mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-06-08 15:05:15 +02:00
[merge] merge master into devel
This commit is contained in:
Max Zwiessele
commit
cf2673632b
12 changed files with 257 additions and 314 deletions
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@ -366,6 +366,7 @@ class InverseGamma(Gamma):
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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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class DGPLVM_KFDA(Prior):
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"""
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Implementation of the Discriminative Gaussian Process Latent Variable function using
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@ -512,6 +513,7 @@ class DGPLVM_KFDA(Prior):
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self.A = self.compute_A(lst_ni)
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self.x_shape = x_shape
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class DGPLVM(Prior):
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"""
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Implementation of the Discriminative Gaussian Process Latent Variable model paper, by Raquel.
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@ -903,7 +905,7 @@ class DGPLVM_Lamda(Prior, Parameterized):
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# Sb_inv_N = np.linalg.inv(Sb + np.eye(Sb.shape[0]) * (np.diag(Sb).min() * 0.1))
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#Sb_inv_N = np.linalg.inv(Sb+np.eye(Sb.shape[0])*0.1)
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#Sb_inv_N = pdinv(Sb+ np.eye(Sb.shape[0]) * (np.diag(Sb).min() * 0.5))[0]
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Sb_inv_N = pdinv(Sb + np.eye(Sb.shape[0])*0.9)[0]
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Sb_inv_N = pdinv(Sb + np.eye(Sb.shape[0])*0.9)[0]
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return (-1 / self.sigma2) * np.trace(Sb_inv_N.dot(Sw))
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# This function calculates derivative of the log of prior function
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@ -927,7 +929,7 @@ class DGPLVM_Lamda(Prior, Parameterized):
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# Sb_inv_N = np.linalg.inv(Sb + np.eye(Sb.shape[0]) * (np.diag(Sb).min() * 0.1))
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#Sb_inv_N = np.linalg.inv(Sb+np.eye(Sb.shape[0])*0.1)
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#Sb_inv_N = pdinv(Sb+ np.eye(Sb.shape[0]) * (np.diag(Sb).min() * 0.5))[0]
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Sb_inv_N = pdinv(Sb + np.eye(Sb.shape[0])*0.9)[0]
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Sb_inv_N = pdinv(Sb + np.eye(Sb.shape[0])*0.9)[0]
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Sb_inv_N_trans = np.transpose(Sb_inv_N)
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Sb_inv_N_trans_minus = -1 * Sb_inv_N_trans
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Sw_trans = np.transpose(Sw)
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@ -1198,6 +1200,7 @@ class DGPLVM_T(Prior):
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class HalfT(Prior):
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"""
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Implementation of the half student t probability function, coupled with random variables.
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@ -1208,15 +1211,17 @@ class HalfT(Prior):
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"""
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domain = _POSITIVE
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_instances = []
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def __new__(cls, A, nu): # Singleton:
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def __new__(cls, A, nu): # 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().nu == nu:
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return instance()
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return instance()
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o = super(Prior, cls).__new__(cls, A, nu)
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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, nu):
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self.A = float(A)
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self.nu = float(nu)
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@ -1225,37 +1230,81 @@ class HalfT(Prior):
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def __str__(self):
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return "hT({:.2g}, {:.2g})".format(self.A, self.nu)
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def lnpdf(self,theta):
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return (theta>0) * ( self.constant -.5*(self.nu+1) * np.log( 1.+ (1./self.nu) * (theta/self.A)**2 ) )
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def lnpdf(self, theta):
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return (theta > 0) * (self.constant - .5*(self.nu + 1) * np.log(1. + (1./self.nu) * (theta/self.A)**2))
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#theta = theta if isinstance(theta,np.ndarray) else np.array([theta])
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#lnpdfs = np.zeros_like(theta)
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#theta = np.array([theta])
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#above_zero = theta.flatten()>1e-6
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#v = self.nu
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#sigma2=self.A
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#stop
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#lnpdfs[above_zero] = (+ gammaln((v + 1) * 0.5)
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# - gammaln(v * 0.5)
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# - 0.5*np.log(sigma2 * v * np.pi)
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# - 0.5*(v + 1)*np.log(1 + (1/np.float(v))*((theta[above_zero][0]**2)/sigma2))
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#)
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#return lnpdfs
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# theta = theta if isinstance(theta,np.ndarray) else np.array([theta])
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# lnpdfs = np.zeros_like(theta)
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# theta = np.array([theta])
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# above_zero = theta.flatten()>1e-6
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# v = self.nu
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# sigma2=self.A
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# stop
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# lnpdfs[above_zero] = (+ gammaln((v + 1) * 0.5)
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# - gammaln(v * 0.5)
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# - 0.5*np.log(sigma2 * v * np.pi)
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# - 0.5*(v + 1)*np.log(1 + (1/np.float(v))*((theta[above_zero][0]**2)/sigma2))
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# )
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# return lnpdfs
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def lnpdf_grad(self,theta):
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theta = theta if isinstance(theta,np.ndarray) else np.array([theta])
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def lnpdf_grad(self, theta):
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theta = theta if isinstance(theta, np.ndarray) else np.array([theta])
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grad = np.zeros_like(theta)
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above_zero = theta>1e-6
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above_zero = theta > 1e-6
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v = self.nu
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sigma2=self.A
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sigma2 = self.A
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grad[above_zero] = -0.5*(v+1)*(2*theta[above_zero])/(v*sigma2 + theta[above_zero][0]**2)
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return grad
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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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from scipy.stats import t
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#[np.abs(x) for x in t.rvs(df=4,loc=0,scale=50, size=10000)])
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ret = t.rvs(self.nu,loc=0,scale=self.A, size=n)
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ret[ret<0] = 0
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return ret
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# return np.random.randn(n) * self.sigma + self.mu
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from scipy.stats import t
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# [np.abs(x) for x in t.rvs(df=4,loc=0,scale=50, size=10000)])
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ret = t.rvs(self.nu, loc=0, scale=self.A, size=n)
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ret[ret < 0] = 0
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return ret
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class Exponential(Prior):
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"""
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Implementation of the Exponential probability function,
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coupled with random variables.
