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Added some numerical stability to link functions with tests for link functions

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This commit is contained in:
Alan Saul 2015-04-10 14:58:02 +01:00
parent 034d141d63
commit 5c9587404d
3 changed files with 197 additions and 27 deletions
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59
GPy/likelihoods/link_functions.py
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@ -5,9 +5,8 @@ import numpy as np
from scipy import stats
import scipy as sp
from GPy.util.univariate_Gaussian import std_norm_pdf,std_norm_cdf,inv_std_norm_cdf
_exp_lim_val = np.finfo(np.float64).max
_lim_val = np.log(_exp_lim_val)
from scipy.special import cbrt
from ..util.misc import safe_exp, safe_square, safe_cube, safe_quad, safe_three_times
class GPTransformation(object):
"""
@ -70,7 +69,7 @@ class Probit(GPTransformation):
.. math::
g(f) = \\Phi^{-1} (mu)
"""
def transf(self,f):
return std_norm_cdf(f)
@ -84,7 +83,7 @@ class Probit(GPTransformation):
def d3transf_df3(self,f):
#FIXME
f2 = f**2
f2 = safe_square(f)
return -(1/(np.sqrt(2*np.pi)))*np.exp(-0.5*(f2))*(1-f2)
@ -98,22 +97,26 @@ class Cloglog(GPTransformation):
or
f = \log (-\log(1-p))
"""
def transf(self,f):
return 1-np.exp(-np.exp(f))
ef = safe_exp(f)
return 1-np.exp(-ef)
def dtransf_df(self,f):
return np.exp(f-np.exp(f))
ef = safe_exp(f)
return np.exp(f-ef)
def d2transf_df2(self,f):
ef = np.exp(f)
ef = safe_exp(f)
return -np.exp(f-ef)*(ef-1.)
def d3transf_df3(self,f):
ef = np.exp(f)
return np.exp(f-ef)*(1.-3*ef + ef**2)
ef = safe_exp(f)
ef2 = safe_square(ef)
three_times_ef = safe_three_times(ef)
r_val = np.exp(f-ef)*(1.-three_times_ef + ef2)
return r_val
class Log(GPTransformation):
"""
@ -123,16 +126,16 @@ class Log(GPTransformation):
"""
def transf(self,f):
return np.exp(np.clip(f, -_lim_val, _lim_val))
return safe_exp(f)
def dtransf_df(self,f):
return np.exp(np.clip(f, -_lim_val, _lim_val))
return safe_exp(f)
def d2transf_df2(self,f):
return np.exp(np.clip(f, -_lim_val, _lim_val))
return safe_exp(f)
def d3transf_df3(self,f):
return np.exp(np.clip(f, -_lim_val, _lim_val))
return safe_exp(f)
class Log_ex_1(GPTransformation):
"""
@ -142,17 +145,20 @@ class Log_ex_1(GPTransformation):
"""
def transf(self,f):
return np.log(1.+np.exp(f))
return np.log1p(safe_exp(f))
def dtransf_df(self,f):
return np.exp(f)/(1.+np.exp(f))
ef = safe_exp(f)
return ef/(1.+ef)
def d2transf_df2(self,f):
aux = np.exp(f)/(1.+np.exp(f))
ef = safe_exp(f)
aux = ef/(1.+ef)
return aux*(1.-aux)
def d3transf_df3(self,f):
aux = np.exp(f)/(1.+np.exp(f))
ef = safe_exp(f)
aux = ef/(1.+ef)
daux_df = aux*(1.-aux)
return daux_df - (2.*aux*daux_df)
@ -160,14 +166,17 @@ class Reciprocal(GPTransformation):
def transf(self,f):
return 1./f
def dtransf_df(self,f):
return -1./(f**2)
def dtransf_df(self, f):
f2 = safe_square(f)
return -1./f2
def d2transf_df2(self,f):
return 2./(f**3)
def d2transf_df2(self, f):
f3 = safe_cube(f)
return 2./f3
def d3transf_df3(self,f):
return -6./(f**4)
f4 = safe_quad(f)
return -6./f4
class Heaviside(GPTransformation):
"""