apunkt/GPy
1
0
Fork 0
mirror of https://github.com/SheffieldML/GPy.git synced 2026-05-15 06:52:39 +02:00
Code Issues Projects Releases Packages Wiki Activity Actions

Added derivatives for poisson and a couple of examples,

Browse source 
need to fix for EP.
This commit is contained in:
Alan Saul 2013-10-25 15:08:53 +01:00
parent ba1cf96cb1
commit 2fdb60287f
3 changed files with 169 additions and 18 deletions
Download patch file Download diff file Expand all files Collapse all files

44
GPy/examples/regression.py
View file

@ -270,6 +270,50 @@ def toy_rbf_1d_50(max_iters=100):
print(m)
return m
def toy_poisson_rbf_1d(optimizer='bfgs', max_nb_eval_optim=100):
"""Run a simple demonstration of a standard Gaussian process fitting it to data sampled from an RBF covariance."""
X = np.linspace(0,10)[:, None]
F = np.round(X*3-4)
F = np.where(F > 0, F, 0)
eps = np.random.randint(0,4, F.shape[0])[:, None]
Y = F + eps
noise_model = GPy.likelihoods.poisson()
likelihood = GPy.likelihoods.EP(Y,noise_model)
# create simple GP Model
m = GPy.models.GPRegression(X, Y, likelihood=likelihood)
# optimize
m.optimize(optimizer, max_f_eval=max_nb_eval_optim)
# plot
m.plot()
print(m)
return m
def toy_poisson_rbf_1d_laplace(optimizer='bfgs', max_nb_eval_optim=100):
"""Run a simple demonstration of a standard Gaussian process fitting it to data sampled from an RBF covariance."""
X = np.linspace(0,10)[:, None]
F = np.round(X*3-4)
F = np.where(F > 0, F, 0)
eps = np.random.randint(0,4, F.shape[0])[:, None]
Y = F + eps
noise_model = GPy.likelihoods.poisson()
likelihood = GPy.likelihoods.Laplace(Y,noise_model)
# create simple GP Model
m = GPy.models.GPRegression(X, Y, likelihood=likelihood)
# optimize
m.optimize(optimizer, max_f_eval=max_nb_eval_optim)
# plot
m.plot()
print(m)
return m
def toy_ARD(max_iters=1000, kernel_type='linear', num_samples=300, D=4):
# Create an artificial dataset where the values in the targets (Y)
# only depend in dimensions 1 and 3 of the inputs (X). Run ARD to