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:param l: shape parameter
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"""
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domain = _POSITIVE
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_instances = []
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def __new__(cls, l): # 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().l == l:
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return instance()
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o = super(Exponential, cls).__new__(cls, l)
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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, l):
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self.l = l
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def __str__(self):
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return "Exp({:.2g})".format(self.l)
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def summary(self):
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ret = {"E[x]": 1. / self.l,
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"E[ln x]": np.nan,
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"var[x]": 1. / self.l**2,
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"Entropy": 1. - np.log(self.l),
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"Mode": 0.}
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return ret
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def lnpdf(self, x):
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return np.log(self.l) - self.l * x
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def lnpdf_grad(self, x):
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return - self.l
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def rvs(self, n):
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return np.random.exponential(scale=self.l, size=n)
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@ -62,7 +62,7 @@ class Transformation(object):
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import matplotlib.pyplot as plt
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from ...plotting.matplot_dep import base_plots
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x = np.linspace(-8,8)
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base_plots.meanplot(x, self.f(x),axes=axes*args,**kw)
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base_plots.meanplot(x, self.f(x), *args, ax=axes, **kw)
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axes = plt.gca()
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axes.set_xlabel(xlabel)
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axes.set_ylabel(ylabel)
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@ -488,7 +488,7 @@ class Logistic(Transformation):
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return instance()
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newfunc = super(Transformation, cls).__new__
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if newfunc is object.__new__:
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o = newfunc(cls)
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o = newfunc(cls)
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else:
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o = newfunc(cls, lower, upper, *args, **kwargs)
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cls._instances.append(weakref.ref(o))
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@ -1 +1,2 @@
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from .hmc import HMC
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from hmc import HMC
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from samplers import *
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@ -18,11 +18,11 @@ class Metropolis_Hastings:
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def __init__(self,model,cov=None):
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"""Metropolis Hastings, with tunings according to Gelman et al. """
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self.model = model
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current = self.model._get_params_transformed()
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current = self.model.optimizer_array
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self.D = current.size
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self.chains = []
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if cov is None:
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self.cov = model.Laplace_covariance()
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self.cov = np.eye(self.D)
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else:
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self.cov = cov
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self.scale = 2.4/np.sqrt(self.D)
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@ -33,20 +33,20 @@ class Metropolis_Hastings:
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if start is None:
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self.model.randomize()
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else:
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self.model._set_params_transformed(start)
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self.model.optimizer_array = start
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def sample(self, Ntotal, Nburn, Nthin, tune=True, tune_throughout=False, tune_interval=400):
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current = self.model._get_params_transformed()
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fcurrent = self.model.log_likelihood() + self.model.log_prior()
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def sample(self, Ntotal=10000, Nburn=1000, Nthin=10, tune=True, tune_throughout=False, tune_interval=400):
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current = self.model.optimizer_array
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fcurrent = self.model.log_likelihood() + self.model.log_prior() + \
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self.model._log_det_jacobian()
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accepted = np.zeros(Ntotal,dtype=np.bool)
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for it in range(Ntotal):
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print("sample %d of %d\r"%(it,Ntotal), end=' ')
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print "sample %d of %d\r"%(it,Ntotal),
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sys.stdout.flush()
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prop = np.random.multivariate_normal(current, self.cov*self.scale*self.scale)
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self.model._set_params_transformed(prop)
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fprop = self.model.log_likelihood() + self.model.log_prior()
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self.model.optimizer_array = prop
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fprop = self.model.log_likelihood() + self.model.log_prior() + \
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self.model._log_det_jacobian()
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if fprop>fcurrent:#sample accepted, going 'uphill'
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accepted[it] = True
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@ -74,10 +74,11 @@ class Metropolis_Hastings:
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def predict(self,function,args):
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"""Make a prediction for the function, to which we will pass the additional arguments"""
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param = self.model._get_params()
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param = self.model.param_array
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fs = []
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for p in self.chain:
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self.model._set_params(p)
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self.model.param_array = p
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fs.append(function(*args))
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self.model._set_params(param)# reset model to starting state
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# reset model to starting state
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self.model.param_array = param
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return fs
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@ -256,8 +256,6 @@ class Kern(Parameterized):
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:param other: the other kernel to be added
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:type other: GPy.kern
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:param tensor: whether or not to use the tensor space (default is false).
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:type tensor: bool
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"""
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assert isinstance(other, Kern), "only kernels can be multiplied to kernels..."
