def estimate_H(X, Y, estimator, B, ratio, discrete_output = None):
"""Estimating H with Block or incomplete U-statistics estimator
:param B: Block size
:param ratio: size of incomplete U-statistics estimator
"""
assert Y.shape[0] == X.shape[0]
n = X.shape[0]
p = X.shape[1]
x_bw = util.meddistance(X, subsample = 1000)**2
kx = kernel.KGauss(x_bw)
if discrete_output is not None:
freq_dict1, freq_dict2 = discrete_output
ky = KDiscrete(freq_dict1, freq_dict2)
else:
y_bw = util.meddistance(Y[:, np.newaxis], subsample = 1000)**2
ky = kernel.KGauss(y_bw)
if estimator == 'inc':
hsic_H = hsic.HSIC_Inc(kx, ky, ratio = ratio)
m = int(n * ratio)
else: # 'block'
hsic_H = hsic.HSIC_Block(kx, ky, bsize = B)
m = int(np.floor(n / B))
H_estimates = np.zeros((p, m))
for i in range(p):
H_estimates[i, :] = np.reshape(hsic_H.estimates(X[:, i, np.newaxis],
Y[:, np.newaxis]), -1)
H = np.mean(H_estimates, axis = 1)
return H_estimates, H, m
def one_trial(i, n_samples, problem, n_select, algo):
p, r = problem.sample(n_samples, i)
if 'MMD' in mmd_or_hsic:
bw = util.meddistance(np.vstack((p, r)), subsample=1000)**2
metric = mmd.MMD_Inc(kernel.KGauss(bw))
else:
p_bw = util.meddistance(p, subsample=1000)**2
r_bw = util.meddistance(r, subsample=1000)**2
metric = hsic.HSIC_Inc(kernel.KGauss(p_bw), kernel.KGauss(r_bw), 5)
feat_select = algo(metric)
results = feat_select.test(
p,
r,
args=n_select,
seed=i,
)
## True selected features.
if results['sel_vars'].shape[0] > 1:
true = problem.is_true(results['sel_vars'])
n_true = np.sum(true)
fpr = np.sum(results['h0_rejs'][np.logical_not(true)]) / max(
n_select - n_true, 1)
tpr = np.sum(results['h0_rejs'][true]) / max(n_true, 1)
else:
tpr, fpr = 0, 0
logging.debug("TPR is :{0:.3f} FPR is :{1:.3f}".format(
tpr,
fpr,
))
return tpr, fpr
def sel_inf(self, X, Y, inf_type, alpha, niv, H0 = None, M0 = None, i = None):
"""Post-selection inference
:param X, Y: covariate and response data
:param inf_type: one-sided hypothesis testing or two-sided confidence interval calculation
:param alpha: level 1-alpha
:param niv: number of important variables, used for reporting results
H0, M0 and i are not used
"""
assert inf_type == 'test'
p = X.shape[1]
# Initialising kernels
x_bw = util.meddistance(X, subsample = 1000)**2
kx = kernel.KGauss(x_bw)
if self.discrete_output:
ky = KDiscrete()
else:
y_bw = util.meddistance(Y[:, np.newaxis], subsample = 1000)**2
ky = kernel.KGauss(y_bw)
if self.estimator == 'inc':
hsic_H = hsic.HSIC_Inc(kx, ky, ratio = self.l)
else: # 'block'
hsic_H = hsic.HSIC_Block(kx, ky, bsize = self.B)
if self.poly:
feat_select = PolySel(hsic_H)
else: # multi
feat_select = MultiSel(hsic_H)
results = feat_select.test(X, Y[:, np.newaxis], args = self.n_select, alpha = alpha)
# Reporting
sel_vars = results['sel_vars']
h0_rejs = results['h0_rejs']
ind_sc_np = None
ind_sel_np = np.zeros(p)
ind_sel_np[sel_vars] = 1
ind_h0_rej = np.zeros(p)
ind_h0_rej[sel_vars[h0_rejs]] = 1
ind_h0_rej = {'H' : ind_h0_rej}
ind_h0_rej_true = np.zeros(p)
ind_h0_rej_true[sel_vars] = 1
ind_h0_rej_true[niv:] = 0
ind_h0_rej_true = {'H' : ind_h0_rej_true}
if self.poly:
# p-values not provided for Poly
p_values = None
else:
p_values = -np.ones(p)
p_values[sel_vars] = results['pvals']
p_values = {'H': p_values}
return sim.Inference_Result(p, ind_sc_np, ind_sel_np, ind_h0_rej,
ind_h0_rej_true, p_values, None)
def estimate_H_unbiased_parallel(X, Y, discrete_output = None):
"""Parallelised estimation of H with unbiased HSIC-estimator"""
assert Y.shape[0] == X.shape[0]
p = X.shape[1]
x_bw = util.meddistance(X, subsample = 1000)**2
kx = kernel.KGauss(x_bw)
if discrete_output is not None:
freq_dict1, freq_dict2 = discrete_output
