def __init__(self,
mult=True,
shannon_co_name='BHShannon_KnnK',
shannon_co_pars=None,
ce_co_name='BCCE_KnnK',
ce_co_pars=None):
""" Initialize the estimator.
Parameters
----------
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
shannon_co_name : str, optional
You can change it to any Shannon entropy
(default is 'BHShannon_KnnK').
shannon_co_pars : dictionary, optional
Parameters for the Shannon entropy estimator (default
is None (=> {}); in this case the default parameter
values of the Shannon entropy estimator are used).
ce_co_name : str, optional
You can change it to any cross-entropy estimator
(default is 'BCCE_KnnK').
ce_co_pars : dictionary, optional
Parameters for the cross-entropy estimator (default
is None (=> {}); in this case the default parameter
values of the cross-entropy estimator are used).
Examples
--------
>>> import ite
>>> co1 = ite.cost.MDKL_HSCE()
>>> co2 = ite.cost.MDKL_HSCE(shannon_co_name='BHShannon_KnnK')
>>> co3 = ite.cost.MDKL_HSCE(shannon_co_name='BHShannon_KnnK',\
shannon_co_pars={'k':6,'eps':0.2})
>>> co4 = ite.cost.MDKL_HSCE(shannon_co_name='BHShannon_KnnK',\
shannon_co_pars={'k':5,'eps':0.2},\
ce_co_name='BCCE_KnnK',\
ce_co_pars={'k':6,'eps':0.1})
"""
# initialize with 'InitX':
super().__init__(mult=mult)
# initialize the Shannon entropy estimator:
shannon_co_pars = shannon_co_pars or {}
shannon_co_pars['mult'] = True # guarantee this property
self.shannon_co = co_factory(shannon_co_name, **shannon_co_pars)
# initialize the cross-entropy estimator:
ce_co_pars = ce_co_pars or {}
ce_co_pars['mult'] = True # guarantee this property
self.ce_co = co_factory(ce_co_name, **ce_co_pars)
def __init__(self, mult=True, l2_co_name='BDL2_KnnK', l2_co_pars=None):
""" Initialize the estimator.
Parameters
----------
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
l2_co_name : str, optional
You can change it to any L2 divergence estimator
(default is 'BDL2_KnnK').
l2_co_pars : dictionary, optional
Parameters for the L2 divergence estimator (default
is None (=> {}); in this case the default parameter
values of the L2 divergence estimator are used).
Examples
--------
>>> import ite
>>> co1 = ite.cost.MIL2_DL2()
>>> co2 = ite.cost.MIL2_DL2(l2_co_name='BDL2_KnnK')
>>> dict_ch = {'knn_method': 'cKDTree', 'k': 2, 'eps': 0.1}
>>> co3 = ite.cost.MIL2_DL2(l2_co_name='BDL2_KnnK',\
l2_co_pars=dict_ch)
"""
# initialize with 'InitX':
super().__init__(mult=mult)
# initialize the L2 divergence estimator:
l2_co_pars = l2_co_pars or {}
l2_co_pars['mult'] = mult # guarantee this property
self.l2_co = co_factory(l2_co_name, **l2_co_pars)
def __init__(self, mult=True, js_co_name='MDJS_HS', js_co_pars=None):
""" Initialize the estimator.
Parameters
----------
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
js_co_name : str, optional
You can change it to any Jensen-Shannon divergence
estimator (default is 'MDJS_HS').
js_co_pars : dictionary, optional
Parameters for the Jensen-Shannnon divergence
estimator (default is None (=> {}); in this case the
default parameter values of the Jensen-Shannon
divergence estimator are used).
Examples
--------
>>> import ite
>>> co1 = ite.cost.MKJS_DJS()
>>> co2 = ite.cost.MKJS_DJS(js_co_name='MDJS_HS')
"""
# initialize with 'InitX':
super().__init__(mult=mult)
# initialize the Jensen-Shannon divergence estimator:
js_co_pars = js_co_pars or {}
js_co_pars['mult'] = True # guarantee this property
js_co_pars['w'] = array([1 / 2, 1 / 2]) # uniform weights
self.js_co = co_factory(js_co_name, **js_co_pars)
def __init__(self, mult=True, kl_co_name='BDKL_KnnK', kl_co_pars=None):
""" Initialize the estimator.
Parameters
----------
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
kl_co_name : str, optional
You can change it to any Kullback-Leibler divergence
estimator. (default is 'BDKL_KnnK')
kl_co_pars : dictionary, optional
Parameters for the KL divergence estimator. (default
is None (=> {}); in this case the default parameter
values of the KL divergence estimator are used)
--------
>>> import ite
>>> co1 = ite.cost.MHShannon_DKLN()
>>> co2 = ite.cost.MHShannon_DKLN(kl_co_name='BDKL_KnnK')
>>> dict_ch = {'knn_method': 'cKDTree', 'k': 4, 'eps': 0.2}
>>> co3 = ite.cost.MHShannon_DKLN(kl_co_name='BDKL_KnnK', \
kl_co_pars=dict_ch)
"""
# initialize with 'InitX':
super().__init__(mult=mult)
# initialize the KL divergence estimator:
kl_co_pars = kl_co_pars or {}
kl_co_pars['mult'] = True # guarantee this property
self.kl_co = co_factory(kl_co_name, **kl_co_pars)
def __init__(self,
mult=True,
alpha=0.99,
w=array([1 / 2, 1 / 2]),
renyi_co_name='BHRenyi_KnnK',
renyi_co_pars=None):
""" Initialize the estimator.
Parameters
----------
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
alpha : float, \ne 1, optional
Parameter of the Jensen-Renyi divergence (default is 0.99).
w : ndarray, w = [w1,w2], w_i > 0, w_2 > 0, w1 + w2 = 1, optional.
Parameters of the Jensen-Renyi divergence (default is w =
array([1/2,1/2]) )
renyi_co_name : str, optional
You can change it to any Renyi entropy estimator
(default is 'BHRenyi_KnnK').
renyi_co_pars : dictionary, optional
Parameters for the Renyi entropy estimator
(default is None (=> {}); in this case the default
parameter values of the Renyi entropy estimator
are used).
