def _each_loss(X, Y, Num, Model_prior, D, F, U):
#U=[tf.contrib.distributions.Uniform().sample(sample_shape=(1,1)) for j in range (D)]
_W = [f(u) for f, u in zip(F, U)]
#variable transformation
W = [minus_inf_inf_to_zero_one(__w) for __w in _W]
raw_params = _W
#Variable transoformation's Log_det_Jacobian
minus_Log_det_J = 0
for i in raw_params:
minus_Log_det_J += tf.log(
tf.abs(tf.reduce_sum(minus_inf_inf_to_zero_one_Log_det_J(i), 1)))
#likelihood and prior calculation
#if you want to consider other than logistic regression, change the model and prior
Log_likelihood, Prior, _ = Model_prior(X, Y, W)
Posteri_numerator = Log_likelihood[:, None] + Prior + minus_Log_det_J[:,
None]
dp_du = [tf.gradients(Posteri_numerator, u)[0] for u in U]
d2w_du2 = [
tf.gradients(tf.log(tf.abs(tf.gradients(_p, __u)[0])), __u)[0]
for _p, __u in zip(raw_params, U)
]
_G = [(i + j)**2 for i, j in zip(d2w_du2, dp_du)]
L_0 = tf.reduce_sum(_G)
return L_0
def _each_loss(X, Y, Num, Model_prior, D, F, U):
_W = [f(u) for f, u in zip(F, U)]
#variable transformation
W = [minus_inf_inf_to_zero_one(__w) for __w in _W]
raw_params = _W
#Variable transoformation's Log_det_Jacobian
minus_Log_det_J = 0
for i in raw_params:
minus_Log_det_J += -tf.reduce_sum(
minus_inf_inf_to_zero_one_Log_det_J(i), 1)
#likelihood and prior calculation
#if you want to consider other than logistic regression, change the model and prior
params = parameter_reshaper(W, b, data_dim, Num_of_hidden)
Minus_Log_likelihood, Minus_Prior = Model_prior(X, Y, params)
Posteri_numerator = Minus_Log_likelihood[:,
None] + Minus_Prior + minus_Log_det_J[:,
None]
dp_du = tf.gradients(Posteri_numerator, U)
d2w_du2 = [
tf.gradients(tf.log(tf.abs(tf.gradients(_p, __u)[0])), __u)[0]
for _p, __u in zip(raw_params, U)
]
_G = [(i - j)**2 for i, j in zip(d2w_du2, dp_du)]
L_0 = tf.reduce_sum(_G)
return L_0
def construct_loss(X, Y, dic, Num, Model_prior, D):
'''
This is the function calculating the loss function.
X,Y : data, they are place holders
dic : this is the ordered dictionally which contains placeholders of U
Num : how many placeholders are included in dic
Model_prior : what kind of model we use
D : how many parameters are in the model
'''
F = make_trials(D)
loss = 0
for i in range(0, Num * D, D):
U = [dic["U_" + str(i + j)] for j in range(D)]
_W = [f(u) for f, u in zip(F, U)]
#variable transformation
W = [minus_inf_inf_to_zero_one(__w) for __w in _W]
raw_params = _W
#Variable transoformation's Log_det_Jacobian
minus_Log_det_J = 0
for i in raw_params:
minus_Log_det_J += -tf.reduce_sum(
minus_inf_inf_to_zero_one_Log_det_J(i), 1)
#likelihood and prior calculation
#if you want to consider other than logistic regression, change the model and prior
params = parameter_reshaper(W, b, data_dim, Num_of_hidden)
Minus_Log_likelihood, Minus_Prior = Model_prior(X, Y, params)
Posteri_numerator = Minus_Log_likelihood[:,
None] + Minus_Prior + minus_Log_det_J[:,
None]
dp_du = [tf.gradients(Posteri_numerator, u)[0] for u in U]
d2w_du2 = [
tf.gradients(tf.log(tf.abs(tf.gradients(_p, __u)[0])), __u)[0]
for _p, __u in zip(raw_params, U)
]
_G = [(i - j)**2 for i, j in zip(d2w_du2, dp_du)]
L_0 = tf.reduce_sum(_G)
loss += L_0
return loss, F
def construct_loss(X, Y, F, dic, Num, Model_prior, D):
'''
This is the function calculating the loss function.
X,Y : data, they are place holders
dic : this is the ordered dictionally which contains placeholders of U
Num : how many placeholders are included in dic
Model_prior : what kind of model we use
D : how many parameters are in the model
'''
loss = 0
for i in range(0, Num):
U = dic["U_" + str(i)]
_W, sigma_list = F(U)
_W = tf.nn.sigmoid(_W)
#variable transformation
W = minus_inf_inf_to_zero_one(_W)
#Variable transoformation's Log_det_Jacobian
Log_det_J = tf.log(
tf.abs(tf.reduce_sum(minus_inf_inf_to_zero_one_Log_det_J(_W), 1)))
#likelihood and prior calculation
#if you want to consider other than logistic regression, change the model and prior
Log_likelihood, Prior = Model_prior(X, Y, W)
Posteri_numerator = Log_likelihood[:, None] + Prior + Log_det_J[:,
None]
dp_du = tf.gradients(Posteri_numerator, U)[0]
log_det_J = tf.reduce_sum(tf.log(sigma_list))
d2w_du2 = tf.gradients(log_det_J, U)[0]
L_0 = tf.reduce_sum((d2w_du2 + dp_du)**2)
loss += L_0
return loss
def construct_loss(dic,Num,Model_prior,D):
'''
This is the function calculating the loss function.
X,Y : data, they are place holders
dic : this is the ordered dictionally which contains placeholders of U
Num : how many placeholders are included in dic
Model_prior : what kind of model we use
D : how many parameters are in the model
'''
F=make_trials(D)
loss = 0
for i in range(0,Num*D,D):
U=[dic["U_"+ str(i+j)] for j in range (D)]
_W=[f(u) for f,u in zip(F,U)]
#variable transformation
W=[minus_inf_inf_to_zero_one(__w) for __w in _W]
raw_params=_W
#Variable transoformation's Log_det_Jacobian
minus_Log_det_J=0
for i in raw_params:
minus_Log_det_J+=tf.log(tf.abs(tf.reduce_sum(minus_inf_inf_to_zero_one_Log_det_J(i),1)))
#likelihood and prior calculation
#if you want to consider other than logistic regression, change the model and prior
Log_joint=-0.5*(W[0]**2)
Posteri_numerator=Log_joint+minus_Log_det_J[:,None]+np.log(1/np.sqrt((2*np.pi*np.square(1.))))
dw_du=[tf.log(tf.abs(tf.gradients(_p,__u)[0])) for _p,__u in zip(raw_params,U)]
#_G=[(i+j-1)**2 for i,j in zip(dw_du,Posteri_numerator)]
_G=(dw_du[0]+Posteri_numerator)**2
L_0=tf.reduce_sum(_G)
loss +=L_0
return loss,F