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rbf kernel now has an ARD flag
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Nicolas
parent
688d6ac7a5
commit
68d7e23648
4 changed files with 57 additions and 28 deletions
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@ -1,7 +1,6 @@
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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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"""
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Simple Gaussian Processes regression with an RBF kernel
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"""
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@ -19,8 +18,11 @@ pb.close('all')
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X = np.random.uniform(-3.,3.,(20,1))
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Y = np.sin(X)+np.random.randn(20,1)*0.05
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# define kernel
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ker = GPy.kern.rbf(1,ARD=False) + GPy.kern.white(1)
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# create simple GP model
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m = GPy.models.GP_regression(X,Y)
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m = GPy.models.GP_regression(X,Y,ker)
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# contrain all parameters to be positive
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m.constrain_positive('')
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@ -30,6 +32,7 @@ m.optimize('tnc', max_f_eval = 1000)
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m.plot()
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print(m)
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######################################
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## 2 dimensional example
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@ -37,8 +40,11 @@ print(m)
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X = np.random.uniform(-3.,3.,(40,2))
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Y = np.sin(X[:,0:1]) * np.sin(X[:,1:2])+np.random.randn(40,1)*0.05
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# define kernel
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ker = GPy.kern.rbf(2,ARD=True) + GPy.kern.white(2)
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# create simple GP model
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m = GPy.models.GP_regression(X,Y)
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m = GPy.models.GP_regression(X,Y,ker)
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# contrain all parameters to be positive
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m.constrain_positive('')
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@ -10,11 +10,11 @@ print "sparse GPLVM with RBF kernel"
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N = 100
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M = 4
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Q = 1
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Q = 2
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D = 2
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#generate GPLVM-like data
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X = np.random.rand(N, Q)
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k = GPy.kern.rbf(Q, 1.0, 2.0) + GPy.kern.white(Q, 0.00001)
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k = GPy.kern.rbf(Q,1.,2*np.ones((1,))) + GPy.kern.white(Q, 0.00001)
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K = k.K(X)
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Y = np.random.multivariate_normal(np.zeros(N),K,D).T
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@ -22,7 +22,7 @@ from Brownian import Brownian as Brownianpart
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#using meta-classes to make the objects construct properly wthout them.
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def rbf(D,variance=1., lengthscale=1.):
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def rbf(D,variance=1., lengthscale=None,ARD=False):
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"""
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Construct an RBF kernel
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@ -33,7 +33,7 @@ def rbf(D,variance=1., lengthscale=1.):
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:param lengthscale: the lengthscale of the kernel
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:type lengthscale: float
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"""
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part = rbfpart(D,variance,lengthscale)
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part = rbfpart(D,variance,lengthscale,ARD)
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return kern(D, [part])
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def rbf_ARD(D,variance=1., lengthscales=None):
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@ -20,16 +20,32 @@ class rbf(kernpart):
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:type D: int
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:param variance: the variance of the kernel
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:type variance: float
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:param lengthscale: the lengthscale of the kernel
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:type lengthscale: float
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:param lengthscale: the vector of lengthscale of the kernel
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:type lengthscale: np.ndarray
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:param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one single lengthscale parameter \ell), otherwise there is one lengthscale parameter per dimension.
