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all parameterization stuff now in seperate module -> GPy.core.parameterization
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Max Zwiessele
parent
acbda64769
commit
0733886ba0
30 changed files with 344 additions and 354 deletions
268
GPy/core/parameterization/priors.py
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268
GPy/core/parameterization/priors.py
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# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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import numpy as np
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import pylab as pb
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from scipy.special import gammaln, digamma
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from ...util.linalg import pdinv
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from domains import _REAL, _POSITIVE
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import warnings
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import weakref
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class Prior:
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domain = None
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def pdf(self, x):
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return np.exp(self.lnpdf(x))
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def plot(self):
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rvs = self.rvs(1000)
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pb.hist(rvs, 100, normed=True)
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xmin, xmax = pb.xlim()
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xx = np.linspace(xmin, xmax, 1000)
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pb.plot(xx, self.pdf(xx), 'r', linewidth=2)
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class Gaussian(Prior):
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"""
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Implementation of the univariate Gaussian probability function, coupled with random variables.
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:param mu: mean
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:param sigma: standard deviation
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.. Note:: Bishop 2006 notation is used throughout the code
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"""
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domain = _REAL
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_instances = []
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def __new__(cls, mu, sigma): # Singleton:
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if cls._instances:
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cls._instances[:] = [instance for instance in cls._instances if instance()]
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for instance in cls._instances:
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if instance().mu == mu and instance().sigma == sigma:
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return instance()
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o = super(Prior, cls).__new__(cls, mu, sigma)
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cls._instances.append(weakref.ref(o))
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return cls._instances[-1]()
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def __init__(self, mu, sigma):
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self.mu = float(mu)
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self.sigma = float(sigma)
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self.sigma2 = np.square(self.sigma)
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self.constant = -0.5 * np.log(2 * np.pi * self.sigma2)
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def __str__(self):
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return "N(" + str(np.round(self.mu)) + ', ' + str(np.round(self.sigma2)) + ')'
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def lnpdf(self, x):
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return self.constant - 0.5 * np.square(x - self.mu) / self.sigma2
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def lnpdf_grad(self, x):
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return -(x - self.mu) / self.sigma2
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def rvs(self, n):
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return np.random.randn(n) * self.sigma + self.mu
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class LogGaussian(Prior):
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"""
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Implementation of the univariate *log*-Gaussian probability function, coupled with random variables.
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:param mu: mean
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:param sigma: standard deviation
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.. Note:: Bishop 2006 notation is used throughout the code
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"""
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domain = _POSITIVE
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_instances = []
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def __new__(cls, mu, sigma): # Singleton:
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if cls._instances:
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cls._instances[:] = [instance for instance in cls._instances if instance()]
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for instance in cls._instances:
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if instance().mu == mu and instance().sigma == sigma:
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return instance()
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o = super(Prior, cls).__new__(cls, mu, sigma)
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cls._instances.append(weakref.ref(o))
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return cls._instances[-1]()
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def __init__(self, mu, sigma):
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self.mu = float(mu)
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self.sigma = float(sigma)
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self.sigma2 = np.square(self.sigma)
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self.constant = -0.5 * np.log(2 * np.pi * self.sigma2)
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def __str__(self):
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return "lnN(" + str(np.round(self.mu)) + ', ' + str(np.round(self.sigma2)) + ')'
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def lnpdf(self, x):
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return self.constant - 0.5 * np.square(np.log(x) - self.mu) / self.sigma2 - np.log(x)
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def lnpdf_grad(self, x):
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return -((np.log(x) - self.mu) / self.sigma2 + 1.) / x
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def rvs(self, n):
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return np.exp(np.random.randn(n) * self.sigma + self.mu)
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class MultivariateGaussian:
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"""
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Implementation of the multivariate Gaussian probability function, coupled with random variables.
