From 8b9d5d8f72f8470759d0920915b6547042686066 Mon Sep 17 00:00:00 2001 From: Michael T Smith Date: Mon, 13 Jun 2016 13:19:33 +0100 Subject: [PATCH] Improved comments. import future added. Fixed exception --- GPy/kern/src/integral.py | 8 ++-- GPy/kern/src/integral_limits.py | 37 +++++++++++++++---- .../src/multidimensional_integral_limits.py | 20 +++++----- 3 files changed, 42 insertions(+), 23 deletions(-) diff --git a/GPy/kern/src/integral.py b/GPy/kern/src/integral.py index 971a48a8..6febf203 100644 --- a/GPy/kern/src/integral.py +++ b/GPy/kern/src/integral.py @@ -1,5 +1,6 @@ # Written by Mike Smith michaeltsmith.org.uk +from __future__ import division import numpy as np from .kern import Kern from ...core.parameterization import Param @@ -24,7 +25,7 @@ class Integral(Kern): #todo do I need to inherit from Stationary self.link_parameters(self.variances, self.lengthscale) #this just takes a list of parameters we need to optimise. def h(self, z): - return 0.5 * z * np.sqrt(math.pi) * math.erf(z) + np.exp(-(z**2)) + return 0.5 * z * np.sqrt(math.pi) * math.erf(z) + np.exp(-(z**2)) def dk_dl(self, t, tprime, l): #derivative of the kernel wrt lengthscale return l * ( self.h(t/l) - self.h((t - tprime)/l) + self.h(tprime/l) - 1) @@ -39,10 +40,8 @@ class Integral(Kern): #todo do I need to inherit from Stationary dK_dv[i,j] = self.k_xx(x[0],x2[0],self.lengthscale[0]) #the gradient wrt the variance is k_xx. self.lengthscale.gradient = np.sum(dK_dl * dL_dK) self.variances.gradient = np.sum(dK_dv * dL_dK) - #print "V%0.5f" % self.variances.gradient - #print "L%0.5f" % self.lengthscale.gradient else: #we're finding dK_xf/Dtheta - print("NEED TO HANDLE TODO!") + raise NotImplementedError("Currently this function only handles finding the gradient of a single vector of inputs (X) not a pair of vectors (X and X2)") #useful little function to help calculate the covariances. def g(self,z): @@ -71,7 +70,6 @@ class Integral(Kern): #todo do I need to inherit from Stationary for i,x in enumerate(X): for j,x2 in enumerate(X2): K_xf[i,j] = self.k_xf(x[0],x2[0],self.lengthscale[0]) - #print self.variances[0] return K_xf * self.variances[0] def Kdiag(self, X): diff --git a/GPy/kern/src/integral_limits.py b/GPy/kern/src/integral_limits.py index 7006ee6f..10370328 100644 --- a/GPy/kern/src/integral_limits.py +++ b/GPy/kern/src/integral_limits.py @@ -1,17 +1,23 @@ # Written by Mike Smith michaeltsmith.org.uk +from __future__ import division +import math import numpy as np from .kern import Kern from ...core.parameterization import Param from paramz.transformations import Logexp -import math -class Integral_Limits(Kern): #todo do I need to inherit from Stationary + +class Integral_Limits(Kern): """ - Integral kernel, can include limits on each integral value. + Integral kernel. This kernel allows 1d histogram or binned data to be modelled. + The outputs are the counts in each bin. The inputs (on two dimensions) are the start and end points of each bin. + The kernel's predictions are the latent function which might have generated those binned results. """ def __init__(self, input_dim, variances=None, lengthscale=None, ARD=False, active_dims=None, name='integral'): + """ + """ super(Integral_Limits, self).__init__(input_dim, active_dims, name) if lengthscale is None: @@ -39,10 +45,8 @@ class Integral_Limits(Kern): #todo do I need to inherit from Stationary dK_dv[i,j] = self.k_xx(x[0],x2[0],x[1],x2[1],self.lengthscale[0]) #the gradient wrt the variance is k_xx. self.lengthscale.gradient = np.sum(dK_dl * dL_dK) self.variances.gradient = np.sum(dK_dv * dL_dK) - #print "V%0.5f" % self.variances.gradient - #print "L%0.5f" % self.lengthscale.gradient else: #we're finding dK_xf/Dtheta - print("NEED TO HANDLE TODO!") + raise NotImplementedError("Currently this function only handles finding the gradient of a single vector of inputs (X) not a pair of vectors (X and X2)") #useful little function to help calculate the covariances. def g(self,z): @@ -71,6 +75,22 @@ class Integral_Limits(Kern): #todo do I need to inherit from Stationary return 0.5 * np.sqrt(math.pi) * l * (math.erf((t-tprime)/l) + math.erf((tprime-s)/l)) def K(self, X, X2=None): + """Note: We have a latent function and an output function. We want to be able to find: + - the covariance between values of the output function + - the covariance between values of the latent function + - the "cross covariance" between