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62 lines
1.9 KiB
Python
62 lines
1.9 KiB
Python
import GPy
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from scipy.special import gamma, gammaln
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class student_t(GPy.likelihoods.likelihood_function):
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"""Student t likelihood distribution
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For nomanclature see Bayesian Data Analysis 2003 p576
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$$\ln(\frac{\Gamma(\frac{(v+1)}{2})}{\Gamma(\sqrt(v \pi \Gamma(\frac{v}{2}))})+ \ln(1+\frac{(y_i-f_i)^2}{\sigma v})^{-\frac{(v+1)}{2}}$$
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TODO:Double check this
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Laplace:
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Needs functions to calculate
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ln p(yi|fi)
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dln p(yi|fi)_dfi
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d2ln p(yi|fi)_d2fi
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"""
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def __init__(self, deg_free, sigma=1):
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self.v = deg_free
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self.sigma = 1
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def link_function(self, y_i, f_i):
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"""link_function $\ln p(y_i|f_i)$
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$$\ln \Gamma(\frac{v+1}{2}) - \ln \Gamma(\frac{v}{2}) - \ln \frac{v \pi \sigma}{2} - \frac{v+1}{2}\ln (1 + \frac{(y_{i} - f_{i})^{2}}{v\sigma})$$
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TODO: Double check this
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:y_i: datum number i
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:f_i: latent variable f_i
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:returns: float(likelihood evaluated for this point)
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"""
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e = y_i - f_i
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return gammaln((v+1)*0.5) - gammaln(v*0.5) - np.ln(v*np.pi*sigma)*0.5 - (v+1)*0.5*np.ln(1 + ((e/sigma)**2)/v) #Check the /v!
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def link_grad(self, y_i, f_i):
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"""gradient of the link function at y_i, given f_i w.r.t f_i
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derivative of log((gamma((v+1)/2)/gamma(sqrt(v*pi*gamma(v/2))))*(1+(t^2)/(a*v))^((-(v+1))/2)) with respect to t
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$$\frac{(y_i - f_i)(v + 1)}{\sigma v (y_{i} - f_{i})^{2}}$$
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TODO: Double check this
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:y_i: datum number i
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:f_i: latent variable f_i
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:returns: float(gradient of likelihood evaluated at this point)
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"""
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pass
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def link_hess(self, y_i, f_i, f_j):
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"""hessian at this point (the hessian will be 0 unless i == j)
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i.e. second derivative w.r.t f_i and f_j
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second derivative of
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:y_i: @todo
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:f_i: @todo
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:f_j: @todo
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:returns: @todo
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"""
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if f_i =
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pass
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