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Added pdf_link's for gaussian and student t, added third derivatives for

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transformations and tests for them
This commit is contained in:
Alan Saul 2013-10-17 14:31:24 +01:00
parent e65548f385
commit afd38df1ef
10 changed files with 203 additions and 615 deletions
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26
GPy/likelihoods/noise_models/student_t_noise.py
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@ -40,12 +40,36 @@ class StudentT(NoiseDistribution):
def variance(self, extra_data=None):
return (self.v / float(self.v - 2)) * self.sigma2
def pdf_link(self, link_f, y, extra_data=None):
"""
Likelihood function given link(f)
.. math::
\\ln p(y_{i}|\\lambda(f_{i})) = \\frac{\\Gamma\\left(\\frac{v+1}{2}\\right)}{\\Gamma\\left(\\frac{v}{2}\\right)\\sqrt{v\\pi\\sigma^{2}}}\\left(1 + \\frac{1}{v}\\left(\\frac{(y_{i} - f_{i})^{2}}{\\sigma^{2}}\\right)\\right)^{\\frac{-v+1}{2}}
:param link_f: latent variables link(f)
:type link_f: Nx1 array
:param y: data
:type y: Nx1 array
:param extra_data: extra_data which is not used in student t distribution - not used
:returns: likelihood evaluated for this point
:rtype: float
"""
assert link_f.shape == y.shape
e = y - link_f
#Careful gamma(big_number) is infinity!
objective = ((np.exp(gammaln((self.v + 1)*0.5) - gammaln(self.v * 0.5))
/ (np.sqrt(self.v * np.pi * self.sigma2)))
* ((1 + (1./float(self.v))*((e**2)/float(self.sigma2)))**(-0.5*(self.v + 1)))
)
return np.prod(objective)
def logpdf_link(self, link_f, y, extra_data=None):
"""
Log Likelihood Function given link(f)
.. math::
\\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
\\ln p(y_{i}|f_{i}) = \\ln \\Gamma\\left(\\frac{v+1}{2}\\right) - \\ln \\Gamma\\left(\\frac{v}{2}\\right) - \\ln \\sqrt{v \\pi\\sigma^{2}} - \\frac{v+1}{2}\\ln \\left(1 + \\frac{1}{v}\\left(\\frac{(y_{i} - f_{i})^{2}}{\\sigma^{2}}\\right)\\right)
:param link_f: latent variables (link(f))
:type link_f: Nx1 array