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:param mu: mean (N-dimensional array)
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:param var: covariance matrix (NxN)
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.. Note:: Bishop 2006 notation is used throughout the code
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"""
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domain = _REAL
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_instances = []
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def __new__(cls, mu, var): # Singleton:
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if cls._instances:
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cls._instances[:] = [instance for instance in cls._instances if instance()]
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for instance in cls._instances:
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if np.all(instance().mu == mu) and np.all(instance().var == var):
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return instance()
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o = super(Prior, cls).__new__(cls, mu, var)
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cls._instances.append(weakref.ref(o))
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return cls._instances[-1]()
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def __init__(self, mu, var):
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self.mu = np.array(mu).flatten()
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self.var = np.array(var)
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assert len(self.var.shape) == 2
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assert self.var.shape[0] == self.var.shape[1]
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assert self.var.shape[0] == self.mu.size
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self.input_dim = self.mu.size
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self.inv, self.hld = pdinv(self.var)
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self.constant = -0.5 * self.input_dim * np.log(2 * np.pi) - self.hld
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def summary(self):
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raise NotImplementedError
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def pdf(self, x):
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return np.exp(self.lnpdf(x))
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def lnpdf(self, x):
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d = x - self.mu
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return self.constant - 0.5 * np.sum(d * np.dot(d, self.inv), 1)
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def lnpdf_grad(self, x):
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d = x - self.mu
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return -np.dot(self.inv, d)
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def rvs(self, n):
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return np.random.multivariate_normal(self.mu, self.var, n)
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def plot(self):
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if self.input_dim == 2:
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rvs = self.rvs(200)
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pb.plot(rvs[:, 0], rvs[:, 1], 'kx', mew=1.5)
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xmin, xmax = pb.xlim()
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ymin, ymax = pb.ylim()
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xx, yy = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
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xflat = np.vstack((xx.flatten(), yy.flatten())).T
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zz = self.pdf(xflat).reshape(100, 100)
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pb.contour(xx, yy, zz, linewidths=2)
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def gamma_from_EV(E, V):
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warnings.warn("use Gamma.from_EV to create Gamma Prior", FutureWarning)
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return Gamma.from_EV(E, V)
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class Gamma(Prior):
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"""
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Implementation of the Gamma probability function, coupled with random variables.
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:param a: shape parameter
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:param b: rate parameter (warning: it's the *inverse* of the scale)
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.. Note:: Bishop 2006 notation is used throughout the code
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"""
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domain = _POSITIVE
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_instances = []
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def __new__(cls, a, b): # Singleton:
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if cls._instances:
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cls._instances[:] = [instance for instance in cls._instances if instance()]
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for instance in cls._instances:
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if instance().a == a and instance().b == b:
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return instance()
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o = super(Prior, cls).__new__(cls, a, b)
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cls._instances.append(weakref.ref(o))
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return cls._instances[-1]()
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def __init__(self, a, b):
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self.a = float(a)
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self.b = float(b)
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self.constant = -gammaln(self.a) + a * np.log(b)
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def __str__(self):
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return "Ga(" + str(np.round(self.a)) + ', ' + str(np.round(self.b)) + ')'
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def summary(self):
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ret = {"E[x]": self.a / self.b, \
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"E[ln x]": digamma(self.a) - np.log(self.b), \
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"var[x]": self.a / self.b / self.b, \
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"Entropy": gammaln(self.a) - (self.a - 1.) * digamma(self.a) - np.log(self.b) + self.a}
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if self.a > 1:
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ret['Mode'] = (self.a - 1.) / self.b
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else:
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ret['mode'] = np.nan
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return ret
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def lnpdf(self, x):
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return self.constant + (self.a - 1) * np.log(x) - self.b * x
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def lnpdf_grad(self, x):
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return (self.a - 1.) / x - self.b
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def rvs(self, n):
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return np.random.gamma(scale=1. / self.b, shape=self.a, size=n)
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@staticmethod
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def from_EV(E, V):
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"""
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Creates an instance of a Gamma Prior by specifying the Expected value(s)
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and Variance(s) of the distribution.
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:param E: expected value
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:param V: variance
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"""
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a = np.square(E) / V
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b = E / V
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return Gamma(a, b)
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class inverse_gamma(Prior):
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"""
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Implementation of the inverse-Gamma probability function, coupled with random variables.
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:param a: shape parameter
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:param b: rate parameter (warning: it's the *inverse* of the scale)
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.. Note:: Bishop 2006 notation is used throughout the code
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"""
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domain = _POSITIVE
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def __new__(cls, a, b): # Singleton:
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if cls._instances:
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cls._instances[:] = [instance for instance in cls._instances if instance()]
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for instance in cls._instances:
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if instance().a == a and instance().b == b:
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return instance()
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o = super(Prior, cls).__new__(cls, a, b)
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cls._instances.append(weakref.ref(o))
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return cls._instances[-1]()
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def __init__(self, a, b):
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self.a = float(a)
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self.b = float(b)
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self.constant = -gammaln(self.a) + a * np.log(b)
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def __str__(self):
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return "iGa(" + str(np.round(self.a)) + ', ' + str(np.round(self.b)) + ')'
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def lnpdf(self, x):
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return self.constant - (self.a + 1) * np.log(x) - self.b / x
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def lnpdf_grad(self, x):
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return -(self.a + 1.) / x + self.b / x ** 2
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def rvs(self, n):
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return 1. / np.random.gamma(scale=1. / self.b, shape=self.a, size=n)
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