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@ -27,8 +27,6 @@ class Prod(CombinationKernel):
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:param k1, k2: the kernels to multiply
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:type k1, k2: Kern
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:param tensor: The kernels are either multiply as functions defined on the same input space (default) or on the product of the input spaces
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:type tensor: Boolean
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:rtype: kernel object
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"""
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@ -1,7 +1,6 @@
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import numpy as np
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import scipy as sp
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from GPy.util.linalg import jitchol
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import GPy
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from ..util.linalg import jitchol,trace_dot
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class LinalgTests(np.testing.TestCase):
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def setUp(self):
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@ -37,12 +36,13 @@ class LinalgTests(np.testing.TestCase):
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except sp.linalg.LinAlgError:
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return True
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def test_einsum_ijk_jlk_to_il(self):
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A = np.random.randn(50, 150, 5)
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B = np.random.randn(150, 100, 5)
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pure = np.einsum('ijk,jlk->il', A, B)
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quick = GPy.util.linalg.ijk_jlk_to_il(A, B)
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np.testing.assert_allclose(pure, quick)
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def test_trace_dot(self):
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N = 5
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A = np.random.rand(N,N)
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B = np.random.rand(N,N)
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trace = np.trace(A.dot(B))
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test_trace = trace_dot(A,B)
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np.testing.assert_allclose(trace,test_trace,atol=1e-13)
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def test_einsum_ij_jlk_to_ilk(self):
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A = np.random.randn(15, 150, 5)
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101
GPy/testing/rv_transformation_tests.py
Normal file
101
GPy/testing/rv_transformation_tests.py
Normal file
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@ -0,0 +1,101 @@
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# Written by Ilias Bilionis
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"""
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Test if hyperparameters in models are properly transformed.
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"""
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import unittest
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import numpy as np
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import scipy.stats as st
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import GPy
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class TestModel(GPy.core.Model):
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"""
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A simple GPy model with one parameter.
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"""
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def __init__(self):
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GPy.core.Model.__init__(self, 'test_model')
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theta = GPy.core.Param('theta', 1.)
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self.link_parameter(theta)
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def log_likelihood(self):
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return 0.
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class RVTransformationTestCase(unittest.TestCase):
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def _test_trans(self, trans):
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m = TestModel()
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prior = GPy.priors.LogGaussian(.5, 0.1)
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m.theta.set_prior(prior)
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m.theta.unconstrain()
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m.theta.constrain(trans)
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# The PDF of the transformed variables
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p_phi = lambda(phi): np.exp(-m._objective_grads(phi)[0])
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# To the empirical PDF of:
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theta_s = prior.rvs(100000)
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phi_s = trans.finv(theta_s)
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# which is essentially a kernel density estimation
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kde = st.gaussian_kde(phi_s)
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# We will compare the PDF here:
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phi = np.linspace(phi_s.min(), phi_s.max(), 100)
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# The transformed PDF of phi should be this:
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pdf_phi = np.array([p_phi(p) for p in phi])
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# UNCOMMENT TO SEE GRAPHICAL COMPARISON
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#import matplotlib.pyplot as plt
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#fig, ax = plt.subplots()
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#ax.hist(phi_s, normed=True, bins=100, alpha=0.25, label='Histogram')
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#ax.plot(phi, kde(phi), '--', linewidth=2, label='Kernel Density Estimation')
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#ax.plot(phi, pdf_phi, ':', linewidth=2, label='Transformed PDF')
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#ax.set_xlabel(r'transformed $\theta$', fontsize=16)
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#ax.set_ylabel('PDF', fontsize=16)
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#plt.legend(loc='best')
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#plt.show(block=True)
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# END OF PLOT
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# The following test cannot be very accurate
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self.assertTrue(np.linalg.norm(pdf_phi - kde(phi)) / np.linalg.norm(kde(phi)) <= 1e-1)
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# Check the gradients at a few random points
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for i in xrange(10):
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m.theta = theta_s[i]
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self.assertTrue(m.checkgrad(verbose=True))
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def test_Logexp(self):
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self._test_trans(GPy.constraints.Logexp())
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self._test_trans(GPy.constraints.Exponent())
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if __name__ == '__main__':
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unittest.main()
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quit()
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m = TestModel()
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prior = GPy.priors.LogGaussian(0., .9)
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m.theta.set_prior(prior)
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# The following should return the PDF in terms of the transformed quantities
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p_phi = lambda(phi): np.exp(-m._objective_grads(phi)[0])
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# Let's look at the transformation phi = log(exp(theta - 1))
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trans = GPy.constraints.Exponent()
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m.theta.constrain(trans)
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# Plot the transformed probability density
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phi = np.linspace(-8, 8, 100)
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fig, ax = plt.subplots()
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# Let's draw some samples of theta and transform them so that we see
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# which one is right
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theta_s = prior.rvs(10000)
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# Transform it to the new variables
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phi_s = trans.finv(theta_s)
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# And draw their histogram
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ax.hist(phi_s, normed=True, bins=100, alpha=0.25, label='Empirical')
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# This is to be compared to the PDF of the model expressed in terms of these new
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# variables
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ax.plot(phi, [p_phi(p) for p in phi], label='Transformed PDF', linewidth=2)
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ax.set_xlim(-3, 10)
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ax.set_xlabel(r'transformed $\theta$', fontsize=16)
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ax.set_ylabel('PDF', fontsize=16)
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plt.legend(loc='best')
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# Now let's test the gradients
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m.checkgrad(verbose=True)
|
||||
# And show the plot
|
||||
plt.show(block=True)
|
||||
|
|
@ -157,7 +157,7 @@ def trace_dot(a, b):
|
|||
"""
|
||||
Efficiently compute the trace of the matrix product of a and b
|
||||
"""
|
||||
return np.sum(a * b)
|
||||
return np.einsum('ij,ji->', a, b)
|
||||
|
||||
def mdot(*args):
|
||||
"""
|
||||
|
|
|
|||
24
README.md
24
README.md
|
|
@ -1,5 +1,6 @@
|
|||
# GPy
|
||||
|
||||
|
||||
A Gaussian processes framework in Python.
