def find_faces_peng(x_bin_k, x_bin_2k, x_bin_kp, x_bin_km, delta, k, rho_min,
verbose):
"""Returns all faces s.t. eta pass the test."""
dim = x_bin_k.shape[1]
faces_pairs = faces_init_peng(x_bin_k, x_bin_2k, x_bin_kp, x_bin_km, delta,
k, rho_min, verbose)
size = 2
faces_dict = {}
faces_dict[size] = faces_pairs
# print('face size : nb faces')
while len(faces_dict[size]) > size:
# print(size, ':', len(faces_dict[size]))
faces_dict[size + 1] = []
faces_to_try = ut.candidate_faces(faces_dict[size], size, dim)
if faces_to_try:
for face in faces_to_try:
r_k = ut.rho_value(x_bin_k, face, k)
if verbose and r_k <= rho_min:
print(f'rho={r_k} for {face}')
if r_k > rho_min:
r_2k = ut.rho_value(x_bin_2k, face, k)
if r_2k > r_k:
eta = np.log(2) / np.log(r_2k / float(r_k))
var = var_eta_peng(x_bin_k, x_bin_2k, x_bin_kp,
x_bin_km, face, k)
if var > 0:
test = 1 - \
st.norm.ppf(1 - delta) * np.sqrt(var/float(k))
if eta > test:
faces_dict[size + 1].append(face)
size += 1
return faces_dict
def var_eta_peng(x_bin_k, x_bin_2k, x_bin_kp, x_bin_km, face, k):
"""Returns the variance of the Peng estimator."""
rho = ut.rho_value(x_bin_k, face, k)
rhos = ut.rhos_face_pairs(x_bin_k, face, k)
r_p = ut.r_partial_derv_centered(x_bin_k, x_bin_kp, x_bin_km, face, k)
r_ij = {(i, j): ut.rho_value(ut.partial_matrix(x_bin_2k, x_bin_k, j),
[i, j], k)
for (i, j) in it.combinations(face, 2)}
r_ji = {(i, j): ut.rho_value(ut.partial_matrix(x_bin_k, x_bin_2k, j),
[i, j], k)
for (i, j) in it.combinations(face, 2)}
var = ((2 * (rho * np.log(2))**2)**-1 * (rho + sum([
r_p[j] *
(-4 * rho +
2 * ut.rho_value(ut.partial_matrix(x_bin_k, x_bin_2k, j), face, k))
for j in face
]) + sum([
r_p[i] * r_p[j] * (3 * rhos[i, j] - 2 * r_ij[i, j])
for (i, j) in it.combinations(face, 2)
]) + sum([
r_p[i] * r_p[j] * (3 * rhos[i, j] - 2 * r_ji[i, j])
for (i, j) in it.combinations(face, 2)
]) + sum([r_p[i]**2 for i in face])))
return var
def rhos(x_bin, face, k):
"""Computes rho(i,j) for each (i,j) in face and rho(-j)."""
rhos_face = {}
for j in face:
face_tronq = [i for i in face]
del face_tronq[face_tronq.index(j)]
rhos_face[j] = ut.rho_value(x_bin, face_tronq, k)
for (i, j) in it.combinations(face, 2):
rhos_face[i, j] = ut.rho_value(x_bin, [i, j], k)
return rhos_face
def eta_peng(x_bin_k, x_bin_2k, face, k):
"""Returns Peng estimator of eta."""
r_k = ut.rho_value(x_bin_k, face, k)
r_2k = ut.rho_value(x_bin_2k, face, k)
if (r_k == 0 or r_2k == 0):
eta_face = 0.
elif r_k == r_2k:
eta_face = 0.
else:
eta_face = np.log(2) / np.log(r_2k / float(r_k))
return eta_face
def find_faces_hill(x_rank, x_bin_k, x_bin_kp, x_bin_km, delta, k, var_max, verbose):
"""Returns all faces s.t. eta pass the test."""
