rbf and white seem to work

GPy/kern/_src/mlp.py

@@ -0,0 +1,162 @@
+# Copyright (c) 2013, GPy authors (see AUTHORS.txt).
+# Licensed under the BSD 3-clause license (see LICENSE.txt)
+
+from kernpart import Kernpart
+import numpy as np
+four_over_tau = 2./np.pi
+
+class MLP(Kernpart):
+    """
+
+    Multi layer perceptron kernel (also known as arc sine kernel or neural network kernel)
+
+    .. math::
+
+          k(x,y) = \\sigma^{2}\\frac{2}{\\pi }  \\text{asin} \\left ( \\frac{ \\sigma_w^2 x^\\top y+\\sigma_b^2}{\\sqrt{\\sigma_w^2x^\\top x + \\sigma_b^2 + 1}\\sqrt{\\sigma_w^2 y^\\top y \\sigma_b^2 +1}} \\right )
+          
+
+    :param input_dim: the number of input dimensions
+    :type input_dim: int 
+    :param variance: the variance :math:`\sigma^2`
+    :type variance: float
+    :param weight_variance: the vector of the variances of the prior over input weights in the neural network :math:`\sigma^2_w`
+    :type weight_variance: array or list of the appropriate size (or float if there is only one weight variance parameter)
+    :param bias_variance: the variance of the prior over bias parameters :math:`\sigma^2_b`
+    :param ARD: Auto Relevance Determination. If equal to "False", the kernel is isotropic (ie. one weight variance parameter \sigma^2_w), otherwise there is one weight variance parameter per dimension.
+    :type ARD: Boolean
+    :rtype: Kernpart object
+
+
+    """
+
+    def __init__(self, input_dim, variance=1., weight_variance=None, bias_variance=100., ARD=False):
+        self.input_dim = input_dim
+        self.ARD = ARD
+        if not ARD:
+            self.num_params=3
+            if weight_variance is not None:
+                weight_variance = np.asarray(weight_variance)
+                assert weight_variance.size == 1, "Only one weight variance needed for non-ARD kernel"
+            else:
+                weight_variance = 100.*np.ones(1)
+        else:
+            self.num_params = self.input_dim + 2
+            if weight_variance is not None:
+                weight_variance = np.asarray(weight_variance)
+                assert weight_variance.size == self.input_dim, "bad number of weight variances"
+            else:
+                weight_variance = np.ones(self.input_dim)
+            raise NotImplementedError
+
+        self.name='mlp'
+        self._set_params(np.hstack((variance, weight_variance.flatten(), bias_variance)))
+
+    def _get_params(self):
+        return np.hstack((self.variance, self.weight_variance.flatten(), self.bias_variance))
+
+    def _set_params(self, x):
+        assert x.size == (self.num_params)
+        self.variance = x[0]
+        self.weight_variance = x[1:-1]
+        self.weight_std = np.sqrt(self.weight_variance)
+        self.bias_variance = x[-1]
+
+    def _get_param_names(self):
+        if self.num_params == 3:
+            return ['variance', 'weight_variance', 'bias_variance']
+        else:
+            return ['variance'] + ['weight_variance_%i' % i for i in range(self.lengthscale.size)] + ['bias_variance']
+
+    def K(self, X, X2, target):
+        """Return covariance between X and X2."""
+        self._K_computations(X, X2)
+        target += self.variance*self._K_dvar
+
+    def Kdiag(self, X, target):
+        """Compute the diagonal of the covariance matrix for X."""
+        self._K_diag_computations(X)
+        target+= self.variance*self._K_diag_dvar
+
+    def _param_grad_helper(self, dL_dK, X, X2, target):
+        """Derivative of the covariance with respect to the parameters."""
