def counterfactuals(args, config):
# we generate the same SEM as in the intervention example
# returns X, coeffs, dag - DAG is adjencency matrix, but not sued
X, _, _ = intervention_sem(n_obs=2500, seed=0, random=False)
(_, _, X3_std, X4_std) = X.std(axis=0)
X /= np.array([1, 1, X3_std, X4_std])
# fit CAReFl to the data
mod = CAREFL(config)
mod.fit_to_sem(X)
def gen_observation(N):
X_0 = N[0, 0]
X_1 = N[0, 1]
X_2 = (X_0 + .5 * X_1 * X_1 * X_1 + N[0, 2]) / X3_std
X_3 = (-X_1 + .5 * X_0 * X_0 + N[0, 3]) / X4_std
return np.array([X_0, X_1, X_2, X_3]).reshape((1, 4))
### now we run some CF trials:
N = np.array([2, 1.5, 1.4, -1]).reshape((1, 4))
# this is the random value of 4D random varibale x we observe. Now we plot the counterfactual
# given x_0 had been other values
xObs = gen_observation(N) # should be (2.00, 1.50, 0.81, −0.28)
# PLOT
xvals = np.arange(-3, 3, .1)
sns.set_style("whitegrid")
sns.set_palette(sns.color_palette("muted", 8))
fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(10, 4))
# fig.suptitle(r'Counterfactual predictions', fontsize=22)
# see quality of counterfactual predictions for X_4
xCF_true = [gen_observation(np.hstack((x, N[0, 1:])).reshape((1, 4)))[0, 3] for x in xvals]
xCF_pred = [mod.predict_counterfactual(x_obs=xObs, cf_val=x, iidx=0)[0, 3] for x in xvals]
ax1.plot(xvals, xCF_true, label=r'True $\mathbb{E} [{X_4}_{X_1 \leftarrow \alpha} (n) ] $', linewidth=3,
linestyle='-.')
ax1.plot(xvals, xCF_pred, label=r'Predicted $\mathbb{E} [{X_4}_{X_1 \leftarrow \alpha} (n) ] $', linewidth=3,
linestyle='-.')
ax1.legend(loc=1, fontsize=15)
ax1.set_xlabel(r'Value of counterfactual variable, $X_1=\alpha$', fontsize=18)
ax1.set_ylabel(r'Predicted value of $X_4$', fontsize=18)
# see quality of counterfactual predictions for X_3
xCF_true = [gen_observation(np.hstack((N[0, 0], x, N[0, 2:])).reshape((1, 4)))[0, 2] for x in xvals]
xCF_pred = [mod.predict_counterfactual(x_obs=xObs, cf_val=x, iidx=1)[0, 2] for x in xvals]
ax2.plot(xvals, xCF_true, label=r'True $\mathbb{E} [{X_3}_{X_2 \leftarrow \alpha} (n) ] $', linewidth=3,
linestyle='-.')
ax2.plot(xvals, xCF_pred, label=r'Predicted $\mathbb{E} [{X_3}_{X_2 \leftarrow \alpha} (n) ] $', linewidth=3,
linestyle='-.')
ax2.legend(loc='best', fontsize=15)
ax2.set_xlabel(r'Value of counterfactual variable, $X_2=\alpha$', fontsize=18)
ax2.set_ylabel(r'Predicted value of $X_3$', fontsize=18)
plt.tight_layout()
plt.subplots_adjust(top=0.925)
plt.savefig(os.path.join(args.run, 'counterfactuals_4d.pdf'), dpi=300)
def true_observation(self, n_samples=100):
"""
We generate the value of x
"""
# sample from prior
z = self.flow.prior.sample((n_samples,)).cpu().detach().numpy()
x = intervention_sem(100, dim=3, seed=0, noise_dist='laplace',
random=True, shuffle=False, nonlin='poly', multiplicative=False)
return x
def run_interventions(args, config):
n_obs = config.data.n_points
model = config.algorithm.lower()
print("** {} observations **".format(n_obs))
# generate coeffcients for equation (12), and data from that SEM
# X, coeffs, dag - DAG is A-matrix - synthetic data generated according to model in paper
data, coeffs, dag = intervention_sem(n_obs, dim=config.data.graphdim, seed=config.data.seed, random=config.data.random,
multiplicative=config.data.multiplicative, nonlin=config.data.nonlin)
print("fitting a {} model".format(model))
# fit to an affine autoregressive flow or ANM with gp/linear functions
mod = CAREFL(config) if model == 'carefl' else ANM(method=model)
# fit here DAG as input - but the function itself does never use DAG
mod.fit_to_sem(data) #removed dag
if config.algorithm =='carefl':
x_obs_dist = mod.generate_observation(n_samples=n_obs)
plot_true_generated(args, data, x_obs_dist, title='observational')
# intervene on X_1 and get a sample of {x | do(X_1=a)} for a in [-3, 3]
# avals = np.arange(-3, 3) #np.arange(-3, 3, .1)
avals = [-1]
x_int_sample = []
x_int_exp = []
for a in avals: # three different values for a for intervention
res = mod.predict_intervention(a, n_samples=n_obs, iidx=config.data.iidx)
x_int_sample.append(res[0].mean(axis=0))
x_int_exp.append(res[1].mean(axis=0))
x_int_dist = res[2]
data_int = intervention_sem(n_obs, dim=config.data.graphdim, seed=config.data.seed, random=config.data.random,
multiplicative=config.data.multiplicative, nonlin=config.data.nonlin,
iidx =config.data.iidx, value=a)
if config.algorithm == 'carefl':
plot_true_generated(args, data_int[0], x_int_dist, title='interventional')
def run_interventions(args, config):
n_obs = config.data.n_points
model = config.algorithm.lower()
print("** {} observations **".format(n_obs))
# generate coeffcients for equation (12), and data from that SEM
data, coeffs, dag = intervention_sem(
n_obs,
dim=4,
seed=config.data.seed,
random=config.data.random,
multiplicative=config.data.multiplicative)
print("fitting a {} model".format(model))
# fit to an affine autoregressive flow or ANM with gp/linear functions
mod = CAREFL(config) if model == 'carefl' else ANM(method=model)
mod.fit_to_sem(data, dag)
# intervene on X_1 and get a sample of {x | do(X_1=a)} for a in [-3, 3]
avals = np.arange(-3, 3, .1)
x_int_sample = []
x_int_exp = []
for a in avals:
res = mod.predict_intervention(a, n_samples=20, iidx=0)
x_int_sample.append(res[0].mean(axis=0))
x_int_exp.append(res[1].mean(axis=0))
x_int_sample = np.array(x_int_sample)
x_int_exp = np.array(x_int_exp)
# compute the MSE between the true E[x_3|x_1=a] to the empirical expectation from the sample
# we know that the true E[x_3|x_1=a] = a
mse_x3 = np.mean((x_int_sample[:, 2] - avals)**2)
mse_x3e = np.mean((x_int_exp[:, 2] - avals)**2)
# do the same for x_4; true E[x_4|x_1=a] = c_1*a^2
mse_x4 = np.mean((x_int_sample[:, 3] - coeffs[1] * avals * avals)**2)
mse_x4e = np.mean((x_int_exp[:, 3] - coeffs[1] * avals * avals)**2)
# store results
results = {}
results["x3"] = mse_x3
results["x4"] = mse_x4
results["x3e"] = mse_x3e
results["x4e"] = mse_x4e
pickle.dump(
results,
open(os.path.join(args.output, res_save_name(config, model)), 'wb'))