dim = x_bin_k.shape[1]
faces_pairs = faces_init_hill(x_rank, x_bin_k, x_bin_kp, x_bin_km,
delta, k, var_max, verbose)
size = 2
faces_dict = {}
faces_dict[size] = faces_pairs
# print('face size : nb faces')
while len(faces_dict[size]) > size:
# print(size, ':', len(faces_dict[size]))
faces_dict[size + 1] = []
faces_to_try = ut.candidate_faces(faces_dict[size], size, dim)
if faces_to_try:
for face in faces_to_try:
rho = ut.rho_value(x_bin_k, face, k)
if rho > 0.:
var = variance_eta_hill(rho, x_bin_k, x_bin_kp, x_bin_km, face, k)
if verbose and var >= var_max:
print(f'var={var} for {face}')
if 0 < var < var_max:
eta = eta_hill(x_rank, face, k)
if eta <= 0 and verbose:
print(f'eta){eta} for {face}')
else:
test = 1 - \
st.norm.ppf(1 - delta) * np.sqrt(var/float(k))
if eta > test:
faces_dict[size + 1].append(face)
size += 1
return faces_dict
def hill_test(x_rank, x_bin_k, x_bin_kp, x_bin_km, face, k, delta):
rho = ut.rho_value(x_bin_k, face, k)
var = variance_eta_hill(rho, x_bin_k, x_bin_kp, x_bin_km, face, k)
eta = eta_hill(x_rank, face, k)
test = eta - (1 - st.norm.ppf(1 - delta) * np.sqrt(var/float(k)))
return test, np.sqrt(var/float(k))
def init_freq(x_bin_k, k, f_min):
"""Return all faces of size 2 s.t. frequency > f_min."""
dim = x_bin_k.shape[1]
faces = []
for (i, j) in it.combinations(range(dim), 2):
face = [i, j]
r_alph = ut.rho_value(x_bin_k, face, k)
if r_alph > f_min:
faces.append(face)
return faces
def faces_init_peng(x_bin_k, x_bin_2k, x_bin_kp, x_bin_km, delta, k, rho_min,
verbose):
"""Returns faces of size 2 s.t. eta pass the test."""
n_dim = np.shape(x_bin_k)[1]
faces = []
for (i, j) in it.combinations(range(n_dim), 2):
face = [i, j]
r_k = ut.rho_value(x_bin_k, face, k)
if verbose and r_k <= rho_min:
print(f'rho={r_k} for {face}')
if r_k > rho_min:
r_2k = ut.rho_value(x_bin_2k, face, k)
if r_2k > r_k:
eta = np.log(2) / np.log(r_2k / float(r_k))
var = var_eta_peng(x_bin_k, x_bin_2k, x_bin_kp, x_bin_km, face,
k)
if var > 0:
test = 1 - st.norm.ppf(1 - delta) * np.sqrt(var / float(k))
if eta > test:
faces.append(face)
return faces
def find_faces_freq(x_bin_k, k, f_min):
"""Return all faces s.t. frequency > f_min."""
dim = x_bin_k.shape[1]
faces_pairs = init_freq(x_bin_k, k, f_min)
size = 2
faces_dict = {}
faces_dict[size] = faces_pairs
while len(faces_dict[size]) > size:
faces_dict[size + 1] = []
faces_to_try = ut.candidate_faces(faces_dict[size], size, dim)
if faces_to_try:
for face in faces_to_try:
r_alph = ut.rho_value(x_bin_k, face, k)
if r_alph > f_min:
faces_dict[size + 1].append(face)
size += 1
return faces_dict
def faces_init_hill(x_rank, x_bin_k, x_bin_kp, x_bin_km, delta, k, var_max, verbose):
"""Returns faces of size 2 s.t. eta pass the test."""
n_dim = np.shape(x_bin_k)[1]
faces = []
for (i, j) in it.combinations(range(n_dim), 2):
face = [i, j]
rho = ut.rho_value(x_bin_k, face, k)
if rho > 0.:
var = variance_eta_hill(rho, x_bin_k, x_bin_kp, x_bin_km,
face, k)
if verbose and var >= var_max:
print(f'var={var} for {face}')
if 0 < var < var_max:
eta = eta_hill(x_rank, face, k)
if verbose and eta <= 0:
print(f'eta={eta} for {face}')
else:
test = 1 - st.norm.ppf(1 - delta) * np.sqrt(var/float(k))
if eta > test:
faces.append(face)
return faces