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Adding weibull likelihood, requires 'extra_data' to be passed to likelihood, i.e. the censoring information

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Alan Saul 2013-04-10 15:43:31 +01:00
parent 65481d7a73
commit 9bbb11b825
2 changed files with 104 additions and 19 deletions
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99
python/likelihoods/likelihood_function.py
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@ -4,6 +4,7 @@ import numpy as np
from GPy.likelihoods.likelihood_functions import likelihood_function
from scipy import stats
class student_t(likelihood_function):
"""Student t likelihood distribution
For nomanclature see Bayesian Data Analysis 2003 p576
@ -24,15 +25,16 @@ class student_t(likelihood_function):
self.log_concave = False
@property
def variance(self):
def variance(self, extra_data=None):
return (self.v / float(self.v - 2)) * (self.sigma**2)
def link_function(self, y, f):
def link_function(self, y, f, extra_data=None):
"""link_function $\ln p(y|f)$
$$\ln p(y_{i}|f_{i}) = \ln \Gamma(\frac{v+1}{2}) - \ln \Gamma(\frac{v}{2})\sqrt{v \pi}\sigma - \frac{v+1}{2}\ln (1 + \frac{1}{v}\left(\frac{y_{i} - f_{i}}{\sigma}\right)^2$$
:y: data
:f: latent variables f
:extra_data: extra_data which is not used in student t distribution
:returns: float(likelihood evaluated for this point)
"""
@ -49,7 +51,7 @@ class student_t(likelihood_function):
)
return np.sum(objective)
def link_grad(self, y, f):
def link_grad(self, y, f, extra_data=None):
"""
Gradient of the link function at y, given f w.r.t f
@ -57,6 +59,7 @@ class student_t(likelihood_function):
:y: data
:f: latent variables f
:extra_data: extra_data which is not used in student t distribution
:returns: gradient of likelihood evaluated at points
"""
@ -67,17 +70,18 @@ class student_t(likelihood_function):
grad = ((self.v + 1) * e) / (self.v * (self.sigma**2) + (e**2))
return np.squeeze(grad)
def link_hess(self, y, f):
def link_hess(self, y, f, extra_data=None):
"""
Hessian at this point (if we are only looking at the link function not the prior) the hessian will be 0 unless i == j
i.e. second derivative link_function at y given f f_j w.r.t f and f_j
Will return diaganol of hessian, since every where else it is 0
Will return diagonal of hessian, since every where else it is 0
$$\frac{d^{2}p(y_{i}|f_{i})}{df^{2}} = \frac{(v + 1)(y - f)}{v \sigma^{2} + (y_{i} - f_{i})^{2}}$$
:y: data
:f: latent variables f
:extra_data: extra_data which is not used in student t distribution
:returns: array which is diagonal of covariance matrix (second derivative of likelihood evaluated at points)
"""
y = np.squeeze(y)
@ -139,7 +143,7 @@ class student_t(likelihood_function):
#size=(num_f_samples, num_y_samples))
#print student_t_samples.shape
student_t_samples = stats.t.rvs(self.v, loc=student_t_means[:,None],
student_t_samples = stats.t.rvs(self.v, loc=student_t_means[:, None],
scale=self.sigma,
size=(num_test_points, num_y_samples, num_f_samples))
student_t_samples = np.reshape(student_t_samples,
@ -152,7 +156,7 @@ class student_t(likelihood_function):
##Alernenately we could sample from int p(y|f*)p(f*|x*) df*
def t_gaussian(f, mu, var):
return (((gamma((self.v+1)*0.5)) / (gamma(self.v*0.5)*self.sigma*np.sqrt(self.v*np.pi))) * ((1+(1/self.v)*(((mu-f)/self.sigma)**2))**(-(self.v+1)*0.5))
* ((1/(np.sqrt(2*np.pi*var)))*np.exp(-(1/(2*var)) *((mu-f)**2)))
* ((1/(np.sqrt(2*np.pi*var)))*np.exp(-(1/(2*var)) *((mu-f)**2)))
)
def t_gauss_int(mu, var):
@ -167,4 +171,83 @@ class student_t(likelihood_function):
p = vec_t_gauss_int(mu, var)
p_025 = mu - p
p_975 = mu + p
import ipdb; ipdb.set_trace() ### XXX BREAKPOINT
return mu, np.nan*mu, p_025, p_975
class weibull_survival(likelihood_function):
"""Weibull t likelihood distribution for survival analysis with censoring
For nomanclature see Bayesian Survival Analysis
Laplace:
Needs functions to calculate
ln p(yi|fi)
dln p(yi|fi)_dfi
d2ln p(yi|fi)_d2fifj
"""
def __init__(self, shape, scale):
self.shape = shape
self.scale = scale
#FIXME: This should be in the superclass
self.log_concave = True
def link_function(self, y, f, extra_data=None):
"""
link_function $\ln p(y|f)$, i.e. log likelihood
$$\ln p(y|f) = v_{i}(\ln \alpha + (\alpha - 1)\ln y_{i} + f_{i}) - y_{i}^{\alpha}\exp(f_{i})$$
:y: time of event data
:f: latent variables f
:extra_data: the censoring indicator, 1 for censored, 0 for not
:returns: float(likelihood evaluated for this point)
"""
y = np.squeeze(y)
f = np.squeeze(f)
assert y.shape == f.shape
v = extra_data
objective = v*(np.log(self.shape) + (self.shape - 1)*np.log(y) + f) - (y**self.shape)*np.exp(f) # FIXME: CHECK THIS WITH BOOK, wheres scale?
return np.sum(objective)
def link_grad(self, y, f, extra_data=None):
"""
Gradient of the link function at y, given f w.r.t f
$$\frac{d}{df} \ln p(y_{i}|f_{i}) = v_{i} - y_{i}\exp(f_{i})
:y: data
:f: latent variables f
:extra_data: the censoring indicator, 1 for censored, 0 for not
:returns: gradient of likelihood evaluated at points
"""
y = np.squeeze(y)
f = np.squeeze(f)
assert y.shape == f.shape
v = extra_data
grad = v - (y**self.shape)*np.exp(f)
return np.squeeze(grad)
def link_hess(self, y, f, extra_data=None):
"""
Hessian at this point (if we are only looking at the link function not the prior) the hessian will be 0 unless i == j
i.e. second derivative link_function at y given f f_j w.r.t f and f_j
Will return diagonal of hessian, since every where else it is 0
$$\frac{d^{2}p(y_{i}|f_{i})}{df^{2}} = \frac{(v + 1)(y - f)}{v \sigma^{2} + (y_{i} - f_{i})^{2}}$$
:y: data
:f: latent variables f
:extra_data: extra_data which is not used hessian
:returns: array which is diagonal of covariance matrix (second derivative of likelihood evaluated at points)
"""
y = np.squeeze(y)
f = np.squeeze(f)
assert y.shape == f.shape
hess = (y**self.shape)*np.exp(f)
return np.squeeze(hess)