Examples
--------
>>> import ite
>>> co1 = ite.cost.MDJR_HR()
>>> co2 = ite.cost.MDJR_HR(renyi_co_name='BHRenyi_KnnK', alpha=0.8)
>>> co3 = ite.cost.MDJR_HR(renyi_co_name='BHRenyi_KnnK',\
renyi_co_pars={'k': 6}, alpha=0.5,\
w=array([1/4,3/4]))
"""
# initialize with 'InitAlpha':
super().__init__(mult=mult, alpha=alpha)
# initialize the Renyi entropy estimator:
renyi_co_pars = renyi_co_pars or {}
renyi_co_pars['mult'] = mult # guarantee this property
renyi_co_pars['alpha'] = alpha # -||-
self.renyi_co = co_factory(renyi_co_name, **renyi_co_pars)
# other attributes (w):
# verification:
if sum(w) != 1:
raise Exception('sum(w) has to be 1!')
if not all(w > 0):
raise Exception('The coordinates of w have to be positive!')
if len(w) != 2:
raise Exception('The length of w has to be 2!')
self.w = w
def main():
# parameters:
dim = 1 # dimension of the distribution
num_of_samples_v = arange(100, 5*1000+1, 100) # number of samples
cost_name = 'BKExpected' # dim >= 1
# initialization:
distr = 'normal' # fixed
num_of_samples_max = num_of_samples_v[-1]
length = len(num_of_samples_v)
# RBF kernel (sigma = std / bandwith parameter):
kernel = Kernel({'name': 'RBF', 'sigma': 1})
# polynomial kernel (quadratic / cubic; c = offset parameter = 1):
# kernel = Kernel({'name': 'polynomial', 'exponent': 2, 'c': 1})
# kernel = Kernel({'name': 'polynomial', 'exponent': 3, 'c': 1})
co = co_factory(cost_name, mult=True, kernel = kernel) # cost object
k_hat_v = zeros(length) # vector of estimated kernel values
# distr, dim -> samples (y1,y2), distribution parameters (par1,par2),
# analytical value (k):
if distr == 'normal':
# mean (m1,m2):
m1 = rand(dim)
m2 = rand(dim)
# (random) linear transformation applied to the data (l1,l2) ->
# covariance matrix (c1,c2):
l2 = rand(dim, dim)
l1 = rand(dim, dim)
c1 = dot(l1, l1.T)
c2 = dot(l2, l2.T)
# generate samples (y1~N(m1,c1), y2~N(m2,c2)):
y1 = multivariate_normal(m1, c1, num_of_samples_max)
y2 = multivariate_normal(m2, c2, num_of_samples_max)
par1 = {"mean": m1, "cov": c1}
par2 = {"mean": m2, "cov": c2}
else:
raise Exception('Distribution=?')
k = analytical_value_k_expected(distr, distr, co.kernel, par1, par2)
# estimation:
for (tk, num_of_samples) in enumerate(num_of_samples_v):
k_hat_v[tk] = co.estimation(y1[0:num_of_samples],
y2[0:num_of_samples]) # broadcast
print("tk={0}/{1}".format(tk+1, length))
# plot:
plt.plot(num_of_samples_v, k_hat_v, num_of_samples_v, ones(length)*k)
plt.xlabel('Number of samples')
plt.ylabel('Expected kernel')
plt.legend(('estimation', 'analytical value'), loc='best')
plt.title("Estimator: " + cost_name)
plt.show()
def main():
# parameters:
alpha = 0.7 # parameter of Sharma-Mittal divergence, >0, \ne 1
beta = 0.5 # parameter of Sharma-Mittal divergence, \ne 1
dim = 1 # dimension of the distribution
num_of_samples_v = arange(1000, 30*1000+1, 2000)
cost_name = 'BDSharmaMittal_KnnK' # dim >= 1
# initialization:
distr = 'normal' # fixed
num_of_samples_max = num_of_samples_v[-1]
length = len(num_of_samples_v)
# cost object:
co = co_factory(cost_name, mult=True, alpha=alpha, beta=beta)
d_hat_v = zeros(length) # vector of estimated divergence values
# distr, dim -> samples (y1,y2), distribution parameters (par1,par2),
# analytical value (d):
if distr == 'normal':
# mean (m1,m2):
m2 = rand(dim)
m1 = m2
# (random) linear transformation applied to the data (l1,l2) ->
# covariance matrix (c1,c2):
l2 = rand(dim, dim)
l1 = rand(1) * l2
# Note: (m2,l2) => (m1,c1) choice guarantees y1<<y2 (in practise,
# too).
c1 = dot(l1, l1.T)
c2 = dot(l2, l2.T)
# generate samples (y1~N(m1,c1), y2~N(m2,c2)):
y1 = multivariate_normal(m1, c1, num_of_samples_max)
y2 = multivariate_normal(m2, c2, num_of_samples_max)
par1 = {"mean": m1, "cov": c1}
par2 = {"mean": m2, "cov": c2}
else:
raise Exception('Distribution=?')
d = analytical_value_d_sharma_mittal(distr, distr, alpha, beta, par1,
par2)
# estimation:
for (tk, num_of_samples) in enumerate(num_of_samples_v):
d_hat_v[tk] = co.estimation(y1[0:num_of_samples],
y2[0:num_of_samples]) # broadcast
print("tk={0}/{1}".format(tk+1, length))
# plot:
plt.plot(num_of_samples_v, d_hat_v, num_of_samples_v, ones(length)*d)
plt.xlabel('Number of samples')
plt.ylabel('Sharma-Mittal divergence')
plt.legend(('estimation', 'analytical value'), loc='best')
plt.title("Estimator: " + cost_name)
plt.show()
def __init__(self,
mult=True,
alpha=0.99,
u=1,
tsallis_co_name='BHTsallis_KnnK',
tsallis_co_pars=None):
""" Initialize the estimator.
Parameters
----------
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
alpha: float, 0 < alpha <= 2, \ne 1, optional
Parameter of the exponentiated Jensen-Tsallis kernel-1
(default is 0.99).
u: float, 0 < u, optional
Parameter of the exponentiated Jensen-Tsallis kernel-1 (default
is 1).
tsallis_co_name : str, optional
You can change it to any Tsallis entropy
estimator (default is 'BHTsallis_KnnK').
tsallis_co_pars : dictionary, optional
Parameters for the Tsallis entropy estimator
(default is None (=> {}); in this case the
default parameter values of the Tsallis entropy
estimator are used).