132
GPy/likelihoods/noise_models/poisson_noise.py
View file

@ -1,7 +1,7 @@
from __future__ import division
# Copyright (c) 2012, 2013 Ricardo Andrade
# Licensed under the BSD 3-clause license (see LICENSE.txt)
import numpy as np
from scipy import stats,special
import scipy as sp
@ -14,9 +14,10 @@ class Poisson(NoiseDistribution):
Poisson likelihood
.. math::
L(x) = \\exp(\\lambda) * \\frac{\\lambda^Y_i}{Y_i!}
p(y_{i}|\\lambda(f_{i})) = \\frac{\\lambda(f_{i})^{y_{i}}}{y_{i}!}e^{-\\lambda(f_{i})}
..Note: Y is expected to take values in {0,1,2,...}
.. Note::
Y is expected to take values in {0,1,2,...}
"""
def __init__(self,gp_link=None,analytical_mean=False,analytical_variance=False):
super(Poisson, self).__init__(gp_link,analytical_mean,analytical_variance)
@ -24,25 +25,108 @@ class Poisson(NoiseDistribution):
def _preprocess_values(self,Y): #TODO
return Y
def _mass(self,gp,obs):
def pdf_link(self, link_f, y, extra_data=None):
"""
Mass (or density) function
"""
return stats.poisson.pmf(obs,self.gp_link.transf(gp))
Likelihood function given link(f)
def _nlog_mass(self,gp,obs):
"""
Negative logarithm of the un-normalized distribution: factors that are not a function of gp are omitted
"""
return self.gp_link.transf(gp) - obs * np.log(self.gp_link.transf(gp)) + np.log(special.gamma(obs+1))
.. math::
p(y_{i}|\\lambda(f_{i})) = \\frac{\\lambda(f_{i})^{y_{i}}}{y_{i}!}e^{-\\lambda(f_{i})}
def _dnlog_mass_dgp(self,gp,obs):
return self.gp_link.dtransf_df(gp) * (1. - obs/self.gp_link.transf(gp))
: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 poisson distribution
:returns: likelihood evaluated for this point
:rtype: float
"""
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
return np.prod(stats.poisson.pmf(y,link_f))
def _d2nlog_mass_dgp2(self,gp,obs):
d2_df = self.gp_link.d2transf_df2(gp)
transf = self.gp_link.transf(gp)
return obs * ((self.gp_link.dtransf_df(gp)/transf)**2 - d2_df/transf) + d2_df
def logpdf_link(self, link_f, y, extra_data=None):
"""
Log Likelihood Function given link(f)
.. math::
\\ln p(y_{i}|\lambda(f_{i})) = -\\lambda(f_{i}) + y_{i}\\log \\lambda(f_{i}) - \\log y_{i}!
: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 poisson distribution
:returns: likelihood evaluated for this point
:rtype: float
"""
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
return np.sum(-link_f + y*np.log(link_f) - special.gammaln(y+1))
def dlogpdf_dlink(self, link_f, y, extra_data=None):
"""
Gradient of the log likelihood function at y, given link(f) w.r.t link(f)
.. math::
\\frac{d \\ln p(y_{i}|\lambda(f_{i}))}{d\\lambda(f)} = \\frac{y_{i}}{\\lambda(f_{i})} - 1
:param link_f: latent variables (f)
:type link_f: Nx1 array
:param y: data
:type y: Nx1 array
:param extra_data: extra_data which is not used in poisson distribution
:returns: gradient of likelihood evaluated at points
:rtype: Nx1 array
"""
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
return y/link_f - 1
def d2logpdf_dlink2(self, link_f, y, extra_data=None):
"""
Hessian at y, given link(f), w.r.t link(f)
i.e. second derivative logpdf at y given link(f_i) and link(f_j) w.r.t link(f_i) and link(f_j)
The hessian will be 0 unless i == j
.. math::
\\frac{d^{2} \\ln p(y_{i}|\lambda(f_{i}))}{d^{2}\\lambda(f)} = \\frac{-y_{i}}{\\lambda(f_{i})^{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 poisson distribution
:returns: Diagonal of hessian matrix (second derivative of likelihood evaluated at points f)
:rtype: Nx1 array
.. Note::
Will return diagonal of hessian, since every where else it is 0, as the likelihood factorizes over cases
(the distribution for y_i depends only on link(f_i) not on link(f_(j!=i))
"""
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
hess = -y/(link_f**2)
return hess
#d2_df = self.gp_link.d2transf_df2(gp)
#transf = self.gp_link.transf(gp)
#return obs * ((self.gp_link.dtransf_df(gp)/transf)**2 - d2_df/transf) + d2_df
def d3logpdf_dlink3(self, link_f, y, extra_data=None):
"""
Third order derivative log-likelihood function at y given link(f) w.r.t link(f)
.. math::
\\frac{d^{3} \\ln p(y_{i}|\lambda(f_{i}))}{d^{3}\\lambda(f)} = \\frac{2y_{i}}{\\lambda(f_{i})^{3}}
: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 poisson distribution
:returns: third derivative of likelihood evaluated at points f
:rtype: Nx1 array
"""
assert np.atleast_1d(link_f).shape == np.atleast_1d(y).shape
d3lik_dlink3 = 2*y/(link_f)**3
return d3lik_dlink3
def _mean(self,gp):
"""
@ -55,3 +139,15 @@ class Poisson(NoiseDistribution):
Mass (or density) function
"""
return self.gp_link.transf(gp)
def samples(self, gp):
"""
Returns a set of samples of observations based on a given value of the latent variable.
:param size: number of samples to compute
:param gp: latent variable
"""
orig_shape = gp.shape
gp = gp.flatten()
Ysim = np.array([np.random.poisson(self.gp_link.transf(gpj),size=1) for gpj in gp])
return Ysim.reshape(orig_shape)

11
GPy/testing/likelihoods_tests.py
View file

@ -84,6 +84,10 @@ class TestNoiseModels(object):
self.f = np.random.rand(self.N, 1)
self.binary_Y = np.asarray(np.random.rand(self.N) > 0.5, dtype=np.int)[:, None]
self.positive_Y = np.exp(self.Y.copy())
self.integer_Y = np.round(self.X[:, 0]*3-3)[:, None] + np.random.randint(0,3, self.X.shape[0])[:, None]
self.integer_Y = np.where(self.integer_Y > 0, self.integer_Y, 0)
print self.integer_Y
print self.Y
self.var = 0.2
@ -223,6 +227,13 @@ class TestNoiseModels(object):
"link_f_constraints": [constrain_positive],
"Y": self.positive_Y,
"laplace": True,
},
"Poisson_default": {
"model": GPy.likelihoods.poisson(),
"link_f_constraints": [constrain_positive],
"Y": self.integer_Y,
"laplace": True,
"ep": False #Should work though...
}
}