|
||||
|
||||
* [GPy homepage](http://sheffieldml.github.io/GPy/)
|
||||
|
|
@ -10,6 +11,19 @@ A Gaussian processes framework in Python.
|
|||
|
||||
Continuous integration status: 
|
||||
|
||||
### Citation
|
||||
|
||||
@Misc{gpy2014,
|
||||
author = {The GPy authors},
|
||||
title = {{GPy}: A Gaussian process framework in python},
|
||||
howpublished = {\url{http://github.com/SheffieldML/GPy}},
|
||||
year = {2012--2014}
|
||||
}
|
||||
|
||||
### Pronounciation
|
||||
|
||||
We like to pronounce it 'Gee-pie'.
|
||||
|
||||
### Getting started: installing with pip
|
||||
|
||||
We are now requiring the newest version of  and thus, we strongly recommend using
|
||||
|
|
@ -83,8 +97,12 @@ clone this git repository and add it to your path:
|
|||
|
||||
### OSX
|
||||
|
||||
Everything appears to work out-of-the box using  on osx Mavericks. Download/clone GPy, and then add GPy to your PYTHONPATH
|
||||
Everything appears to work out-of-the box using
|
||||
|
||||
on osx Mavericks.
|
||||
Download/clone GPy, and then add GPy to your PYTHONPATH
|
||||
|
||||
conda update scipy
|
||||
git clone git@github.com:SheffieldML/GPy.git ~/SheffieldML
|
||||
echo 'PYTHONPATH=$PYTHONPATH:~/SheffieldML' >> ~/.profile
|
||||
|
||||
|
|
@ -137,7 +155,9 @@ Run nosetests from the root directory of the repository:
|
|||
or from within IPython
|
||||
|
||||
import GPy; GPy.tests()
|
||||
|
||||
|
||||
|
||||
|
||||
## Funding Acknowledgements
|
||||
|
||||
|
||||
|
|
|
|||
222
doc/log.txt
222
doc/log.txt
|
|
@ -1,222 +0,0 @@
|
|||
/home/maxz/Documents/gpy/GPy/__init__.py:docstring of GPy.load:1: WARNING: Inline interpreted text or phrase reference start-string without end-string.
|
||||
/home/maxz/Documents/gpy/GPy/core/gp.py:docstring of GPy.core.gp.GP.optimize:8: ERROR: Unknown interpreted text role "module".
|
||||
/home/maxz/Documents/gpy/GPy/core/gp.py:docstring of GPy.core.gp.GP.predict_wishard_embedding:6: WARNING: Field list ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/GPy/core/gp.py:docstring of GPy.core.gp.GP.predictive_gradients:5: ERROR: Unexpected indentation.
|
||||
/home/maxz/Documents/gpy/GPy/core/gp.py:docstring of GPy.core.gp.GP.predictive_gradients:10: WARNING: Block quote ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/GPy/core/model.py:docstring of GPy.core.model.Model.optimize_restarts:29: WARNING: Explicit markup ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/doc/GPy.core.rst:57: WARNING: autodoc: failed to import module u'GPy.core.svigp'; the following exception was raised:
|
||||
Traceback (most recent call last):
|
||||
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
|
||||
__import__(self.modname)
|
||||
ImportError: No module named svigp
|
||||
/home/maxz/Documents/gpy/doc/GPy.core.rst:65: WARNING: autodoc: failed to import module u'GPy.core.symbolic'; the following exception was raised:
|
||||
Traceback (most recent call last):
|
||||
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
|
||||
__import__(self.modname)
|
||||
File "/home/maxz/Documents/gpy/GPy/core/symbolic.py", line 10, in <module>
|
||||
from sympy.utilities.lambdify import lambdastr, _imp_namespace, _get_namespace
|
||||
ImportError: No module named lambdify
|
||||
/home/maxz/Documents/gpy/GPy/core/parameterization/parameter_core.py:docstring of GPy.core.parameterization.parameter_core.Indexable.unset_priors:1: WARNING: Inline emphasis start-string without end-string.
|
||||
/home/maxz/Documents/gpy/GPy/core/parameterization/parameter_core.py:docstring of GPy.core.parameterization.parameter_core.Nameable.hierarchy_name:4: WARNING: Field list ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/GPy/core/parameterization/parameter_core.py:docstring of GPy.core.parameterization.parameter_core.Parameterizable.traverse:1: WARNING: Inline emphasis start-string without end-string.
|
||||
/home/maxz/Documents/gpy/GPy/core/parameterization/parameter_core.py:docstring of GPy.core.parameterization.parameter_core.Parameterizable.traverse:1: WARNING: Inline strong start-string without end-string.
|
||||
/home/maxz/Documents/gpy/GPy/core/parameterization/parameterized.py:docstring of GPy.core.parameterization.parameterized.Parameterized:18: ERROR: Unexpected indentation.
|
||||
/home/maxz/Documents/gpy/GPy/core/parameterization/parameterized.py:docstring of GPy.core.parameterization.parameterized.Parameterized:20: WARNING: Block quote ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/GPy/core/parameterization/ties_and_remappings.py:docstring of GPy.core.parameterization.ties_and_remappings.Tie:18: SEVERE: Unexpected section title or transition.