+        self._K_computations(X, X2)
+        denom3 = self._K_denom*self._K_denom*self._K_denom
+        base = four_over_tau*self.variance/np.sqrt(1-self._K_asin_arg*self._K_asin_arg)
+        base_cov_grad = base*dL_dK
+
+        if X2 is None:
+            vec = np.diag(self._K_inner_prod)
+            target[1] += ((self._K_inner_prod/self._K_denom 
+                           -.5*self._K_numer/denom3
+                           *(np.outer((self.weight_variance*vec+self.bias_variance+1.), vec) 
+                             +np.outer(vec,(self.weight_variance*vec+self.bias_variance+1.))))*base_cov_grad).sum()
+            target[2] += ((1./self._K_denom 
+                           -.5*self._K_numer/denom3 
+                           *((vec[None, :]+vec[:, None])*self.weight_variance
+                           +2.*self.bias_variance + 2.))*base_cov_grad).sum()
+        else:
+            vec1 = (X*X).sum(1)
+            vec2 = (X2*X2).sum(1)
+            target[1] += ((self._K_inner_prod/self._K_denom 
+                           -.5*self._K_numer/denom3
+                           *(np.outer((self.weight_variance*vec1+self.bias_variance+1.), vec2) + np.outer(vec1, self.weight_variance*vec2 + self.bias_variance+1.)))*base_cov_grad).sum()
+            target[2] += ((1./self._K_denom 
+                           -.5*self._K_numer/denom3 
+                           *((vec1[:, None]+vec2[None, :])*self.weight_variance
+                             + 2*self.bias_variance + 2.))*base_cov_grad).sum()
+            
+        target[0] += np.sum(self._K_dvar*dL_dK)
+
+    def gradients_X(self, dL_dK, X, X2, target):
+        """Derivative of the covariance matrix with respect to X"""
+        self._K_computations(X, X2)
+        arg = self._K_asin_arg
+        numer = self._K_numer
+        denom = self._K_denom
+        denom3 = denom*denom*denom
+        if X2 is not None:
+            vec2 = (X2*X2).sum(1)*self.weight_variance+self.bias_variance + 1.
+            target += four_over_tau*self.weight_variance*self.variance*((X2[None, :, :]/denom[:, :, None] - vec2[None, :, None]*X[:, None, :]*(numer/denom3)[:, :, None])*(dL_dK/np.sqrt(1-arg*arg))[:, :, None]).sum(1)
+        else:
+            vec = (X*X).sum(1)*self.weight_variance+self.bias_variance + 1.
+            target += 2*four_over_tau*self.weight_variance*self.variance*((X[None, :, :]/denom[:, :, None] - vec[None, :, None]*X[:, None, :]*(numer/denom3)[:, :, None])*(dL_dK/np.sqrt(1-arg*arg))[:, :, None]).sum(1)
+            
+    def dKdiag_dX(self, dL_dKdiag, X, target):
+        """Gradient of diagonal of covariance with respect to X"""
+        self._K_diag_computations(X)
+        arg = self._K_diag_asin_arg
+        denom = self._K_diag_denom
+        numer = self._K_diag_numer
+        target += four_over_tau*2.*self.weight_variance*self.variance*X*(1/denom*(1 - arg)*dL_dKdiag/(np.sqrt(1-arg*arg)))[:, None] 
+
+    
+    def _K_computations(self, X, X2):
+        """Pre-computations for the covariance matrix (used for computing the covariance and its gradients."""
+        if self.ARD:
+            pass
+        else:
+            if X2 is None:
+                self._K_inner_prod = np.dot(X,X.T)
+                self._K_numer = self._K_inner_prod*self.weight_variance+self.bias_variance
+                vec = np.diag(self._K_numer) + 1.
+                self._K_denom = np.sqrt(np.outer(vec,vec))
+                self._K_asin_arg = self._K_numer/self._K_denom
+                self._K_dvar = four_over_tau*np.arcsin(self._K_asin_arg)
+            else:
+                self._K_inner_prod = np.dot(X,X2.T)
+                self._K_numer = self._K_inner_prod*self.weight_variance + self.bias_variance
+                vec1 = (X*X).sum(1)*self.weight_variance + self.bias_variance + 1.
+                vec2 = (X2*X2).sum(1)*self.weight_variance + self.bias_variance + 1.
+                self._K_denom = np.sqrt(np.outer(vec1,vec2))
+                self._K_asin_arg = self._K_numer/self._K_denom
+                self._K_dvar = four_over_tau*np.arcsin(self._K_asin_arg)
+
+    def _K_diag_computations(self, X):
+        """Pre-computations concerning the diagonal terms (used for computation of diagonal and its gradients)."""
+        if self.ARD:
+            pass
+        else:
+            self._K_diag_numer = (X*X).sum(1)*self.weight_variance + self.bias_variance
+            self._K_diag_denom = self._K_diag_numer+1.
+            self._K_diag_asin_arg = self._K_diag_numer/self._K_diag_denom
+            self._K_diag_dvar = four_over_tau*np.arcsin(self._K_diag_asin_arg)