Examples
--------
>>> import ite
>>> co1 = ite.cost.MKExpJT1_HT()
>>> co2 = ite.cost.MKExpJT1_HT(tsallis_co_name='BHTsallis_KnnK')
>>> co3 = ite.cost.MKExpJT1_HT(alpha=0.7,u=1.2,\
tsallis_co_name='BHTsallis_KnnK')
>>> dict_ch = {'knn_method': 'cKDTree', 'k': 4, 'eps': 0.1}
>>> co4 = ite.cost.MKExpJT1_HT(tsallis_co_name='BHTsallis_KnnK',\
tsallis_co_pars=dict_ch)
"""
# verification (alpha == 1 is checked via 'InitUAlpha'):
# if alpha <= 0 or alpha > 2:
# raise Exception('0 < alpha <= 2 has to hold!')
# initialize with 'InitUAlpha':
super().__init__(mult=mult, u=u, alpha=alpha)
# initialize the Tsallis entropy estimator:
tsallis_co_pars = tsallis_co_pars or {}
tsallis_co_pars['mult'] = True # guarantee this property
tsallis_co_pars['alpha'] = alpha # -||-
self.tsallis_co = co_factory(tsallis_co_name, **tsallis_co_pars)
# other attributes (u):
self.u = u
def main():
# parameters:
distr = 'normal' # distribution: 'uniform', 'normal'
dim = 2 # dimension of the distribution
num_of_samples_v = arange(1000, 50 * 1000 + 1, 1000)
cost_name = 'BHShannon_KnnK' # dim >= 1
# cost_name = 'BHShannon_SpacingV' # dim = 1
# cost_name = 'BHShannon_MaxEnt1' # dim = 1; approximation around N
# cost_name = 'BHShannon_MaxEnt2' # dim = 1; approximation around N
# cost_name = 'MHShannon_DKLN' # dim >= 1
# cost_name = 'MHShannon_DKLU' # dim >= 1
# initialization:
num_of_samples_max = num_of_samples_v[-1]
length = len(num_of_samples_v)
co = co_factory(cost_name, mult=True) # cost object
h_hat_v = zeros(length) # vector of estimated entropy values
# distr, dim -> samples (y), distribution parameters (par), analytical
# value (h):
if distr == 'uniform':
# U[a,b], (random) linear transformation applied to the data (l):
a = -rand(1, dim)
b = rand(1, dim) # guaranteed that a<=b (coordinate-wise)
l = rand(dim, dim)
y = dot(rand(num_of_samples_max, dim) * (b - a) + a, l.T) # lxU[a,b]
par = {"a": a, "b": b, "l": l}
elif distr == 'normal':
# mean (m), covariance matrix (c):
m = rand(dim)
l = rand(dim, dim)
c = dot(l, l.T)
# generate samples (y~N(m,c)):
y = multivariate_normal(m, c, num_of_samples_max)
par = {"cov": c}
else:
raise Exception('Distribution=?')
h = analytical_value_h_shannon(distr, par)
# estimation:
for (tk, num_of_samples) in enumerate(num_of_samples_v):
h_hat_v[tk] = co.estimation(y[0:num_of_samples]) # broadcast
print("tk={0}/{1}".format(tk + 1, length))
# plot:
plt.plot(num_of_samples_v, h_hat_v, num_of_samples_v, ones(length) * h)
plt.xlabel('Number of samples')
plt.ylabel('Shannon entropy')
plt.legend(('estimation', 'analytical value'), loc='best')
plt.title("Estimator: " + cost_name)
plt.show()
def __init__(self,
mult=True,
w=array([1 / 2, 1 / 2]),
shannon_co_name='BHShannon_KnnK',
shannon_co_pars=None):
""" Initialize the estimator.
Parameters
----------
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
w : ndarray, w = [w1,w2], w_i > 0, w_2 > 0, w1 + w2 = 1, optional.
Parameters of the Jensen-Shannon divergence (default is
w = array([1/2,1/2]) )
shannon_co_name : str, optional
You can change it to any Shannon entropy
estimator (default is 'BHShannon_KnnK').
shannon_co_pars : dictionary, optional
Parameters for the Shannon entropy estimator
(default is None (=> {}); in this case the
default parameter values of the Shannon entropy
estimator are used).
Examples
--------
>>> import ite
>>> co1 = ite.cost.MDJS_HS()
>>> co2 = ite.cost.MDJS_HS(shannon_co_name='BHShannon_KnnK')
>>> co3 = ite.cost.MDJS_HS(shannon_co_name='BHShannon_KnnK',\
shannon_co_pars={'k':6,'eps':0.2},\
w=array([1/4,3/4]))
"""
# initialize with 'InitX':
super().__init__(mult=mult)
# initialize the Shannon entropy estimator:
shannon_co_pars = shannon_co_pars or {}
shannon_co_pars['mult'] = mult # guarantee this property
self.shannon_co = co_factory(shannon_co_name, **shannon_co_pars)
# other attributes (w):
# verification:
if sum(w) != 1:
raise Exception('sum(w) has to be 1!')
if not all(w > 0):
raise Exception('The coordinates of w have to be positive!')
if len(w) != 2:
raise Exception('The length of w has to be 2!')
self.w = w
def main():
# parameters:
dim = 1 # dimension of the distribution
num_of_samples_v = arange(1000, 50 * 1000 + 1, 1000)
rho = 0.9 # parameter of the probability product kernel, >0
cost_name = 'BKProbProd_KnnK' # dim >= 1
# initialization:
distr = 'normal' # fixed
num_of_samples_max = num_of_samples_v[-1]
length = len(num_of_samples_v)
co = co_factory(cost_name, mult=True, rho=rho) # cost object
k_hat_v = zeros(length) # vector of estimated kernel values
# distr, dim -> samples (y1,y2), distribution parameters (par1,par2),
# analytical value (k):
if distr == 'normal':
# mean (m1,m2):
m2 = rand(dim)
m1 = m2
# (random) linear transformation applied to the data (l1,l2) ->
# covariance matrix (c1,c2):
l2 = rand(dim, dim)
l1 = rand(1) * l2
# Note: (m2,l2) => (m1,l1) choice guarantees y1<<y2 (in practise,
# too).
c1 = dot(l1, l1.T)
c2 = dot(l2, l2.T)
# generate samples (y1~N(m1,c1), y2~N(m2,c2)):
y1 = multivariate_normal(m1, c1, num_of_samples_max)
y2 = multivariate_normal(m2, c2, num_of_samples_max)
par1 = {"mean": m1, "cov": c1}
par2 = {"mean": m2, "cov": c2}
else:
raise Exception('Distribution=?')
k = analytical_value_k_prob_product(distr, distr, rho, par1, par2)
# estimation:
for (tk, num_of_samples) in enumerate(num_of_samples_v):
k_hat_v[tk] = co.estimation(y1[0:num_of_samples],
y2[0:num_of_samples]) # broadcast
print("tk={0}/{1}".format(tk + 1, length))
# plot:
plt.plot(num_of_samples_v, k_hat_v, num_of_samples_v, ones(length) * k)
plt.xlabel('Number of samples')
plt.ylabel('Probability product kernel')
plt.legend(('estimation', 'analytical value'), loc='best')
plt.title("Estimator: " + cost_name)
plt.show()
def __init__(self,
mult=True,
alpha=0.99,
u=1,
jr_co_name='MDJR_HR',
jr_co_pars=None):
""" Initialize the estimator.