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:type ARD: Boolean
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.. Note: for rbf with different lengthscale on each dimension, see rbf_ARD
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"""
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def __init__(self,D,variance=1.,lengthscale=1.):
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def __init__(self,D,variance=1.,lengthscale=None,ARD=False):
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self.D = D
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self.ARD = ARD
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if ARD == False:
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self.Nparam = 2
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self.name = 'rbf'
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if lengthscale is not None:
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assert lengthscale.shape == (1,)
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else:
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lengthscale = np.ones(1)
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else:
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self.Nparam = self.D + 1
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self.name = 'rbf_ARD'
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if lengthscale is not None:
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assert lengthscale.shape == (self.D,)
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else:
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lengthscale = np.ones(self.D)
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self.set_param(np.hstack((variance,lengthscale)))
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#initialize cache
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@ -40,14 +56,19 @@ class rbf(kernpart):
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return np.hstack((self.variance,self.lengthscale))
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def set_param(self,x):
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self.variance, self.lengthscale = x
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assert x.size==(self.Nparam)
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self.variance = x[0]
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self.lengthscale = x[1:]
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self.lengthscale2 = np.square(self.lengthscale)
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#reset cached results
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self._X, self._X2, self._params = np.empty(shape=(3,1))
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self._Z, self._mu, self._S = np.empty(shape=(3,1)) # cached versions of Z,mu,S
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def get_param_names(self):
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if self.Nparam == 2:
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return ['variance','lengthscale']
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else:
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return ['variance']+['lengthscale_%i'%i for i in range(self.lengthscale.size)]
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def K(self,X,X2,target):
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if X2 is None:
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@ -61,7 +82,12 @@ class rbf(kernpart):
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def dK_dtheta(self,partial,X,X2,target):
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self._K_computations(X,X2)
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target[0] += np.sum(self._K_dvar*partial)
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target[1] += np.sum(self._K_dvar*self.variance*self._K_dist2/self.lengthscale*partial)
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if self.ARD == True:
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dl = self._K_dvar[:,:,None]*self.variance*self._K_dist2/self.lengthscale
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target[1:] += (dl*partial[:,:,None]).sum(0).sum(0)
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else:
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target[1] += np.sum(self._K_dvar*self.variance*(self._K_dist2.sum(-1))/self.lengthscale*partial)
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#np.sum(self._K_dvar*self.variance*self._K_dist2/self.lengthscale*partial)
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def dKdiag_dtheta(self,partial,X,target):
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#NB: derivative of diagonal elements wrt lengthscale is 0
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@ -81,15 +107,13 @@ class rbf(kernpart):
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self._X = X
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self._X2 = X2
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if X2 is None: X2 = X
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XXT = np.dot(X,X2.T)
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if X is X2:
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self._K_dist2 = (-2.*XXT + np.diag(XXT)[:,np.newaxis] + np.diag(XXT)[np.newaxis,:])/self.lengthscale2
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else:
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self._K_dist2 = (-2.*XXT + np.sum(np.square(X),1)[:,None] + np.sum(np.square(X2),1)[None,:])/self.lengthscale2
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# TODO Remove comments if this is fine.
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# Commented out by Neil as doesn't seem to be used elsewhere.
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#self._K_exponent = -0.5*self._K_dist2
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self._K_dvar = np.exp(-0.5*self._K_dist2)
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self._K_dist = X[:,None,:]-X2[None,:,:] # this can be computationally heavy
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self._params = np.empty(shape=(1,0))#ensure the next section gets called
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if not np.all(self._params == self.get_param()):
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self._params == self.get_param()
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self._K_dist2 = np.square(self._K_dist/self.lengthscale)
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#self._K_exponent = -0.5*self._K_dist2.sum(-1) #ND: commented out because seems not to be used
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self._K_dvar = np.exp(-0.5*self._K_dist2.sum(-1))
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def psi0(self,Z,mu,S,target):
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target += self.variance
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@ -132,7 +156,7 @@ class rbf(kernpart):
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d_length = self._psi2[:,:,:,None]*(0.5*self._psi2_Zdist_sq*self._psi2_denom + 2.*self._psi2_mudist_sq + 2.*S[:,None,None,:]/self.lengthscale2)/(self.lengthscale*self._psi2_denom)
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d_length = d_length.sum(0)
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target[0] += np.sum(partial*d_var)
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target[1] += np.sum(d_length*partial)
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target[1:] += (d_length*partial[:,:,None]).sum(0).sum(0)
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def dpsi2_dZ(self,partial,Z,mu,S,target):
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"""Returns shape N,M,M,Q"""
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@ -175,4 +199,3 @@ class rbf(kernpart):
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self._psi2 = np.square(self.variance)*np.exp(self._psi2_exponent) # N,M,M
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self._Z, self._mu, self._S = Z, mu,S
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