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Implemented MLP gradients with respect to X.

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This commit is contained in:
Neil Lawrence 2013-08-28 01:19:43 +02:00
parent b127c96bf2
commit 84b7156d23
4 changed files with 32 additions and 46 deletions
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46
GPy/kern/parts/mlp.py
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@ -27,7 +27,6 @@ class MLP(Kernpart):
"""
def __init__(self, input_dim, variance=1., weight_variance=None, bias_variance=100., ARD=False):
ARD = False
self.input_dim = input_dim
self.ARD = ARD
if not ARD:
@ -44,6 +43,7 @@ class MLP(Kernpart):
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)))
@ -104,47 +104,27 @@ class MLP(Kernpart):
target[0] += np.sum(self._K_dvar*dL_dK)
def dK_dX(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
post_div = np.sqrt(1-arg*arg)
numer = self._K_numer
denom = self._K_denom
vec2 = (X2*X2).sum(1)*self.weight_variance + self.bias_variance + 1.
denom3 = denom*denom*denom
target += (((X2[None,:, :]/denom[None, :, None]+vec2[None, None, :]*X[:, :, None]*numer/denom)/post_div[:, :, None]) * dL_dK[:, :, None]).sum(1)
target *= four_over_tau*self.weight_variance*self.variance
raise NotImplementedError
gX = np.zeros((X2.shape[0], X.shape[1], X.shape[0]))
for i in range(X.shape[0]):
gX[:, :, i] = self._dK_dX_point(dL_dK, X, X2, target, i)
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)
def _dK_dX_point(self, dL_dK, X, X2, target, i):
"""Gradient with respect to one point of X"""
inner_prod = self._K_inner_prod[i, :].T
numer = self._K_numer[i, :].T
denom = self._K_denom[i, :].T
arg = self._K_asin_arg[i, :].T
vec1 = (X[i, :]*X[i, :]).sum()*self.weight_variance + self.bias_variance + 1.
vec2 = (X2*X2).sum(1)*self.weight_variance + self.bias_variance + 1.
#denom = np.sqrt(np.outer(vec2,vec1))
#arg = numer/denom
gX = np.zeros(X2.shape)
denom3 = denom*denom*denom
gX = np.zeros((X2.shape[0], X2.shape[1]))
for j in range(X2.shape[1]):
gX[:, j] = X2[:, j]/denom - vec2*X[i, j]*numer/denom3
gX[:, j] = four_over_tau*self.weight_variance*self.variance*gX[:, j]/np.sqrt(1-arg*arg)
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:
@ -165,9 +145,11 @@ class MLP(Kernpart):
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_dvar = four_over_tau*np.arcsin(self._K_diag_numer/self._K_diag_denom)
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)

2
GPy/kern/parts/poly.py
View file

@ -39,7 +39,6 @@ class POLY(Kernpart):
"""
def __init__(self, input_dim, variance=1., weight_variance=None, bias_variance=1., degree=2, ARD=False):
ARD = False
self.input_dim = input_dim
self.ARD = ARD
if not ARD:
@ -56,6 +55,7 @@ class POLY(Kernpart):
assert weight_variance.size == self.input_dim, "bad number of weight variances"
else:
weight_variance = np.ones(self.input_dim)
raise NotImplementedError
self.degree=degree
self.name='poly_deg' + str(self.degree)
self._set_params(np.hstack((variance, weight_variance.flatten(), bias_variance)))