values of the output function and the latent function + This method is used by GPy to either get the covariance between the outputs (K_xx) or + is used to get the cross covariance (between the latent function and the outputs (K_xf). + We take advantage of the places where this function is used: + - if X2 is none, then we know that the items being compared (to get the covariance for) + are going to be both from the OUTPUT FUNCTION. + - if X2 is not none, then we know that the items being compared are from two different + sets (the OUTPUT FUNCTION and the LATENT FUNCTION). + + If we want the covariance between values of the LATENT FUNCTION, we take advantage of + the fact that we only need that when we do prediction, and this only calls Kdiag (not K). + So the covariance between LATENT FUNCTIONS is available from Kdiag. + """ if X2 is None: K_xx = np.zeros([X.shape[0],X.shape[0]]) for i,x in enumerate(X): @@ -85,8 +105,9 @@ class Integral_Limits(Kern): #todo do I need to inherit from Stationary return K_xf * self.variances[0] def Kdiag(self, X): - """I've used the fact that we call this method for K_ff when finding the covariance as a hack so - I know if I should return K_ff or K_xx. In this case we're returning K_ff!! + """I've used the fact that we call this method during prediction (instead of K). When we + do prediction we want to know the covariance between LATENT FUNCTIONS (K_ff) (as that's probably + what the user wants). $K_{ff}^{post} = K_{ff} - K_{fx} K_{xx}^{-1} K_{xf}$""" K_ff = np.zeros(X.shape[0]) for i,x in enumerate(X): diff --git a/GPy/kern/src/multidimensional_integral_limits.py b/GPy/kern/src/multidimensional_integral_limits.py index 0f473742..8a07595b 100644 --- a/GPy/kern/src/multidimensional_integral_limits.py +++ b/GPy/kern/src/multidimensional_integral_limits.py @@ -1,5 +1,6 @@ # Written by Mike Smith michaeltsmith.org.uk +from __future__ import division import numpy as np from .kern import Kern from ...core.parameterization import Param @@ -8,7 +9,11 @@ import math class Multidimensional_Integral_Limits(Kern): #todo do I need to inherit from Stationary """ - Integral kernel, can include limits on each integral value. + Integral kernel, can include limits on each integral value. This kernel allows an n-dimensional + histogram or binned data to be modelled. The outputs are the counts in each bin. The inputs + are the start and end points of each bin: Pairs of inputs act as the limits on each bin. So + inputs 4 and 5 provide the start and end values of each bin in the 3rd dimension. + The kernel's predictions are the latent function which might have generated those binned results. """ def __init__(self, input_dim, variances=None, lengthscale=None, ARD=False, active_dims=None, name='integral'): @@ -30,7 +35,6 @@ class Multidimensional_Integral_Limits(Kern): #todo do I need to inherit from St return l * ( self.h((t-sprime)/l) - self.h((t - tprime)/l) + self.h((tprime-s)/l) - self.h((s-sprime)/l)) def update_gradients_full(self, dL_dK, X, X2=None): - #print self.variances if X2 is None: #we're finding dK_xx/dTheta dK_dl_term = np.zeros([X.shape[0],X.shape[0],self.lengthscale.shape[0]]) k_term = np.zeros([X.shape[0],X.shape[0],self.lengthscale.shape[0]]) @@ -47,14 +51,12 @@ class Multidimensional_Integral_Limits(Kern): #todo do I need to inherit from St for jl, l in enumerate(self.lengthscale): if jl!=il: dK_dl *= k_term[:,:,jl] - #dK_dl = np.dot(dK_dl,k_term[:,:,il]) - #print k_term[:,:,il] self.lengthscale.gradient[il] = np.sum(dK_dl * dL_dK) dK_dv = self.calc_K_xx_wo_variance(X) #the gradient wrt the variance is k_xx. self.variances.gradient = np.sum(dK_dv * dL_dK) else: #we're finding dK_xf/Dtheta - print("NEED TO HANDLE TODO!") - #print self.variances[0],self.lengthscale[0],self.lengthscale[1] #np.sum(dK_dv*dL_dK) + raise NotImplementedError("Currently this function only handles finding the gradient of a single vector of inputs (X) not a pair of vectors (X and X2)") + #useful little function to help calculate the covariances. @@ -94,12 +96,10 @@ class Multidimensional_Integral_Limits(Kern): #todo do I need to inherit from St return K_xx def K(self, X, X2=None): - if X2 is None: - #print "X x X" + if X2 is None: #X vs X K_xx = self.calc_K_xx_wo_variance(X) return K_xx * self.variances[0] - else: - #print "X x X2" + else: #X vs X2 K_xf = np.ones([X.shape[0],X2.shape[0]]) for i,x in enumerate(X): for j,x2 in enumerate(X2):