def kci_invariance_test(
suffstat: Dict,
context,
i: int,
cond_set: Optional[Union[List[int], int]] = None,
width: float = 0,
alpha: float = 0.05,
unbiased: bool = False,
regress: bool = True,
gamma_approx: bool = True,
n_draws: int = 500,
lam: float = 1e-3,
thresh: float = 1e-5,
num_eig: int = 0,
):
cond_set = to_list(cond_set)
obs_samples = suffstat['obs_samples']
iv_samples = suffstat[context]
mat = combined_mat(obs_samples, iv_samples, i, cond_set)
return kci_test(
mat,
0,
1,
list(range(2, 2 + len(cond_set))),
width=width,
alpha=alpha,
unbiased=unbiased,
gamma_approx=gamma_approx,
regress=regress,
n_draws=n_draws,
lam=lam,
thresh=thresh,
num_eig=num_eig,
)
def hsic_test(suffstat: np.ndarray,
i: int,
j: int,
cond_set: Union[List[int], int] = None,
alpha: float = 0.05) -> Dict:
"""
Test for (conditional) independence using the Hilbert-Schmidt Information Criterion. If a conditioning set is
specified, first perform non-parametric regression, then test residuals.
Parameters
----------
suffstat:
Matrix of samples.
i:
column position of first variable.
j:
column position of second variable.
cond_set:
column positions of conditioning set.
alpha:
Significance level of the test.
Returns
-------
"""
cond_set = to_list(cond_set)
if len(cond_set) == 0:
return hsic_test_vector(suffstat[:, i], suffstat[:, j], alpha=alpha)
else:
residuals_i, residuals_j = residuals(suffstat, i, j, cond_set)
return hsic_test_vector(residuals_i, residuals_j, alpha=alpha)
def hsic_test(suffstat: Any,
i: int,
j: int,
cond_set: Union[List[int], int] = None,
alpha: float = 0.05):
cond_set = to_list(cond_set)
if len(cond_set) == 0:
return hsic_test_vector(suffstat[:, i], suffstat[:, j], alpha=alpha)
else:
residuals_i, residuals_j = residuals(suffstat, i, j, cond_set)
return hsic_test_vector(residuals_i, residuals_j, alpha=alpha)
def hsic_invariance_test(suffstat,
context,
i: int,
cond_set: Optional[Union[List[int], int]] = None,
alpha: float = 0.05):
"""
TODO
Parameters
----------
TODO
Examples
--------
TODO
"""
cond_set = to_list(cond_set)
obs_samples = suffstat['obs_samples']
iv_samples = suffstat[context]
mat = combined_mat(obs_samples, iv_samples, i, cond_set)
return hsic_test(mat, 0, 1, list(range(2, 2 + len(cond_set))), alpha=alpha)
def gauss_invariance_test(suffstat,
context,
i: int,
cond_set: Optional[Union[List[int], int]] = None,
alpha: float = 0.05,
new=True,
zero_mean=False,
zero_coeffs=False):
"""
Test the null hypothesis that two Gaussian distributions are equal.
Parameters
----------
suffstat:
dictionary containing:
'obs' -- number of samples
'G' -- Gram matrix
'contexts'
context:
which context to test.
i:
position of marginal distribution.
cond_set:
positions of conditioning set in correlation matrix.
alpha:
Significance level.
Return
------
dictionary containing ttest_stat, ftest_stat, f_pvalue, t_pvalue, and reject.
"""
cond_set = to_list(cond_set)
obs_samples = suffstat['obs']['samples']
iv_samples = suffstat['contexts'][context]['samples']
n1, p = obs_samples.shape
n2 = iv_samples.shape[0]
# === FIND REGRESSION COEFFICIENTS AND RESIDUALS
if len(cond_set) != 0:
cond_ix = cond_set if zero_mean else [*cond_set, -1]
gram1 = suffstat['obs']['G'][np.ix_(cond_ix, cond_ix)]
gram2 = suffstat['contexts'][context]['G'][np.ix_(cond_ix, cond_ix)]
coefs1 = np.linalg.inv(gram1) @ obs_samples[:,
cond_ix].T @ obs_samples[:,
i]
coefs2 = np.linalg.inv(gram2) @ iv_samples[:,
cond_ix].T @ iv_samples[:,
i]
residuals1 = obs_samples[:, i] - obs_samples[:, cond_ix] @ coefs1
residuals2 = iv_samples[:, i] - iv_samples[:, cond_ix] @ coefs2
elif not zero_mean:
gram1 = n1 * np.ones([1, 1])
gram2 = n2 * np.ones([1, 1])
cond_ix = [-1]
coefs1 = np.array([np.mean(obs_samples[:, i])]) if not zero_mean else 0
coefs2 = np.array([np.mean(iv_samples[:, i])]) if not zero_mean else 0
residuals1 = obs_samples[:, i] - coefs1
residuals2 = iv_samples[:, i] - coefs2
else:
residuals1 = obs_samples[:, i]
residuals2 = iv_samples[:, i]
# means and variances of residuals
var1, var2 = np.var(residuals1,
ddof=len(cond_ix)), np.var(residuals2,
ddof=len(cond_ix))
# calculate regression coefficient invariance statistic
if len(cond_ix) != 0:
p = len(cond_ix)
rc_stat = (coefs1 - coefs2) @ inv(var1 * inv(gram1) + var2 *
inv(gram2)) @ (coefs1 - coefs2).T / p
rc_pvalue = ncfdtr(p, n1 + n2 - p, 0, rc_stat)
rc_pvalue = 2 * min(rc_pvalue, 1 - rc_pvalue)
# calculate statistic for F-Test
ftest_stat = var1 / var2
f_pvalue = ncfdtr(n1 - 1, n2 - 1, 0, ftest_stat)
f_pvalue = 2 * min(f_pvalue, 1 - f_pvalue)
# === ACCEPT/REJECT INVARIANCE HYPOTHESIS BASED ON P-VALUES WITH BONFERRONI CORRECTION
if len(cond_ix) != 0:
reject = f_pvalue < alpha / 2 or rc_pvalue < alpha / 2
else:
reject = f_pvalue < alpha
# === FORM RESULT DICT AND RETUR
result_dict = dict(ftest_stat=ftest_stat, f_pvalue=f_pvalue, reject=reject)
if len(cond_ix) > 0:
result_dict['rc_stat'] = rc_stat
result_dict['rc_pvalue'] = rc_pvalue
return result_dict