def __init__(self, random_state=None, mu=0.0, sigma=1.0):
super(Normal, self).__init__(mu=mu,
sigma=sigma,
random_state=random_state,
optimizer=None)
# pdf
self.pdf_ = (
(1. / np.sqrt(2. * np.pi)) / self.sigma *
T.exp(-(self.X - self.mu) ** 2 / (2. * self.sigma ** 2))).ravel()
self.make_(self.pdf_, "pdf")
# -log pdf
self.nnlf_ = bound(
T.log(self.sigma) + T.log(np.sqrt(2. * np.pi)) +
(self.X - self.mu) ** 2 / (2. * self.sigma ** 2),
np.inf,
self.sigma > 0.).ravel()
self.make_(self.nnlf_, "nnlf")
# cdf
self.cdf_ = 0.5 * (1. + T.erf((self.X - self.mu) /
(self.sigma * np.sqrt(2.)))).ravel()
self.make_(self.cdf_, "cdf")
# ppf
self.ppf_ = (self.mu +
np.sqrt(2.) * self.sigma * T.erfinv(2. * self.p - 1.))
self.make_(self.ppf_, "ppf", args=[self.p])
def __init__(self, mu=0.0, sigma=1.0):
super(Normal, self).__init__(mu=mu, sigma=sigma)
# pdf
self.pdf_ = ((1. / np.sqrt(2. * np.pi)) / self.sigma *
T.exp(-(self.X - self.mu)**2 /
(2. * self.sigma**2))).ravel()
self.make_(self.pdf_, "pdf")
# -log pdf
self.nll_ = bound(
T.log(self.sigma) + T.log(np.sqrt(2. * np.pi)) +
(self.X - self.mu)**2 / (2. * self.sigma**2), np.inf,
self.sigma > 0.).ravel()
self.make_(self.nll_, "nll")
# cdf
self.cdf_ = 0.5 * (1. + T.erf(
(self.X - self.mu) / (self.sigma * np.sqrt(2.)))).ravel()
self.make_(self.cdf_, "cdf")
# ppf
self.ppf_ = (self.mu +
np.sqrt(2.) * self.sigma * T.erfinv(2. * self.p - 1.))
self.make_(self.ppf_, "ppf", args=[self.p])
def get_output_for(self, inputs, **kwargs):
"""
:param inputs[0]: (batch, 600)
:param inputs[1]: (batch, 1)
:return:
"""
result = (T.erf( T.erfinv( T.clip(inputs[1].dimshuffle(0,'x',1)*2-1, -1+3e-8, 1-3e-8) ) * inputs[0].dimshuffle(0,1,'x') )+1)/2
return result[:,0,:]
def get_output_for(self, inputs, **kwargs):
"""
:param inputs[0]: (batch, 600)
:param inputs[1]: (batch, 1)
:return:
"""
result = (T.erf(
T.erfinv(
T.clip(inputs[1].dimshuffle(0, 'x', 1) * 2 - 1, -1 + 3e-8,
1 - 3e-8)) * inputs[0].dimshuffle(0, 1, 'x')) + 1) / 2
return result[:, 0, :]
def __init__(self, mu=0.0, sigma=1.0):
"""Constructor.
Parameters
----------
* `mu` [float]:
The distribution mean.
* `sigma` [float]:
The distribution standard deviation.
"""
super(Normal, self).__init__(mu=mu, sigma=sigma)
# pdf
self.pdf_ = (
(1. / np.sqrt(2. * np.pi)) / self.sigma *
T.exp(-(self.X - self.mu) ** 2 / (2. * self.sigma ** 2))).ravel()
self._make(self.pdf_, "pdf")
# -log pdf
self.nll_ = bound(
T.log(self.sigma) + T.log(np.sqrt(2. * np.pi)) +
(self.X - self.mu) ** 2 / (2. * self.sigma ** 2),
np.inf,
self.sigma > 0.).ravel()
self._make(self.nll_, "nll")
# cdf
self.cdf_ = 0.5 * (1. + T.erf((self.X - self.mu) /
(self.sigma * np.sqrt(2.)))).ravel()
self._make(self.cdf_, "cdf")
# ppf
self.ppf_ = (self.mu +
np.sqrt(2.) * self.sigma * T.erfinv(2. * self.p - 1.))
self._make(self.ppf_, "ppf", args=[self.p])
def theano(self, x):
return tt.erfinv(x)
def Phi_inv(y, eps=3e-8):
""" eps was calibrated for cublas.erfinv using float32 """
temp = 2. * y - 1.
erfinv_input = T.clip(temp, -1+eps, 1-eps)
rval = avg + std * SQRT2 * T.erfinv(erfinv_input)
return rval.astype(dtype)
def phi_inv(phi_x):
erfinv_input = T.clip(2. * phi_x - 1., -1. + 1e-6, 1. - 1e-6)
rval = avg + std * SQRT2 * T.erfinv(erfinv_input)
return rval.astype(dtype)
def inverse_theano(self, y):
x = tt.switch(tt.abs_(y) < self.b, tt.erfinv(y) * 2.**0.5,
(self.alpha * y**2 + self.gamma) * tt.sgn(y)
+ self.beta * y)
return x
def phi_inv(phi_x):
erfinv_input = T.clip(2. * phi_x - 1., -1.+1e-6, 1.-1e-6)
rval = avg + std * SQRT2 * T.erfinv(erfinv_input)
return rval.astype(dtype)
#%%
M = np.stack([[[1,0],[0,1]], [[-1,0],[-1,1]], [[0,-1],[1,-1]]])
MS = T.dot(M, S).dimshuffle((0,2,1,3)).reshape((ngroup*nchoice, nchoice-1, nchoice-1))
Sigma = T.batched_dot(MS, MS.dimshuffle((0,2,1))).reshape((nchoice, ngroup, nchoice-1, nchoice-1))
#%%
c00 = T.sqrt(Sigma[:,:,0,0])
c10 = Sigma[:,:,1,0]/c00
c11 = T.sqrt(Sigma[:,:,1,1] - c10**2)
iii = (choice-1, groupid)
normcdf = lambda x: 0.5 + 0.5*T.erf(x/np.sqrt(2))
norminv = lambda p: np.sqrt(2)*T.erfinv(2*p-1)
ndraws = 10
#draws = np.random.random((ndraws,nobs))
draws = (np.tile(np.arange(ndraws), (nobs,1)).transpose() + 0.5)/ndraws
prob0 = normcdf(-Vnonchoice[0,:]/c00[iii])
draws1 = norminv(draws*prob0)
prob1 = normcdf(-(Vnonchoice[1,:] + c10[iii]*draws1)/c11[iii])
nlogl_i = -T.log(prob0) - T.log(prob1.sum(axis=0)/ndraws)
nlogl = nlogl_i.sum()
obj = nlogl
eval_f = theano.function([theta], outputs = obj)
