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new implementation for mlp kernel (speed improvemd)
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Zhenwen Dai
parent
368f975aa9
commit
e906da0309
1 changed files with 59 additions and 77 deletions
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@ -5,6 +5,7 @@ from .kern import Kern
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from ...core.parameterization import Param
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from ...core.parameterization.transformations import Logexp
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import numpy as np
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from ...util.caching import Cache_this
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four_over_tau = 2./np.pi
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class MLP(Kern):
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@ -31,7 +32,7 @@ class MLP(Kern):
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"""
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def __init__(self, input_dim, variance=1., weight_variance=1., bias_variance=100., active_dims=None, name='mlp'):
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def __init__(self, input_dim, variance=1., weight_variance=1., bias_variance=1., active_dims=None, name='mlp'):
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super(MLP, self).__init__(input_dim, active_dims, name)
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self.variance = Param('variance', variance, Logexp())
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self.weight_variance = Param('weight_variance', weight_variance, Logexp())
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@ -40,96 +41,77 @@ class MLP(Kern):
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def K(self, X, X2=None):
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self._K_computations(X, X2)
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return self.variance*self._K_dvar
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if X2 is None:
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X_denom = np.sqrt(self._comp_prod(X)+1.)
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X2_denom = X_denom
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X2 = X
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else:
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X_denom = np.sqrt(self._comp_prod(X)+1.)
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X2_denom = np.sqrt(self._comp_prod(X2)+1.)
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XTX = self._comp_prod(X,X2)/X_denom[:,None]/X2_denom[None,:]
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return self.variance*four_over_tau*np.arcsin(XTX)
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def Kdiag(self, X):
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"""Compute the diagonal of the covariance matrix for X."""
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self._K_diag_computations(X)
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return self.variance*self._K_diag_dvar
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X_prod = self._comp_prod(X)
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return self.variance*four_over_tau*np.arcsin(X_prod/(X_prod+1.))
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def update_gradients_full(self, dL_dK, X, X2=None):
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"""Derivative of the covariance with respect to the parameters."""
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self._K_computations(X, X2)
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self.variance.gradient = np.sum(self._K_dvar*dL_dK)
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denom3 = self._K_denom**3
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base = four_over_tau*self.variance/np.sqrt(1-self._K_asin_arg*self._K_asin_arg)
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base_cov_grad = base*dL_dK
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if X2 is None:
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vec = np.diag(self._K_inner_prod)
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self.weight_variance.gradient = ((self._K_inner_prod/self._K_denom
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-.5*self._K_numer/denom3
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*(np.outer((self.weight_variance*vec+self.bias_variance+1.), vec)
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+np.outer(vec,(self.weight_variance*vec+self.bias_variance+1.))))*base_cov_grad).sum()
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self.bias_variance.gradient = ((1./self._K_denom
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-.5*self._K_numer/denom3
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*((vec[None, :]+vec[:, None])*self.weight_variance
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+2.*self.bias_variance + 2.))*base_cov_grad).sum()
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else:
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vec1 = (X*X).sum(1)
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vec2 = (X2*X2).sum(1)
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self.weight_variance.gradient = ((self._K_inner_prod/self._K_denom
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-.5*self._K_numer/denom3
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*(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()
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self.bias_variance.gradient = ((1./self._K_denom
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-.5*self._K_numer/denom3
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*((vec1[:, None]+vec2[None, :])*self.weight_variance
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+ 2*self.bias_variance + 2.))*base_cov_grad).sum()
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dvar, dw, db = self._comp_grads(dL_dK, X, X2)[:3]
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self.variance.gradient = dvar
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self.weight_variance.gradient = dw
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self.bias_variance.gradient = db
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def update_gradients_diag(self, dL_dKdiag, X):
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self._K_diag_computations(X)
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self.variance.gradient = np.sum(self._K_diag_dvar*dL_dKdiag)
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dvar, dw, db = self._comp_grads_diag(dL_dKdiag, X)[:3]
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self.variance.gradient = dvar
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self.weight_variance.gradient = dw
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self.bias_variance.gradient = db
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base = four_over_tau*self.variance/np.sqrt(1-self._K_diag_asin_arg*self._K_diag_asin_arg)
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base_cov_grad = base*dL_dKdiag/np.square(self._K_diag_denom)
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self.weight_variance.gradient = (base_cov_grad*np.square(X).sum(axis=1)).sum()
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self.bias_variance.gradient = base_cov_grad.sum()
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def gradients_X(self, dL_dK, X, X2):
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"""Derivative of the covariance matrix with respect to X"""
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self._K_computations(X, X2)
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arg = self._K_asin_arg
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numer = self._K_numer
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denom = self._K_denom
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denom3 = denom*denom*denom
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if X2 is not None:
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vec2 = (X2*X2).sum(1)*self.weight_variance+self.bias_variance + 1.