|
||||
|
||||
================================
|
||||
/home/maxz/Documents/gpy/doc/GPy.examples.rst:50: WARNING: autodoc: failed to import module u'GPy.examples.stochastic'; the following exception was raised:
|
||||
Traceback (most recent call last):
|
||||
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
|
||||
__import__(self.modname)
|
||||
ImportError: No module named stochastic
|
||||
/home/maxz/Documents/gpy/doc/GPy.examples.rst:58: WARNING: autodoc: failed to import module u'GPy.examples.tutorials'; the following exception was raised:
|
||||
Traceback (most recent call last):
|
||||
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
|
||||
__import__(self.modname)
|
||||
ImportError: No module named tutorials
|
||||
/home/maxz/Documents/gpy/doc/GPy.inference.latent_function_inference.rst:82: WARNING: autodoc: failed to import module u'GPy.inference.latent_function_inference.var_dtc_gpu'; the following exception was raised:
|
||||
Traceback (most recent call last):
|
||||
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
|
||||
__import__(self.modname)
|
||||
ImportError: No module named var_dtc_gpu
|
||||
/home/maxz/Documents/gpy/doc/GPy.inference.optimization.rst:42: WARNING: autodoc: failed to import module u'GPy.inference.optimization.sgd'; the following exception was raised:
|
||||
Traceback (most recent call last):
|
||||
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
|
||||
__import__(self.modname)
|
||||
ImportError: No module named sgd
|
||||
/home/maxz/Documents/gpy/GPy/kern/_src/coregionalize.py:docstring of GPy.kern._src.coregionalize.Coregionalize:5: ERROR: Unexpected indentation.
|
||||
/home/maxz/Documents/gpy/doc/GPy.kern._src.rst:73: WARNING: autodoc: failed to import module u'GPy.kern._src.hierarchical'; the following exception was raised:
|
||||
Traceback (most recent call last):
|
||||
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
|
||||
__import__(self.modname)
|
||||
ImportError: No module named hierarchical
|
||||
/home/maxz/Documents/gpy/GPy/kern/_src/independent_outputs.py:docstring of GPy.kern._src.independent_outputs.IndependentOutputs:9: WARNING: Field list ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:24: ERROR: Unexpected indentation.
|
||||
/home/maxz/Documents/gpy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:22: WARNING: Inline literal start-string without end-string.
|
||||
/home/maxz/Documents/gpy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:25: WARNING: Block quote ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:27: WARNING: Definition list ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:27: WARNING: Inline literal start-string without end-string.
|
||||
/home/maxz/Documents/gpy/GPy/kern/_src/stationary.py:docstring of GPy.kern._src.stationary.Stationary:27: WARNING: Inline interpreted text or phrase reference start-string without end-string.
|
||||
/home/maxz/Documents/gpy/doc/GPy.kern._src.rst:177: WARNING: autodoc: failed to import module u'GPy.kern._src.symbolic'; the following exception was raised:
|
||||
Traceback (most recent call last):
|
||||
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
|
||||
__import__(self.modname)
|
||||
File "/home/maxz/Documents/gpy/GPy/kern/_src/symbolic.py", line 5, in <module>
|
||||
from ...core.symbolic import Symbolic_core
|
||||
File "/home/maxz/Documents/gpy/GPy/core/symbolic.py", line 10, in <module>
|
||||
from sympy.utilities.lambdify import lambdastr, _imp_namespace, _get_namespace
|
||||
ImportError: No module named lambdify
|
||||
/home/maxz/Documents/gpy/GPy/models/gp_kronecker_gaussian_regression.py:docstring of GPy.models.gp_kronecker_gaussian_regression.GPKroneckerGaussianRegression:13: ERROR: Unexpected indentation.
|
||||
/home/maxz/Documents/gpy/GPy/models/gp_kronecker_gaussian_regression.py:docstring of GPy.models.gp_kronecker_gaussian_regression.GPKroneckerGaussianRegression:18: WARNING: Block quote ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/doc/GPy.models.rst:66: WARNING: autodoc: failed to import module u'GPy.models.gp_multioutput_regression'; the following exception was raised:
|
||||
Traceback (most recent call last):
|
||||
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
|
||||
__import__(self.modname)
|
||||
ImportError: No module named gp_multioutput_regression
|
||||
/home/maxz/Documents/gpy/GPy/models/gp_var_gauss.py:docstring of GPy.models.gp_var_gauss.GPVariationalGaussianApproximation:9: WARNING: Definition list ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/GPy/models/mrd.py:docstring of GPy.models.mrd.MRD:32: WARNING: Field list ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/GPy/models/mrd.py:docstring of GPy.models.mrd.MRD:32: WARNING: Inline interpreted text or phrase reference start-string without end-string.
|
||||
/home/maxz/Documents/gpy/GPy/models/mrd.py:docstring of GPy.models.mrd.MRD:34: WARNING: Definition list ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/doc/GPy.models.rst:138: WARNING: autodoc: failed to import module u'GPy.models.sparse_gp_multioutput_regression'; the following exception was raised:
|
||||
Traceback (most recent call last):
|
||||
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
|
||||
__import__(self.modname)
|
||||
ImportError: No module named sparse_gp_multioutput_regression
|
||||
/home/maxz/Documents/gpy/doc/GPy.models.rst:178: WARNING: autodoc: failed to import module u'GPy.models.svigp_regression'; the following exception was raised:
|
||||
Traceback (most recent call last):
|
||||
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
|
||||
__import__(self.modname)
|
||||
ImportError: No module named svigp_regression
|
||||
/home/maxz/Documents/gpy/GPy/plotting/matplot_dep/netpbmfile.py:docstring of GPy.plotting.matplot_dep.netpbmfile.imread:6: SEVERE: Unexpected section title.
