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 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_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