Parameters
----------
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
alpha: float, 0 < alpha < 1, optional
Parameter of the exponentiated Jensen-Renyi kernel-2
(default is 0.99).
u: float, 0 < u, optional
Parameter of the exponentiated Jensen-Renyi kernel-2 (default
is 1).
jr_co_name : str, optional
You can change it to any Jensen-Renyi divergence
estimator (default is 'MDJR_HR').
jr_co_pars : dictionary, optional
Parameters for the Jensen-Renyi divergence estimator
(default is None (=> {}); in this case the default
parameter values of the Jensen-Renyi divergence
estimator are used).
Examples
--------
>>> import ite
>>> co1 = ite.cost.MKExpJR2_DJR()
>>> co2 = ite.cost.MKExpJR2_DJR(jr_co_name='MDJR_HR')
>>> co3 = ite.cost.MKExpJR2_DJR(alpha=0.7,u=1.2,\
jr_co_name='MDJR_HR')
"""
# verification (alpha == 1 is checked via 'InitUAlpha'):
# if alpha <= 0 or alpha > 1:
# raise Exception('0 < alpha < 1 has to hold!')
# initialize with 'InitUAlpha':
super().__init__(mult=mult, u=u, alpha=alpha)
# initialize the Jensen-Renyi divergence estimator:
jr_co_pars = jr_co_pars or {}
jr_co_pars['mult'] = True # guarantee this property
jr_co_pars['alpha'] = alpha # -||-
jr_co_pars['w'] = array([1 / 2, 1 / 2]) # uniform weights
self.jr_co = co_factory(jr_co_name, **jr_co_pars)
# other attributes (u):
self.u = u
def main():
# parameters:
distr = 'normalI' # 'uniform', 'normalI' (isotropic normal, Id cov.)
dim = 1 # dimension of the distribution
num_of_samples_v = arange(1000, 50*1000+1, 1000)
cost_name = 'BDChi2_KnnK' # dim >= 1
# initialization:
num_of_samples_max = num_of_samples_v[-1]
length = len(num_of_samples_v)
co = co_factory(cost_name, mult=True) # cost object
d_hat_v = zeros(length) # vector of estimated divergence values
# distr, dim -> samples (y1<<y2), distribution parameters (par1,par2),
# analytical value (d):
if distr == 'uniform':
b = 3 * rand(dim)
a = b * rand(dim)
y1 = rand(num_of_samples_max, dim) * a # U[0,a]
y2 = rand(num_of_samples_max, dim) * b
# U[0,b], a<=b (coordinate-wise) => y1<<y2
par1 = {"a": a}
par2 = {"a": b}
elif distr == 'normalI':
# mean (m1,m2):
m1 = 2 * rand(dim)
m2 = 2 * rand(dim)
# generate samples (y1~N(m1,I), y2~N(m2,I)):
y1 = multivariate_normal(m1, eye(dim), num_of_samples_max)
y2 = multivariate_normal(m2, eye(dim), num_of_samples_max)
par1 = {"mean": m1}
par2 = {"mean": m2}
else:
raise Exception('Distribution=?')
d = analytical_value_d_chi_square(distr, distr, par1, par2)
# estimation:
for (tk, num_of_samples) in enumerate(num_of_samples_v):
d_hat_v[tk] = co.estimation(y1[0:num_of_samples],
y2[0:num_of_samples]) # broadcast
print("tk={0}/{1}".format(tk+1, length))
# plot:
plt.plot(num_of_samples_v, d_hat_v, num_of_samples_v, ones(length)*d)
plt.xlabel('Number of samples')
plt.ylabel('Chi square divergence')
plt.legend(('estimation', 'analytical value'), loc='best')
plt.title("Estimator: " + cost_name)
plt.show()
def main():
# parameters:
distr = 'uniform' # possibilities: 'uniform', 'normal'
dim = 2 # dimension of the distribution
num_of_distributions = 5
# each distribution is represented by num_of_samples samples:
num_of_samples = 500
# kernel used to evaluate the distributions:
cost_name = 'BKExpected'
# cost_name = 'BKProbProd_KnnK'
# cost_name = 'MKExpJR1_HR'
# cost_name = 'MKExpJR2_DJR'
# cost_name = 'MKExpJS_DJS'
# cost_name = 'MKExpJT1_HT'
# cost_name = 'MKExpJT2_DJT'
# cost_name = 'MKJS_DJS'
# cost_name = 'MKJT_HT'
# initialization:
co = co_factory(cost_name, mult=True)
ys = list()
# generate samples from the distributions (ys):
for n in range(num_of_distributions):
# generate samples from the n^th distribution (y):
if distr == 'uniform':
a, b = -rand(dim), rand(dim) # a,b
# (random) linear transformation applied to the data (r x
# U[a,b]):
r = randn(dim, dim)
y = dot(rand(num_of_samples, dim) * (b - a).T + a.T, r)
elif distr == 'normal':
m = rand(dim) # mean
# cov:
l = rand(dim, dim)
c = dot(l, l.T) # cov
# generate samples (yy~N(m,c)):
y = multivariate_normal(m, c, num_of_samples)
ys.append(y)
# Gram matrix and its minimal eigenvalue:
g = co.gram_matrix(ys)
eigenvalues = eigh(g)[0] # eigenvalues: reals, in increasing order
min_eigenvalue = eigenvalues[0]
# plot:
plt.plot(range(1, num_of_distributions + 1), eigenvalues)
plt.xlabel('Index of the sorted eigenvalues: i')
plt.ylabel('Eigenvalues of the (estimated) Gram matrix')
plt.title("Minimal eigenvalue: " + str(round(min_eigenvalue, 2)))
plt.show()
def __init__(self,
hess=2,
mult=True,
chi_square_co_name='BDChi2_KnnK',
chi_square_co_pars=None):
""" Initialize the estimator.
Parameters
----------
hess : float, optional
=f^{(2)}(1), the second derivative of f at 1 (default is 2).