ky = KDiscrete(freq_dict1, freq_dict2)
else:
y_bw = util.meddistance(Y[:, np.newaxis], subsample = 1000)**2
ky = kernel.KGauss(y_bw)
hsic_H = hsic.HSIC_U(kx, ky)
def one_calc(i):
return hsic_H.compute(X[:,i,np.newaxis], Y[:,np.newaxis])
par = Parallel(n_jobs = -1)
res = par(delayed(one_calc)(i) for i in range(p))
return np.array(res)
def estimate_H_unbiased(X, Y, discrete_output = None):
"""Estimating H with unbiased HSIC-estimator"""
assert Y.shape[0] == X.shape[0]
p = X.shape[1]
# Creating X- and Y-kernels
x_bw = util.meddistance(X, subsample = 1000)**2 # bandwith of Gaussian kernel
kx = kernel.KGauss(x_bw)
if discrete_output is not None:
freq_dict1, freq_dict2 = discrete_output
ky = KDiscrete(freq_dict1, freq_dict2)
else:
y_bw = util.meddistance(Y[:, np.newaxis], subsample = 1000)**2
ky = kernel.KGauss(y_bw)
# H estimation
hsic_H = hsic.HSIC_U(kx, ky)
H = np.zeros(p)
for i in range(p):
H[i] = hsic_H.compute(X[:,i,np.newaxis], Y[:,np.newaxis])
return H
def estimate_M_unbiased(X):
"""Estimating M with unbiased HSIC-estimator"""
p = X.shape[1]
x_bw = util.meddistance(X, subsample = 1000)**2
kx = kernel.KGauss(x_bw)
hsic_M = hsic.HSIC_U(kx, kx)
M_true = np.zeros((p, p))
for i in range(p):
for j in range(i+1):
M_true[i, j] = hsic_M.compute(X[:,i,np.newaxis], X[:, j, np.newaxis])
M_true[j, i] = M_true[i, j] # due to symmetry
M = nearestPD(M_true) # positive definite approximation
return M_true, M
def one_trial(i, n_samples, algsel, problem, n_select, hsic_e, params):
p, r = problem.sample(n_samples, i)
p_bw = util.meddistance(p, subsample=1000)**2
r_bw = util.meddistance(r, subsample=1000)**2
hsic_e = hsic_e(kernel.KGauss(p_bw), kernel.KGauss(r_bw),
params(n_samples))
feat_select = algsel(hsic_e, params=True)
results = feat_select.test(p, r, args=n_select, seed=i)
## True selected features.
if results['sel_vars'].shape[0] > 1:
true = problem.is_true(results['sel_vars'])
n_true = np.sum(true)
fpr = np.sum(results['h0_rejs'][np.logical_not(true)]) / max(
n_select - n_true, 1)
tpr = np.sum(results['h0_rejs'][true]) / max(n_true, 1)
else:
tpr, fpr = 0, 0
logging.debug("TPR is :{0:.3f} FPR is :{1:.3f}".format(tpr, fpr))
return tpr, fpr
def estimate_M(X, estimator, B, ratio):
"""Estimating M with Block or incomplete U-statistics estimator
:param B: Block size
:param ratio: size of incomplete U-statistics estimator
"""
p = X.shape[1]
x_bw = util.meddistance(X, subsample = 1000)**2
kx = kernel.KGauss(x_bw)
if estimator == 'inc':
hsic_M = hsic.HSIC_Inc(kx, kx, ratio = ratio)
else: # 'block'
hsic_M = hsic.HSIC_Block(kx, kx, bsize = B)
M_true = np.zeros((p, p))
for i in range(p):
for j in range(i+1):
M_true[i, j] = np.mean(hsic_M.estimates(X[:, i, np.newaxis], X[:, j, np.newaxis]))
M_true[j, i] = M_true[i, j]
M = nearestPD(M_true) # positive definite approximation
return M_true, M
def estimate_M_unbiased_parallel(X):
"""Parallelised estimation of M with unbiased HSIC-estimator"""
p = X.shape[1]
x_bw = util.meddistance(X, subsample = 1000)**2
kx = kernel.KGauss(x_bw)
hsic_M = hsic.HSIC_U(kx, kx)
M_true = np.zeros((p, p))
def one_calc(i, j):
return hsic_M.compute(X[:,i,np.newaxis], X[:, j, np.newaxis])
par = Parallel(n_jobs = -1)
res = par(delayed(one_calc)(i, j) for i in range(p) for j in range(i+1))
sp = 0
for i in range(p):
for j in range(i+1):
M_true[i, j] = M_true[j, i] = res[sp + j]
sp += i+1
M = nearestPD(M_true) # positive definite approximation
return M_true, M
def one_trial(i, n_samples, algsel, problem, n_select, mmd_e):
p, r = problem.sample(n_samples, i)
bw = util.meddistance(np.vstack((p, r)), subsample=1000)**2
mmd_u = mmd_e(kernel.KGauss(bw))
feat_select = algsel(mmd_u)
results = feat_select.test(p, r, args=n_select, seed=i)