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return 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)
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else:
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vec = (X*X).sum(1)*self.weight_variance+self.bias_variance + 1.
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return 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)
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return self._comp_grads(dL_dK, X, X2)[3]
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def gradients_X_diag(self, dL_dKdiag, X):
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"""Gradient of diagonal of covariance with respect to X"""
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self._K_diag_computations(X)
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arg = self._K_diag_asin_arg
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denom = self._K_diag_denom
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#numer = self._K_diag_numer
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return four_over_tau*2.*self.weight_variance*self.variance*X*(1./denom*(1. - arg)*dL_dKdiag/(np.sqrt(1-arg*arg)))[:, None]
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return self._comp_grads_diag(dL_dKdiag, X)[3]
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def _K_computations(self, X, X2):
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"""Pre-computations for the covariance matrix (used for computing the covariance and its gradients."""
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@Cache_this(limit=50, ignore_args=())
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def _comp_prod(self, X, X2=None):
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if X2 is None:
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self._K_inner_prod = np.dot(X,X.T)
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self._K_numer = self._K_inner_prod*self.weight_variance + self.bias_variance
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vec = np.diag(self._K_numer) + 1.
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self._K_denom = np.sqrt(np.outer(vec,vec))
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return (np.square(X)*self.weight_variance).sum(axis=1)+self.bias_variance
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else:
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self._K_inner_prod = np.dot(X,X2.T)
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self._K_numer = self._K_inner_prod*self.weight_variance + self.bias_variance
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vec1 = (X*X).sum(1)*self.weight_variance + self.bias_variance + 1.
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vec2 = (X2*X2).sum(1)*self.weight_variance + self.bias_variance + 1.
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self._K_denom = np.sqrt(np.outer(vec1,vec2))
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self._K_asin_arg = self._K_numer/self._K_denom
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self._K_dvar = four_over_tau*np.arcsin(self._K_asin_arg)
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def _K_diag_computations(self, X):
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"""Pre-computations concerning the diagonal terms (used for computation of diagonal and its gradients)."""
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self._K_diag_numer = (X*X).sum(1)*self.weight_variance + self.bias_variance
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self._K_diag_denom = self._K_diag_numer+1.
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self._K_diag_asin_arg = self._K_diag_numer/self._K_diag_denom
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self._K_diag_dvar = four_over_tau*np.arcsin(self._K_diag_asin_arg)
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return (X*self.weight_variance).dot(X2.T)+self.bias_variance
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@Cache_this(limit=20, ignore_args=(1,))
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def _comp_grads(self, dL_dK, X, X2=None):
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var,w,b = self.variance, self.weight_variance, self.bias_variance
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K = self.K(X, X2)
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dvar = (dL_dK*K).sum()/var
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X_prod = self._comp_prod(X)
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X2_prod = self._comp_prod(X2) if X2 is not None else X_prod
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XTX = self._comp_prod(X,X2) if X2 is not None else self._comp_prod(X, X)
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common = var*four_over_tau/np.sqrt((X_prod[:,None]+1.)*(X2_prod[None,:]+1.)-np.square(XTX))*dL_dK
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dw = (common*((XTX-b)/w-XTX*(((X_prod-b)/(w*(X_prod+1.)))[:,None]+((X2_prod-b)/(w*(X2_prod+1.)))[None,:])/2.)).sum()
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db = (common*(1.-XTX*(1./(X_prod[:,None]+1.)+1./(X2_prod[None,:]+1.))/2.)).sum()
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if X2 is None:
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common = common+common.T
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dX = common.dot(X)*w-((common*XTX).sum(axis=1)/(X_prod+1.))[:,None]*X*w
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dX2 = dX
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else:
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dX = common.dot(X2)*w-((common*XTX).sum(axis=1)/(X_prod+1.))[:,None]*X*w
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dX2 = common.T.dot(X)*w-((common*XTX).sum(axis=0)/(X2_prod+1.))[:,None]*X2*w
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return dvar, dw, db, dX, dX2
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@Cache_this(limit=20, ignore_args=(1,))
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def _comp_grads_diag(self, dL_dKdiag, X):
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var,w,b = self.variance, self.weight_variance, self.bias_variance
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K = self.Kdiag(X)
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dvar = (dL_dKdiag*K).sum()/var
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X_prod = self._comp_prod(X)
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common = var*four_over_tau/(np.sqrt(1-np.square(X_prod/(X_prod+1)))*np.square(X_prod+1))*dL_dKdiag
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dw = (common*(X_prod-b)).sum()/w
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db = common.sum()
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dX = common[:,None]*X*w*2
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return dvar, dw, db, dX
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