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
chi_square_co_name : str, optional
You can change it to any Pearson chi square
divergence estimator (default is
'BDChi2_KnnK').
chi_square_co_pars : dictionary, optional
Parameters for the Pearson chi-square
divergence estimator (default is None
(=> {}); in this case the default parameter
values of the Pearson chi square divergence
estimator are used).
Examples
--------
>>> import ite
>>> co1 = ite.cost.MDf_DChi2(hess=2)
>>> co2 = ite.cost.MDf_DChi2(hess=1,\
chi_square_co_name='BDChi2_KnnK')
>>> dict_ch = {'k': 6}
>>> co3 = ite.cost.MDf_DChi2(hess=2,\
chi_square_co_name='BDChi2_KnnK',\
chi_square_co_pars=dict_ch)
"""
# initialize with 'InitX':
super().__init__(mult=mult)
# initialize the chi^2 divergence estimator:
chi_square_co_pars = chi_square_co_pars or {}
chi_square_co_pars['mult'] = mult # guarantee this property
self.chi_square_co = co_factory(chi_square_co_name,
**chi_square_co_pars)
# other attributes (hess):
self.hess = hess
def main():
# parameters:
dim = 1 # dimension of the distribution
num_of_samples_v = arange(100, 12 * 1000 + 1, 500)
u = 1 # >0, parameter of the Jensen-Renyi kernel
cost_name = 'MKExpJR2_DJR' # dim >= 1
# initialization:
alpha = 2
# fixed; parameter of the Jensen-Renyi kernel; for alpha = 2 we have
# explicit formula for the Jensen-Renyi divergence, and hence for the
# Jensen-Renyi kernel(-2).
distr = 'normal' # fixed
num_of_samples_max = num_of_samples_v[-1]
length = len(num_of_samples_v)
co = co_factory(cost_name, mult=True, alpha=alpha, u=u) # cost object
k_hat_v = zeros(length) # vector of estimated kernel values
# distr, dim -> samples (y1,y2), distribution parameters (par1,par2),
# analytical value (k):
if distr == 'normal':
# generate samples (y1,y2); y1~N(m1,s1^2xI), y2~N(m2,s2^2xI):
m1, s1 = randn(dim), rand(1)
m2, s2 = randn(dim), rand(1)
y1 = multivariate_normal(m1, s1**2 * eye(dim), num_of_samples_max)
y2 = multivariate_normal(m2, s2**2 * eye(dim), num_of_samples_max)
par1 = {"mean": m1, "std": s1}
par2 = {"mean": m2, "std": s2}
else:
raise Exception('Distribution=?')
k = analytical_value_k_ejr2(distr, distr, u, par1, par2)
# estimation:
for (tk, num_of_samples) in enumerate(num_of_samples_v):
k_hat_v[tk] = co.estimation(y1[0:num_of_samples],
y2[0:num_of_samples]) # broadcast
print("tk={0}/{1}".format(tk + 1, length))
# plot:
plt.plot(num_of_samples_v, k_hat_v, num_of_samples_v, ones(length) * k)
plt.xlabel('Number of samples')
plt.ylabel('Exponentiated Jensen-Renyi kernel-2')
plt.legend(('estimation', 'analytical value'), loc='best')
plt.title("Estimator: " + cost_name)
plt.show()
def __init__(self,
mult=True,
alpha=0.99,
tsallis_co_name='BDTsallis_KnnK',
tsallis_co_pars=None):
""" Initialize the estimator.
Parameters
----------
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
alpha : float, optional
Parameter of the Renyi mutual information (default is
0.99).
tsallis_co_name : str, optional
You can change it to any Tsallis divergence
estimator (default is 'BDTsallis_KnnK').
tsallis_co_pars : dictionary, optional
Parameters for the Tsallis divergence estimator
(default is None (=> {}); in this case the
default parameter values of the Tsallis
divergence estimator are used).
Examples
--------
>>> import ite
>>> co1 = ite.cost.MITsallis_DT()
>>> co2 = ite.cost.MITsallis_DT(tsallis_co_name='BDTsallis_KnnK')
>>> co3 = ite.cost.MITsallis_DT(tsallis_co_name='BDTsallis_KnnK',\
alpha=0.4)
>>> dict_ch = {'knn_method': 'cKDTree', 'k': 2, 'eps': 0.1}
>>> co4 = ite.cost.MITsallis_DT(mult=True,alpha=0.9,\
tsallis_co_name='BDTsallis_KnnK',\
tsallis_co_pars=dict_ch)
"""
# initialize with 'InitAlpha':
super().__init__(mult=mult, alpha=alpha)
# initialize the Tsallis divergence estimator:
tsallis_co_pars = tsallis_co_pars or {}
tsallis_co_pars['mult'] = mult # guarantee this property
tsallis_co_pars['alpha'] = alpha # -||-
self.tsallis_co = co_factory(tsallis_co_name, **tsallis_co_pars)
def main():
# parameters:
ds = array([4, 1]) # subspace dimensions: ds[0], ..., ds[M-1]
num_of_samples_v = arange(1000, 20 * 1000 + 1, 1000)
cost_name = 'MIShannon_DKL' # d_m >= 1, M >= 2
# cost_name = 'MIShannon_HS' # d_m >= 1, M >= 2
# initialization:
distr = 'normal' # distribution; fixed
num_of_samples_max = num_of_samples_v[-1]
length = len(num_of_samples_v)
co = co_factory(cost_name, mult=True) # cost object
# vector of estimated mutual information values:
i_hat_v = zeros(length)
# distr, ds -> samples (y), distribution parameters (par), analytical
# value (i):
if distr == 'normal':
dim = sum(ds) # dimension of the joint distribution
# mean (m), covariance matrix (c):
m = rand(dim)
l = rand(dim, dim)
c = dot(l, l.T)
# generate samples (y~N(m,c)):
y = multivariate_normal(m, c, num_of_samples_max)
par = {"ds": ds, "cov": c}
else:
raise Exception('Distribution=?')
