cyc_mat = cyc_mat @ pred_dag
if np.sum(cyc_mat) == 0:
print(f'Longest path in the graph: {i-1} steps')
break
# --- plotting the graph and matrix ---
# graph
g_pred = nx.DiGraph(pred_dag)
plt.figure(figsize=(4,3))
nx.draw(
G=g_pred,
node_color=NODE_COLORS,
node_size=1000,
arrowsize=6,
with_labels=True,
font_color='white',
font_size=14,
pos=nx.circular_layout(g_pred)
)
if save_plots:
plt.savefig(SAVE_DIR + SAVE_FILE + '-graph.png')
# colored adjacency matrix
_, ax1 = plt.subplots(figsize=(4, 3), ncols=1)
color_dag = np.ones((NUM_TOTAL,NUM_TOTAL,3)).astype(int)*255
color_dag[0:2,:,[0,1]] -= 55
color_dag[2:5,:,[0,2]] -= 55
color_dag[5:NUM_DATA,:,2] -= 55
if which_label == 'isSpeedLimit':
color_dag[-1,:,[1,2]] -= 55
else:
color_dag[-4:,:,[1,2]] -= 55
color_dag[:,0:2,[0,1]] -= 55
color_dag[:,2:5,[0,2]] -= 55
color_dag[:,5:NUM_DATA,2] -= 55
if which_label == 'isSpeedLimit':
color_dag[:,-1,[1,2]] -= 55
else:
color_dag[:,-4:,[1,2]] -= 55
color_dag[pred_dag==1,:] -= 145
ax1.set_title('est_graph')
ax1.imshow(color_dag)
size = pred_dag.shape[0]
ticks = np.array(range(size))
if which_label in ['shapes', 'colors']:
tick_labels = ['s0', 's1', 'c0', 'c1', 'c2', 'u0', 'u1', 'u2', 'u3']
elif which_label == 'isSpeedLimit':
tick_labels = ['s0', 's1', 'c0', 'c1', 'c2'] + \
[f'y{i}' for i in range(SYMBOL_DIM)] + ['u']
ax1.set_xticks(ticks, tick_labels)
ax1.set_yticks(ticks, tick_labels)
secondary_ticks = np.array(range(size-1))+0.5
ax1.set_xticks(secondary_ticks, minor=True)
ax1.set_yticks(secondary_ticks, minor=True)
ax1.grid(which='minor')
if save_plots:
plt.savefig(SAVE_DIR + SAVE_FILE + '-adj.png')
# heat maps of soft labels
fig, ax2 = plt.subplots(figsize=(4, 3), ncols=1)
cmap = plt.get_cmap('seismic')
norm = Normalize(vmin=-1.0, vmax=1.0)
ax2.set_title('soft_graph')
cax2 = ax2.imshow(soft_dag, cmap=cmap, norm=norm)
ax2.set_xticks(ticks, tick_labels)
ax2.set_yticks(ticks, tick_labels)
secondary_ticks = np.array(range(size-1))+0.5
ax2.set_xticks(secondary_ticks, minor=True)
ax2.set_yticks(secondary_ticks, minor=True)
ax2.grid(which='minor')
fig.colorbar(cax2, ax=ax2, orientation='vertical')
if save_plots:
plt.savefig(SAVE_DIR + SAVE_FILE + '-heat.png')
if show_plots:
plt.show()
return soft_dag
# ------------------------------------------------------------------------------
if __name__ == '__main__':
WHICH_LABELS = ['shapes', 'colors', 'isSpeedLimit']
SAVE_PLOTS = False
SHOW_PLOTS = False
VERBOSE = False
for which_label in WHICH_LABELS:
soft_dag = main(which_label, SAVE_PLOTS, SHOW_PLOTS, VERBOSE)
idx = np.where(np.abs(soft_dag) > 0.0)
hard_dag = np.zeros_like(soft_dag)
hard_dag[idx] = 1.0
print(f'{which_label} hard_dag:')
print(hard_dag)
# ------------------------------------------------------------------------------