|
||||
|
||||
Examples
|
||||
--------
|
||||
/home/maxz/Documents/gpy/GPy/plotting/matplot_dep/netpbmfile.py:docstring of GPy.plotting.matplot_dep.netpbmfile.imsave:4: SEVERE: Unexpected section title.
|
||||
|
||||
Examples
|
||||
--------
|
||||
/home/maxz/Documents/gpy/GPy/testing/likelihood_tests.py:docstring of GPy.testing.likelihood_tests.dparam_checkgrad:6: ERROR: Unexpected indentation.
|
||||
/home/maxz/Documents/gpy/GPy/testing/likelihood_tests.py:docstring of GPy.testing.likelihood_tests.dparam_checkgrad:7: WARNING: Block quote ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/GPy/testing/likelihood_tests.py:docstring of GPy.testing.likelihood_tests.dparam_partial:7: WARNING: Definition list ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/GPy/testing/likelihood_tests.py:docstring of GPy.testing.likelihood_tests.dparam_partial:9: ERROR: Unexpected indentation.
|
||||
docstring of GPy.util.datasets.hapmap3:7: WARNING: Block quote ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/doc/GPy.util.rst:74: WARNING: autodoc: failed to import module u'GPy.util.erfcx'; the following exception was raised:
|
||||
Traceback (most recent call last):
|
||||
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
|
||||
__import__(self.modname)
|
||||
ImportError: No module named erfcx
|
||||
/home/maxz/Documents/gpy/doc/GPy.util.rst:146: WARNING: autodoc: failed to import module u'GPy.util.mpi'; the following exception was raised:
|
||||
Traceback (most recent call last):
|
||||
File "/home/maxz/anaconda/lib/python2.7/site-packages/Sphinx-1.3.1-py2.7.egg/sphinx/ext/autodoc.py", line 385, in import_object
|
||||
__import__(self.modname)
|
||||
ImportError: No module named mpi
|
||||
/home/maxz/Documents/gpy/GPy/util/netpbmfile.py:docstring of GPy.util.netpbmfile.imread:6: SEVERE: Unexpected section title.
|
||||
|
||||
Examples
|
||||
--------
|
||||
/home/maxz/Documents/gpy/GPy/util/netpbmfile.py:docstring of GPy.util.netpbmfile.imsave:4: SEVERE: Unexpected section title.
|
||||
|
||||
Examples
|
||||
--------
|
||||
/home/maxz/Documents/gpy/doc/GPy.util.rst:2: SEVERE: Duplicate ID: "module-GPy.util.subarray_and_sorting".
|
||||
/home/maxz/Documents/gpy/GPy/util/subarray_and_sorting.py:docstring of GPy.util.subarray_and_sorting.common_subarrays:8: ERROR: Unexpected indentation.
|
||||
/home/maxz/Documents/gpy/GPy/util/subarray_and_sorting.py:docstring of GPy.util.subarray_and_sorting.common_subarrays:11: SEVERE: Unexpected section title.
|
||||
|
||||
Examples:
|
||||
=========
|
||||
/home/maxz/Documents/gpy/GPy/util/subarray_and_sorting.py:docstring of GPy.util.subarray_and_sorting.common_subarrays:19: ERROR: Unexpected indentation.
|
||||
/home/maxz/Documents/gpy/GPy/util/subarray_and_sorting.py:docstring of GPy.util.subarray_and_sorting.common_subarrays:21: WARNING: Block quote ends without a blank line; unexpected unindent.
|
||||
/home/maxz/Documents/gpy/GPy/util/block_matrices.py:docstring of GPy.util.block_matrices.block_dot:3: ERROR: Undefined substitution referenced: "A11.B11|B12.B12".
|
||||
/home/maxz/Documents/gpy/GPy/util/block_matrices.py:docstring of GPy.util.block_matrices.block_dot:3: ERROR: Undefined substitution referenced: "A21.B21|A22.B22".
|
||||
/home/maxz/Documents/gpy/doc/installation.rst:22: ERROR: Unexpected indentation.
|
||||
/home/maxz/Documents/gpy/doc/installation.rst:27: ERROR: Unexpected indentation.
|
||||
/home/maxz/Documents/gpy/doc/tuto_creating_new_kernels.rst:58: WARNING: Inline literal start-string without end-string.
|
||||
/home/maxz/Documents/gpy/doc/tuto_creating_new_models.rst:24: ERROR: Unknown target name: "parameterized".
|
||||
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:83: WARNING: Title underline too short.
|
||||
|
||||
Interacting with Parameters:
|
||||
=======================
|
||||
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:83: WARNING: Title underline too short.
|
||||
|
||||
Interacting with Parameters:
|
||||
=======================
|
||||
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:109: WARNING: Title underline too short.
|
||||
|
||||
Regular expressions
|
||||
----------------
|
||||
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:164: WARNING: Title underline too short.
|
||||
|
||||
Setting and fetching parameters `parameter_array`
|
||||
------------------------------------------
|
||||
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:164: WARNING: Title underline too short.
|
||||
|
||||
Setting and fetching parameters `parameter_array`
|
||||
------------------------------------------
|
||||
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:220: WARNING: Title underline too short.
|
||||
|
||||
Getting the model parameter's gradients
|
||||
============================
|
||||
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:220: WARNING: Title underline too short.
|
||||
|
||||
Getting the model parameter's gradients
|
||||
============================
|
||||
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:236: WARNING: Title underline too short.