i = analytical_value_i_shannon(distr, par)
# estimation:
for (tk, num_of_samples) in enumerate(num_of_samples_v):
i_hat_v[tk] = co.estimation(y[0:num_of_samples], ds) # broadcast
print("tk={0}/{1}".format(tk + 1, length))
# plot:
plt.plot(num_of_samples_v, i_hat_v, num_of_samples_v, ones(length) * i)
plt.xlabel('Number of samples')
plt.ylabel('Shannon mutual information')
plt.legend(('estimation', 'analytical value'), loc='best')
plt.title("Estimator: " + cost_name)
plt.show()
def main():
# parameters:
alpha = 0.7 # parameter of Renyi mutual information, \ne 1
dim = 2 # >=2; dimension of the distribution
num_of_samples_v = arange(100, 10*1000+1, 500)
cost_name = 'MIRenyi_DR'
# cost_name = 'MIRenyi_HR'
# initialization:
distr = 'normal' # distribution; fixed
ds = ones(dim, dtype='int') # dimensions of the 'subspaces'
num_of_samples_max = num_of_samples_v[-1]
length = len(num_of_samples_v)
co = co_factory(cost_name, mult=True, alpha=alpha) # cost object
# vector of estimated mutual information values:
i_hat_v = zeros(length)
# distr, dim -> samples (y), distribution parameters (par), analytical
# value (i):
if distr == 'normal':
# mean (m), covariance matrix (c):
m = rand(dim)
l = rand(dim, dim)
c = dot(l, l.T)
# generate samples (y~N(m,c)):
y = multivariate_normal(m, c, num_of_samples_max)
par = {"cov": c}
else:
raise Exception('Distribution=?')
i = analytical_value_i_renyi(distr, alpha, par)
# estimation:
for (tk, num_of_samples) in enumerate(num_of_samples_v):
i_hat_v[tk] = co.estimation(y[0:num_of_samples], ds) # broadcast
print("tk={0}/{1}".format(tk+1, length))
# plot:
plt.plot(num_of_samples_v, i_hat_v, num_of_samples_v, ones(length)*i)
plt.xlabel('Number of samples')
plt.ylabel('Renyi mutual information')
plt.legend(('estimation', 'analytical value'), loc='best')
plt.title("Estimator: " + cost_name)
plt.show()
def main():
# parameters:
dim = 2 # dimension of the distribution
num_of_samples_v = arange(1000, 50 * 1000 + 1, 2000)
cost_name = 'BDHellinger_KnnK' # dim >= 1
# initialization:
distr = 'normal' # fixed
num_of_samples_max = num_of_samples_v[-1]
length = len(num_of_samples_v)
co = co_factory(cost_name, mult=True) # cost object
d_hat_v = zeros(length) # vector of estimated divergence values
# distr, dim -> samples (y1,y2), distribution parameters (par1,par2),
# analytical value (d):
if distr == 'normal':
# mean (m1,m2):
m1, m2 = rand(dim), rand(dim)
# (random) linear transformation applied to the data (l1,l2) ->
# covariance matrix (c1,c2):
l1, l2 = rand(dim, dim), rand(dim, dim)
c1, c2 = dot(l1, l1.T), dot(l2, l2.T)
# generate samples (y1~N(m1,c1), y2~N(m2,c2)):
y1 = multivariate_normal(m1, c1, num_of_samples_max)
y2 = multivariate_normal(m2, c2, num_of_samples_max)
par1, par2 = {"mean": m1, "cov": c1}, {"mean": m2, "cov": c2}
else:
raise Exception('Distribution=?')
d = analytical_value_d_hellinger(distr, distr, par1, par2)
# estimation:
for (tk, num_of_samples) in enumerate(num_of_samples_v):
# with broadcasting:
d_hat_v[tk] = co.estimation(y1[0:num_of_samples], y2[0:num_of_samples])
print("tk={0}/{1}".format(tk + 1, length))
# plot:
plt.plot(num_of_samples_v, d_hat_v, num_of_samples_v, ones(length) * d)
plt.xlabel('Number of samples')
plt.ylabel('Hellinger distance')
plt.legend(('estimation', 'analytical value'), loc='best')
plt.title("Estimator: " + cost_name)
plt.show()
def main():
# parameters:
dim1 = 1 # dimension of y1
dim2 = 2 # dimension of y2
num_of_samples_v = arange(1000, 30 * 1000 + 1, 1000)
cost_name = 'BcondHShannon_HShannon' # dim1 >= 1, dim2 >= 1
# initialization:
distr = 'normal' # fixed
num_of_samples_max = num_of_samples_v[-1]
length = len(num_of_samples_v)
co = co_factory(cost_name, mult=True) # cost object
# vector of estimated conditional entropy values:
cond_h_hat_v = zeros(length)
dim = dim1 + dim2
# distr, dim1 -> samples (y), distribution parameters (par),
# analytical value (cond_h):
if distr == 'normal':
# mean (m), covariance matrix (c):
m, l = rand(dim), rand(dim, dim)
c = dot(l, l.T)
# generate samples (y~N(m,c)):
y = multivariate_normal(m, c, num_of_samples_max)
par = {"dim1": dim1, "cov": c}
else:
raise Exception('Distribution=?')
cond_h = analytical_value_cond_h_shannon(distr, par)
# estimation:
for (tk, num_of_samples) in enumerate(num_of_samples_v):
# broadcasting:
cond_h_hat_v[tk] = co.estimation(y[:num_of_samples], dim1)
print("tk={0}/{1}".format(tk + 1, length))
# plot:
plt.plot(num_of_samples_v, cond_h_hat_v,
num_of_samples_v, ones(length) * cond_h)
plt.xlabel('Number of samples')
plt.ylabel('Conditional Shannon entropy')
plt.legend(('estimation', 'analytical value'), loc='best')
plt.title("Estimator: " + cost_name)
plt.show()
def main():
# parameters:
dim = 1 # dimension of the distribution
num_of_samples_v = arange(1000, 30 * 1000 + 1, 1000)
alpha = 0.8 # parameter of the Sharma-Mittal entropy; alpha \ne 1
beta = 0.6 # parameter of the Sharma-Mittal entropy; beta \ne 1
cost_name = 'BHSharmaMittal_KnnK' # dim >= 1
# initialization:
distr = 'normal' # fixed
num_of_samples_max = num_of_samples_v[-1]
length = len(num_of_samples_v)
# cost object:
co = co_factory(cost_name, mult=True, alpha=alpha, beta=beta)
h_hat_v = zeros(length) # vector of estimated entropy values
# distr, dim -> samples (y), distribution parameters (par), analytical
# value (h):
if distr == 'normal':
# mean (m), covariance matrix (c):
m = rand(dim)
l = rand(dim, dim)
c = dot(l, l.T)
# generate samples (y~N(m,c)):
y = multivariate_normal(m, c, num_of_samples_max)
par = {"cov": c}
else:
raise Exception('Distribution=?')
h = analytical_value_h_sharma_mittal(distr, alpha, beta, par)
# estimation:
for (tk, num_of_samples) in enumerate(num_of_samples_v):
h_hat_v[tk] = co.estimation(y[0:num_of_samples]) # broadcast
print("tk={0}/{1}".format(tk + 1, length))
# plot:
plt.plot(num_of_samples_v, h_hat_v, num_of_samples_v, ones(length) * h)
plt.xlabel('Number of samples')
plt.ylabel('Sharma-Mittal entropy')
plt.legend(('estimation', 'analytical value'), loc='best')
plt.title("Estimator: " + cost_name)
plt.show()
def __init__(self,
mult=True,
alpha=0.99,
bregman_co_name='BDBregman_KnnK',
bregman_co_pars=None):
""" Initialize the estimator.
