def fit(self, X, B, T):
n, k = X.shape
with pymc3.Model() as m:
beta_sd = pymc3.Exponential(
'beta_sd', 1.0) # Weak prior for the regression coefficients
beta = pymc3.Normal('beta', mu=0, sd=beta_sd,
shape=(k, )) # Regression coefficients
c = sigmoid(dot(X, beta)) # Conversion rates for each example
k = pymc3.Lognormal('k', mu=0, sd=1.0) # Weak prior around k=1
lambd = pymc3.Exponential('lambd', 0.1) # Weak prior
# PDF of Weibull: k * lambda * (x * lambda)^(k-1) * exp(-(t * lambda)^k)
LL_observed = log(c) + log(k) + log(
lambd) + (k - 1) * (log(T) + log(lambd)) - (T * lambd)**k
# CDF of Weibull: 1 - exp(-(t * lambda)^k)
LL_censored = log((1 - c) + c * exp(-(T * lambd)**k))
# We need to implement the likelihood using pymc3.Potential (custom likelihood)
# https://github.com/pymc-devs/pymc3/issues/826
logp = B * LL_observed + (1 - B) * LL_censored
logpvar = pymc3.Potential('logpvar', logp.sum())
self.trace = pymc3.sample(n_simulations=500,
tune=500,
discard_tuned_samples=True,
njobs=1)
print('done')
print('done 2')
def __init__(self, eta, cutpoints, *args, **kwargs):
self.eta = tt.as_tensor_variable(eta)
self.cutpoints = tt.as_tensor_variable(cutpoints)
pa = sigmoid(tt.shape_padleft(self.cutpoints) - tt.shape_padright(self.eta))
p_cum = tt.concatenate([
tt.zeros_like(tt.shape_padright(pa[:, 0])),
pa,
tt.ones_like(tt.shape_padright(pa[:, 0]))
], axis=1)
p = p_cum[:, 1:] - p_cum[:, :-1]
super().__init__(p=p, *args, **kwargs)
def __init__(self, eta, cutpoints, *args, **kwargs):
self.eta = tt.as_tensor_variable(eta)
self.cutpoints = tt.as_tensor_variable(cutpoints)
pa = sigmoid(tt.shape_padleft(self.cutpoints) - tt.shape_padright(self.eta))
p_cum = tt.concatenate([
tt.zeros_like(tt.shape_padright(pa[:, 0])),
pa,
tt.ones_like(tt.shape_padright(pa[:, 0]))
], axis=1)
p = p_cum[:, 1:] - p_cum[:, :-1]
super(OrderedLogistic, self).__init__(p=p, *args, **kwargs)
def __init__(self, eta, cutpoints, *args, **kwargs):
self.eta = tt.as_tensor_variable(floatX(eta))
self.cutpoints = tt.as_tensor_variable(cutpoints)
pa = sigmoid(self.cutpoints - tt.shape_padright(self.eta))
p_cum = tt.concatenate([
tt.zeros_like(tt.shape_padright(pa[..., 0])), pa,
tt.ones_like(tt.shape_padright(pa[..., 0]))
],
axis=-1)
p = p_cum[..., 1:] - p_cum[..., :-1]
super().__init__(p=p, *args, **kwargs)
def __init_probs(self):
theta, alpha, kappa, gamma, sigma = self.param_list
# Initialize probabilities
# Compute the response cumulative probability functions
resp_funcs = (sigma - gamma) * sigmoid(alpha * theta + kappa) + gamma
# CDF for responses range from 0 to 1
# reversing the category order to make the order of cprobs s.t.
# index i is P(X >= i)
cprobst = tt.concatenate([
tt.ones_like(tt.shape_padright(resp_funcs[..., 0])),
resp_funcs[..., ::-1],
tt.zeros_like(tt.shape_padright(resp_funcs[..., 0]))
],
axis=-1)
# Discrete difference across response categories to get
# marginal probabilities.
# Identical to tt.extra_ops.diff
probst = (cprobst[..., :-1] - cprobst[..., 1:])
return cprobst, probst