|
||||
|
||||
Adjusting the model's constraints
|
||||
================================
|
||||
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:236: WARNING: Title underline too short.
|
||||
|
||||
Adjusting the model's constraints
|
||||
================================
|
||||
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:287: WARNING: Title underline too short.
|
||||
|
||||
Available Constraints
|
||||
==============
|
||||
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:287: WARNING: Title underline too short.
|
||||
|
||||
Available Constraints
|
||||
==============
|
||||
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:299: WARNING: Title underline too short.
|
||||
|
||||
Tying Parameters
|
||||
============
|
||||
/home/maxz/Documents/gpy/doc/tuto_interacting_with_models.rst:299: WARNING: Title underline too short.
|
||||
|
||||
Tying Parameters
|
||||
============
|
||||
/home/maxz/Documents/gpy/doc/tuto_parameterized.rst:3: WARNING: Title overline too short.
|
||||
|
||||
*******************
|
||||
Parameterization handling
|
||||
*******************
|
||||
/home/maxz/Documents/gpy/doc/tuto_parameterized.rst:10: WARNING: Title underline too short.
|
||||
|
||||
Parameter handles
|
||||
==============
|
||||
/home/maxz/Documents/gpy/doc/tuto_parameterized.rst:16: WARNING: Title underline too short.
|
||||
|
||||
:py:class:`~GPy.core.parameterization.parameterized.Parameterized`
|
||||
==========
|
||||
/home/maxz/Documents/gpy/doc/tuto_parameterized.rst:16: WARNING: Title underline too short.
|
||||
|
||||
:py:class:`~GPy.core.parameterization.parameterized.Parameterized`
|
||||
==========
|
||||
/home/maxz/Documents/gpy/doc/tuto_parameterized.rst:21: WARNING: Title underline too short.
|
||||
|
||||
:py:class:`~GPy.core.parameterization.param.Param`
|
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===========
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:py:class:`~GPy.core.parameterization.param.Param`
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===========
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@ -13,9 +13,9 @@ First we import the libraries we will need ::
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For most kernels, the dimension is the only mandatory parameter to define a kernel object. However, it is also possible to specify the values of the parameters. For example, the three following commands are valid for defining a squared exponential kernel (ie rbf or Gaussian) ::
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ker1 = GPy.kern.rbf(1) # Equivalent to ker1 = GPy.kern.rbf(input_dim=1, variance=1., lengthscale=1.)
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ker2 = GPy.kern.rbf(input_dim=1, variance = .75, lengthscale=2.)
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ker3 = GPy.kern.rbf(1, .5, .5)
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ker1 = GPy.kern.RBF(1) # Equivalent to ker1 = GPy.kern.RBF(input_dim=1, variance=1., lengthscale=1.)
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ker2 = GPy.kern.RBF(input_dim=1, variance = .75, lengthscale=2.)
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ker3 = GPy.kern.RBF(1, .5, .5)
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A ``print`` and a ``plot`` functions are implemented to represent kernel objects. The commands ::
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@ -52,21 +52,18 @@ Operations to combine kernels
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In ``GPy``, kernel objects can be added or multiplied. In both cases, two kinds of operations are possible since one can assume that the kernels to add/multiply are defined on the same space or on different subspaces. In other words, it is possible to use two kernels :math:`k_1,\ k_2` over :math:`\mathbb{R} \times \mathbb{R}` to create
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* a kernel over :math:`\mathbb{R} \times \mathbb{R}`: :math:`k(x,y) = k_1(x,y) \times k_2(x,y)`
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* a kernel over :math:`\mathbb{R}^2 \times \mathbb{R}^2`: :math:`k(\mathbf{x},\mathbf{y}) = k_1(x_1,y_1) \times k_2(x_2,y_2)`
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* a kernel over :math:`\mathbb{R} \times \mathbb{R}`: :math:`k(x,y) = k_1(x,y) \times k_2(x,y)`.
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These two options are available in GPy using the flag ``tensor`` in the ``add`` and ``prod`` functions. Here is a quick example ::
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This is available in GPy via the ``add`` and ``prod`` functions. Here is a quick example ::
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k1 = GPy.kern.rbf(1,1.,2.)
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k1 = GPy.kern.RBF(1,1.,2.)