Parameters
----------
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
alpha : float, \ne 1, optional
Parameter of the symmetric Bregman distance (default is
0.99).
bregman_co_name : str, optional
You can change it to any nonsymmetric Bregman
distance estimator (default is 'BDBregman_KnnK').
bregman_co_pars : dictionary, optional
Parameters for the nonsymmetric Bregman distance
estimator (default is None (=> {}); in this case
the default parameter values of the nonsymmetric
Bregman distance estimator are used).
Examples
--------
>>> import ite
>>> co1 = ite.cost.MDSymBregman_DB()
>>> co2 =\
ite.cost.MDSymBregman_DB(bregman_co_name='BDBregman_KnnK')
>>> co3 =\
ite.cost.MDSymBregman_DB(bregman_co_name='BDBregman_KnnK',\
bregman_co_pars={'k':6,'eps':0.2})
"""
# initialize with 'InitAlpha':
super().__init__(mult=mult, alpha=alpha)
# initialize the nonsymmetric Bregman distance estimator:
bregman_co_pars = bregman_co_pars or {}
bregman_co_pars['mult'] = mult # guarantee this property
bregman_co_pars['alpha'] = alpha # guarantee this property
self.bregman_co = co_factory(bregman_co_name, **bregman_co_pars)
def main():
# parameters:
dim = 2 # dimension of the distribution
w = array([1/3, 2/3]) # weight in the Jensen-Renyi divergence
num_of_samples_v = arange(100, 12*1000+1, 500)
cost_name = 'MDJR_HR' # dim >= 1
# initialization:
alpha = 2 # parameter of the Jensen-Renyi divergence, \ne 1; fixed
distr = 'normal' # fixed
num_of_samples_max = num_of_samples_v[-1]
length = len(num_of_samples_v)
co = co_factory(cost_name, mult=True, alpha=alpha, w=w) # cost object
d_hat_v = zeros(length) # vector of estimated divergence values
# distr, dim -> samples (y1,y2), distribution parameters (par1,par2),
# analytical value (d):
if distr == 'normal':
# generate samples (y1,y2); y1~N(m1,s1^2xI), y2~N(m2,s2^2xI):
m1, s1 = randn(dim), rand(1)
m2, s2 = randn(dim), rand(1)
y1 = multivariate_normal(m1, s1**2 * eye(dim), num_of_samples_max)
y2 = multivariate_normal(m2, s2**2 * eye(dim), num_of_samples_max)
par1 = {"mean": m1, "std": s1}
par2 = {"mean": m2, "std": s2}
else:
raise Exception('Distribution=?')
d = analytical_value_d_jensen_renyi(distr, distr, w, par1, par2)
# estimation:
for (tk, num_of_samples) in enumerate(num_of_samples_v):
d_hat_v[tk] = co.estimation(y1[0:num_of_samples],
y2[0:num_of_samples]) # broadcast
print("tk={0}/{1}".format(tk+1, length))
# plot:
plt.plot(num_of_samples_v, d_hat_v, num_of_samples_v, ones(length)*d)
plt.xlabel('Number of samples')
plt.ylabel('Jensen-Renyi divergence')
plt.legend(('estimation', 'analytical value'), loc='best')
plt.title("Estimator: " + cost_name)
plt.show()
def main():
# parameters:
distr = 'uniform' # possibilities: 'uniform', 'normal'
m = 2 # number of components
num_of_samples_v = arange(1000, 30 * 1000 + 1, 1000)
cost_name = 'BASpearman1' # m >= 2
# cost_name = 'BASpearman2' # m >= 2
# cost_name = 'BASpearman3' # m >= 2
# cost_name = 'BASpearman4' # m >= 2
# cost_name = 'BASpearmanCondLT' # m >= 2
# cost_name = 'BASpearmanCondUT' # m >= 2
# cost_name = 'BABlomqvist' # m >= 2
# cost_name = 'MASpearmanUT' # m >= 2
# cost_name = 'MASpearmanLT' # m >= 2
# initialization:
num_of_samples_max = num_of_samples_v[-1]
length = len(num_of_samples_v)
co = co_factory(cost_name, mult=True) # cost object
a_hat_v = zeros(length) # vector to store the association values
ds = ones(m, dtype='int')
# distr -> samples (y); analytical value (a):
if distr == 'uniform':
y = rand(num_of_samples_max, m)
elif distr == 'normal':
y = randn(num_of_samples_max, m)
else:
raise Exception('Distribution=?')
a = 0
# estimation:
for (tk, num_of_samples) in enumerate(num_of_samples_v):
a_hat_v[tk] = co.estimation(y[0:num_of_samples], ds) # broadcast
print("tk={0}/{1}".format(tk + 1, length))
# plot:
plt.plot(num_of_samples_v, a_hat_v, num_of_samples_v, ones(length) * a)
plt.xlabel('Number of samples')
plt.ylabel('Association')
plt.legend(('estimation', 'analytical value'), loc='best')
plt.title("Estimator: " + cost_name)
plt.show()
def __init__(self,
mult=True,
alpha=0.99,
tsallis_co_name='BHTsallis_KnnK',
tsallis_co_pars=None):
""" Initialize the estimator.
Parameters
----------
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
alpha : float, \ne 1, optional
Parameter of the Jensen-Tsallis divergence (default is
0.99).
tsallis_co_name : str, optional
You can change it to any Tsallis entropy
estimator (default is 'BHTsallis_KnnK').
tsallis_co_pars : dictionary, optional
Parameters for the Tsallis entropy estimator
(default is None (=> {}); in this case the
default parameter values of the Tsallis entropy
estimator are used).