## True selected features.
if results['sel_vars'].shape[0] > 1:
true = problem.is_true(results['sel_vars'])
n_true = np.sum(true)
fpr = np.sum(results['h0_rejs'][np.logical_not(true)]) / max(
n_select - n_true, 1)
tpr = np.sum(results['h0_rejs'][true]) / max(n_true, 1)
else:
tpr, fpr = 0, 0
logging.debug("TPR is :{0:.3f} FPR is :{1:.3f}".format(tpr, fpr))
return tpr, fpr
def sel_inf(self,
X,
Y,
inf_type,
alpha,
niv,
H0=None,
M0=None,
i=None,
unbiased_parallel=False,
n_jobs=20):
"""Post-selection inference
:param X, Y: covariate and response data
:param inf_type: one-sided hypothesis testing or two-sided confidence interval calculation
:param alpha: level 1-alpha
:param niv: number of important variables, used for reporting results
H0, M0, i, unbiased_parallel and n_jobs are not used
"""
assert inf_type == 'test'
p = X.shape[1]
# Initialising kernels
x_bw = util.meddistance(X, subsample=1000)**2
kx = kernel.KGauss(x_bw)
if self.discrete_output:
values, counts = np.unique(Y, return_counts=True)
freq_dict = dict(zip(values, counts))
ky = KDiscrete(freq_dict, freq_dict)
else:
y_bw = util.meddistance(Y[:, np.newaxis], subsample=1000)**2
ky = kernel.KGauss(y_bw)
if self.estimator == 'inc':
hsic_H = hsic.HSIC_Inc(kx, ky, ratio=self.l)
else: # 'block'
hsic_H = hsic.HSIC_Block(kx, ky, bsize=self.B)
if self.poly:
feat_select = PolySel(hsic_H)
else: # multi
feat_select = MultiSel(hsic_H)
# Behaviour for evaluation of power w.r.t. first feature
if self.only_evaluate_first:
params = hsic_H.compute(X, Y[:, np.newaxis])
sel_vars = np.argpartition(params, -self.n_select,
axis=0)[-self.n_select:]
# only continue if the first feature was selected
if 0 in sel_vars:
results = feat_select.test(X,
Y[:, np.newaxis],
args=self.n_select,
alpha=alpha)
sel_vars = results['sel_vars']
h0_rejs = results['h0_rejs']
else:
# fake values
sel_vars = np.arange(p - self.n_select, p)
h0_rejs = np.array([self.n_select - 1])
# Regular behaviour
else:
results = feat_select.test(X,
Y[:, np.newaxis],
args=self.n_select,
alpha=alpha)
sel_vars = results['sel_vars']
h0_rejs = results['h0_rejs']
# Reporting
ind_sc_np = None
ind_sel_np = np.zeros(p)
ind_sel_np[sel_vars] = 1
ind_h0_rej = np.zeros(p)
ind_h0_rej[sel_vars[h0_rejs]] = 1
ind_h0_rej = {'H': ind_h0_rej}
ind_h0_rej_true = np.zeros(p)
ind_h0_rej_true[sel_vars] = 1
ind_h0_rej_true[niv:] = 0
ind_h0_rej_true = {'H': ind_h0_rej_true}
p_values = -np.ones(p)
# p-values not provided for Poly
# p-values not of interest for evaluation of empirical power
if not self.poly and not self.only_evaluate_first:
p_values[sel_vars] = results['pvals']
p_values = {'H': p_values}
inf_res = sim.Inference_Result(p, ind_sc_np, ind_sel_np, ind_h0_rej,
ind_h0_rej_true, p_values, None)
return inf_res