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k2 = GPy.kern.Matern32(1, 0.5, 0.2)
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# Product of kernels
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k_prod = k1.prod(k2) # By default, tensor=False
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k_prodtens = k1.prod(k2,tensor=True)
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k_prod = k1.prod(k2)
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# Sum of kernels
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k_add = k1.add(k2) # By default, tensor=False
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k_addtens = k1.add(k2,tensor=True)
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k_add = k1.add(k2)
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.. # plots
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pb.figure(figsize=(8,8))
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@ -75,23 +72,23 @@ These two options are available in GPy using the flag ``tensor`` in the ``add``
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pb.title('prod')
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pb.subplot(2,2,2)
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k_prodtens.plot()
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pb.title('tensor prod')
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pb.title('prod')
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pb.subplot(2,2,3)
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k_add.plot()
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pb.title('sum')
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pb.subplot(2,2,4)
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k_addtens.plot()
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pb.title('tensor sum')
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pb.title('sum')
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pb.subplots_adjust(wspace=0.3, hspace=0.3)
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.. figure:: Figures/tuto_kern_overview_multadd.png
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:align: center
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:height: 500px
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A shortcut for ``add`` and ``prod`` (with default flag ``tensor=False``) is provided by the usual ``+`` and ``*`` operators. Here is another example where we create a periodic kernel with some decay ::
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A shortcut for ``add`` and ``prod`` is provided by the usual ``+`` and ``*`` operators. Here is another example where we create a periodic kernel with some decay ::
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k1 = GPy.kern.rbf(1,1.,2)
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k2 = GPy.kern.periodic_Matern52(1,variance=1e3, lengthscale=1, period = 1.5, lower=-5., upper = 5)
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k1 = GPy.kern.RBF(1,1.,2)
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k2 = GPy.kern.PeriodicMatern52(1,variance=1e3, lengthscale=1, period = 1.5, lower=-5., upper = 5)
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k = k1 * k2 # equivalent to k = k1.prod(k2)
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print k
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@ -116,14 +113,14 @@ A shortcut for ``add`` and ``prod`` (with default flag ``tensor=False``) is prov
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In general, ``kern`` objects can be seen as a sum of ``kernparts`` objects, where the later are covariance functions defined on the same space. For example, the following code ::
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k = (k1+k2)*(k1+k2)
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print k.parts[0].name, '\n', k.parts[1].name, '\n', k.parts[2].name, '\n', k.parts[3].name
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print k.parts[0].name, '\n', k.parts[1].name, '\n', k.parts[1].parts[0].name, '\n', k.parts[1].parts[1].name, '\n'
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returns ::
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add_1
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add_2
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rbf
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periodic_Matern52
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rbf<times>rbf
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rbf<times>periodic_Mat52
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periodic_Mat52<times>rbf
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periodic_Mat52<times>periodic_Mat52
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Constraining the parameters
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===========================
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@ -137,9 +134,9 @@ Various constrains can be applied to the parameters of a kernel
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When calling one of these functions, the parameters to constrain can either by specified by a regular expression that matches its name or by a number that corresponds to the rank of the parameter. Here is an example ::
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k1 = GPy.kern.rbf(1)
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k1 = GPy.kern.RBF(1)
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k2 = GPy.kern.Matern32(1)
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k3 = GPy.kern.white(1)
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k3 = GPy.kern.White(1)
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k = k1 + k2 + k3
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print k
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@ -182,9 +179,9 @@ In two dimensions ANOVA kernels have the following form:
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Let us assume that we want to define an ANOVA kernel with a Matern 3/2 kernel for :math:`k_i`. As seen previously, we can define this kernel as follows ::
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k_cst = GPy.kern.bias(1,variance=1.)
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k_mat = GPy.kern.Matern52(1,variance=1., lengthscale=3)
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Kanova = (k_cst + k_mat).prod(k_cst + k_mat,tensor=True)
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k_cst = GPy.kern.Bias(1,variance=1.)
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k_mat = GPy.kern.Matern52(1,variance=1.,lengthscale=3)
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Kanova = (k_cst + k_mat).prod(k_cst + k_mat)
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print Kanova
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Printing the resulting kernel outputs the following ::
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import GPy
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pb.ion()
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ker1 = GPy.kern.rbf(D=1) # Equivalent to ker1 = GPy.kern.rbf(D=1, variance=1., lengthscale=1.)
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ker2 = GPy.kern.rbf(D=1, variance = .75, lengthscale=3.)
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ker3 = GPy.kern.rbf(1, .5, .25)
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ker1 = GPy.kern.RBF(D=1) # Equivalent to ker1 = GPy.kern.RBF(D=1, variance=1., lengthscale=1.)
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ker2 = GPy.kern.RBF(D=1, variance = .75, lengthscale=3.)
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ker3 = GPy.kern.RBF(1, .5, .25)
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ker1.plot()
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ker2.plot()
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ker3.plot()
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#pb.savefig("Figures/tuto_kern_overview_basicdef.png")
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kernels = [GPy.kern.rbf(1), GPy.kern.exponential(1), GPy.kern.Matern32(1), GPy.kern.Matern52(1), GPy.kern.Brownian(1), GPy.kern.bias(1), GPy.kern.linear(1), GPy.kern.spline(1), GPy.kern.periodic_exponential(1), GPy.kern.periodic_Matern32(1), GPy.kern.periodic_Matern52(1), GPy.kern.white(1)]
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kernel_names = ["GPy.kern.rbf", "GPy.kern.exponential", "GPy.kern.Matern32", "GPy.kern.Matern52", "GPy.kern.Brownian", "GPy.kern.bias", "GPy.kern.linear", "GPy.kern.spline", "GPy.kern.periodic_exponential", "GPy.kern.periodic_Matern32", "GPy.kern.periodic_Matern52", "GPy.kern.white"]
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kernels = [GPy.kern.RBF(1), GPy.kern.Exponential(1), GPy.kern.Matern32(1), GPy.kern.Matern52(1), GPy.kern.Brownian(1), GPy.kern.Bias(1), GPy.kern.Linear(1), GPy.kern.PeriodicExponential(1), GPy.kern.PeriodicMatern32(1), GPy.kern.PeriodicMatern52(1), GPy.kern.White(1)]
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kernel_names = ["GPy.kern.RBF", "GPy.kern.Exponential", "GPy.kern.Matern32", "GPy.kern.Matern52", "GPy.kern.Brownian", "GPy.kern.Bias", "GPy.kern.Linear", "GPy.kern.PeriodicExponential", "GPy.kern.PeriodicMatern32", "GPy.kern.PeriodicMatern52", "GPy.kern.White"]
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pb.figure(figsize=(16,12))
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pb.subplots_adjust(wspace=.5, hspace=.5)
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