Examples
--------
>>> import ite
>>> co1 = ite.cost.MDJT_HT()
>>> co2 = ite.cost.MDJT_HT(tsallis_co_name='BHTsallis_KnnK',\
alpha=0.8)
>>> co3 = ite.cost.MDJT_HT(tsallis_co_name='BHTsallis_KnnK',\
tsallis_co_pars={'k':6}, alpha=0.5)
"""
# initialize with 'InitAlpha':
super().__init__(mult=mult, alpha=alpha)
# initialize the Tsallis entropy estimator:
tsallis_co_pars = tsallis_co_pars or {}
tsallis_co_pars['mult'] = mult # guarantee this property
tsallis_co_pars['alpha'] = alpha # -||-
self.tsallis_co = co_factory(tsallis_co_name, **tsallis_co_pars)
def __init__(self, mult=True, u=1, js_co_name='MDJS_HS', js_co_pars=None):
""" Initialize the estimator.
Parameters
----------
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
u: float, 0 < u, optional
Parameter of the exponentiated Jensen-Shannon kernel (default
is 1).
js_co_name : str, optional
You can change it to any Jensen-Shannon divergence
estimator (default is 'MDJS_HS').
js_co_pars : dictionary, optional
Parameters for the Jensen-Shannnon divergence
estimator (default is None (=> {}); in this case the
default parameter values of the Jensen-Shannon
divergence estimator are used).
Examples
--------
>>> import ite
>>> co1 = ite.cost.MKExpJS_DJS()
>>> co2 = ite.cost.MKExpJS_DJS(u=1.2, js_co_name='MDJS_HS')
"""
if u <= 0:
raise Exception('u has to be positive!')
# initialize with 'InitX':
super().__init__(mult=mult)
# initialize the Jensen-Shannon divergence estimator:
js_co_pars = js_co_pars or {}
js_co_pars['mult'] = True # guarantee this property
js_co_pars['w'] = array([1 / 2, 1 / 2]) # uniform weights
self.js_co = co_factory(js_co_name, **js_co_pars)
# other attributes (u):
self.u = u
def __init__(self, mult=True, alpha=0.99, renyi_co_name='BHRenyi_KnnK',
renyi_co_pars=None):
""" Initialize the estimator.
Parameters
----------
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
alpha : float, alpha \ne 1, optional
alpha in the Tsallis entropy. (default is 0.99)
renyi_co_name : str, optional
You can change it to any Renyi entropy estimator.
(default is 'BHRenyi_KnnK')
renyi_co_pars : dictionary, optional
Parameters for the Renyi entropy estimator. (default
is None (=> {}); in this case the default parameter
values of the Renyi entropy estimator are used)
Examples
--------
>>> import ite
>>> co1 = ite.cost.MHTsallis_HR()
>>> co2 = ite.cost.MHTsallis_HR(renyi_co_name='BHRenyi_KnnK')
>>> co3 = ite.cost.MHTsallis_HR(alpha=0.9, \
renyi_co_name='BHRenyi_KnnK')
>>> dict_ch = {'knn_method': 'cKDTree', 'k': 5, 'eps': 0.1}
>>> co4 = ite.cost.MHTsallis_HR(alpha=0.9, \
renyi_co_name='BHRenyi_KnnK', \
renyi_co_pars=dict_ch)
"""
# initialize with 'InitX':
super().__init__(mult=mult, alpha=alpha)
# initialize the Renyi entropy estimator:
renyi_co_pars = renyi_co_pars or {}
renyi_co_pars['mult'] = mult # guarantee this property
renyi_co_pars['alpha'] = alpha # -||-
self.renyi_co = co_factory(renyi_co_name, **renyi_co_pars)
def main():
# parameters:
alpha = 0.7 # parameter of Bregman divergence, \ne 1
dim = 1 # dimension of the distribution
num_of_samples_v = arange(1000, 10 * 1000 + 1, 1000)
cost_name = 'BDBregman_KnnK' # dim >= 1
# initialization:
distr = 'uniform' # fixed
num_of_samples_max = num_of_samples_v[-1]
length = len(num_of_samples_v)
co = co_factory(cost_name, mult=True, alpha=alpha) # cost object
d_hat_v = zeros(length) # vector of estimated divergence values
# distr, dim -> samples (y1<<y2), distribution parameters (par1,par2),
# analytical value (d):
if distr == 'uniform':
b = 3 * rand(dim)
a = b * rand(dim)
y1 = rand(num_of_samples_max, dim) * a # U[0,a]
y2 = rand(num_of_samples_max, dim) * b
# Note: y2 ~ U[0,b], a<=b (coordinate-wise) => y1<<y2
par1 = {"a": a}
par2 = {"a": b}
else:
raise Exception('Distribution=?')
d = analytical_value_d_bregman(distr, distr, alpha, par1, par2)
# estimation:
for (tk, num_of_samples) in enumerate(num_of_samples_v):
d_hat_v[tk] = co.estimation(y1[0:num_of_samples],
y2[0:num_of_samples]) # broadcast
print("tk={0}/{1}".format(tk + 1, length))
# plot:
plt.plot(num_of_samples_v, d_hat_v, num_of_samples_v, ones(length) * d)
plt.xlabel('Number of samples')
plt.ylabel('Bregman divergence')
plt.legend(('estimation', 'analytical value'), loc='best')
plt.title("Estimator: " + cost_name)
plt.show()
def __init__(self,
mult=True,
mmd_co_name='BDMMD_UStat_IChol',
mmd_co_pars=None):
""" Initialize the estimator.
Parameters
----------
mult : bool, optional
'True': multiplicative constant relevant (needed) in the
estimation. 'False': estimation up to 'proportionality'.
(default is True)
mmd_co_name : str, optional
You can change it to any MMD estimator (default is
'BDMMD_UStat_IChol').
mmd_co_pars : dictionary, optional
Parameters for the MMD estimator (default is None
(=> {}); in this case the default parameter values
of the MMD estimator are used).
Examples
--------
>>> import ite
>>> from ite.cost.x_kernel import Kernel
>>> co1 = ite.cost.MDEnergyDist_DMMD()
>>> co2 =\
ite.cost.MDEnergyDist_DMMD(mmd_co_name='BDMMD_UStat_IChol')
>>> dict_ch = {'kernel': \
Kernel({'name': 'RBF','sigma': 0.1}), 'eta': 1e-2}
>>> co3 =\
ite.cost.MDEnergyDist_DMMD(mmd_co_name='BDMMD_UStat_IChol',\
mmd_co_pars=dict_ch)
"""
# initialize with 'InitX':
super().__init__(mult=mult)
# initialize the MMD estimator:
mmd_co_pars = mmd_co_pars or {}
mmd_co_pars['mult'] = mult # guarantee this property
self.mmd_co = co_factory(mmd_co_name, **mmd_co_pars)