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add truncated linear kernel
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Zhenwen Dai
parent
c2a1ea9cbd
commit
0b75aa8b0f
4 changed files with 219 additions and 5 deletions
208
GPy/kern/_src/trunclinear.py
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208
GPy/kern/_src/trunclinear.py
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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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import numpy as np
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from scipy import weave
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from kern import Kern
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from ...util.linalg import tdot
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from ...util.misc import param_to_array
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from ...core.parameterization import Param
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from ...core.parameterization.transformations import Logexp
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from ...util.caching import Cache_this
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from ...core.parameterization import variational
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from ...util.config import *
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class TruncLinear(Kern):
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"""
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Truncated Linear kernel
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.. math::
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k(x,y) = \sum_{i=1}^input_dim \sigma^2_i \max(0, x_iy_i - \simga_q)
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:param input_dim: the number of input dimensions
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:type input_dim: int
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:param variances: the vector of variances :math:`\sigma^2_i`
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:type variances: array or list of the appropriate size (or float if there
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is only one variance parameter)
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:param ARD: Auto Relevance Determination. If False, the kernel has only one
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variance parameter \sigma^2, otherwise there is one variance
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parameter per dimension.
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:type ARD: Boolean
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:rtype: kernel object
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"""
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def __init__(self, input_dim, variances=None, delta=None, ARD=False, active_dims=None, name='linear'):
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super(TruncLinear, self).__init__(input_dim, active_dims, name)
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self.ARD = ARD
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if not ARD:
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if variances is not None:
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variances = np.asarray(variances)
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delta = np.asarray(delta)
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assert variances.size == 1, "Only one variance needed for non-ARD kernel"
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else:
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variances = np.ones(1)
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delta = np.zeros(1)
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else:
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if variances is not None:
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variances = np.asarray(variances)
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delta = np.asarray(delta)
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assert variances.size == self.input_dim, "bad number of variances, need one ARD variance per input_dim"
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else:
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variances = np.ones(self.input_dim)
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delta = np.zeros(self.input_dim)
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self.variances = Param('variances', variances, Logexp())
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self.delta = Param('delta', delta)
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self.add_parameter(self.variances)
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self.add_parameter(self.delta)
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@Cache_this(limit=2)
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def K(self, X, X2=None):
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XX = self.variances*self._product(X, X2)
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return XX.sum(axis=-1)
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@Cache_this(limit=2)
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def _product(self, X, X2=None):
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if X2 is None:
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X2 = X
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XX = np.einsum('nq,mq->nmq',X-self.delta,X2-self.delta)
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XX[XX<0] = 0
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return XX
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def Kdiag(self, X):
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return self.variances*(np.square(X-self.delta)).sum(axis=-1)
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def update_gradients_full(self, dL_dK, X, X2=None):
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dK_dvar = self._product(X, X2)
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if X2 is None:
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X2=X
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dK_ddelta = self.variances*(2*self.delta-X[:,None,:]-X2[None,:,:])*(dK_dvar>0)
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if self.ARD:
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self.variances.gradient[:] = np.einsum('nmq,nm->q',dK_dvar,dL_dK)
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self.delta.gradient[:] = np.einsum('nmq,nm->q',dK_ddelta,dL_dK)
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else:
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self.variances.gradient[:] = np.einsum('nmq,nm->',dK_dvar,dL_dK)
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self.delta.gradient[:] = np.einsum('nmq,nm->',dK_ddelta,dL_dK)
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def update_gradients_diag(self, dL_dKdiag, X):
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if self.ARD:
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self.variances.gradient[:] = np.einsum('nq,n->q',np.square(X-self.delta),dL_dKdiag)
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self.delta.gradient[:] = np.einsum('nq,n->q',2*self.variances*(self.delta-X),dL_dKdiag)
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else:
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self.variances.gradient[:] = np.einsum('nq,n->',np.square(X-self.delta),dL_dKdiag)
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self.delta.gradient[:] = np.einsum('nq,n->',2*self.variances*(self.delta-X),dL_dKdiag)
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def gradients_X(self, dL_dK, X, X2=None):
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XX = self._product(X, X2)
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if X2 is None:
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Xp = (self.variances*(X-self.delta))*(XX>0)
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else:
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Xp = (self.variances*(X2-self.delta))*(XX>0)
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if X2 is None:
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return np.einsum('nmq,nm->nq',Xp,dL_dK)+np.einsum('mnq,nm->mq',Xp,dL_dK)
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else:
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return np.einsum('nmq,nm->nq',Xp,dL_dK)
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def gradients_X_diag(self, dL_dKdiag, X):
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return 2.*self.variances*dL_dKdiag[:,None]*(X-self.delta)
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def input_sensitivity(self):
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return np.ones(self.input_dim) * self.variances
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class TruncLinear_inf(Kern):
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"""
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Truncated Linear kernel
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.. math::
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k(x,y) = \sum_{i=1}^input_dim \sigma^2_i \max(0, x_iy_i - \simga_q)
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:param input_dim: the number of input dimensions
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:type input_dim: int
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:param variances: the vector of variances :math:`\sigma^2_i`
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:type variances: array or list of the appropriate size (or float if there
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is only one variance parameter)
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:param ARD: Auto Relevance Determination. If False, the kernel has only one
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variance parameter \sigma^2, otherwise there is one variance
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parameter per dimension.
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:type ARD: Boolean
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:rtype: kernel object
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"""
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def __init__(self, input_dim, interval, variances=None, ARD=False, active_dims=None, name='linear'):
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super(TruncLinear_inf, self).__init__(input_dim, active_dims, name)
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self.interval = interval
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self.ARD = ARD
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if not ARD:
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if variances is not None:
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variances = np.asarray(variances)
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assert variances.size == 1, "Only one variance needed for non-ARD kernel"
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else:
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variances = np.ones(1)
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else:
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if variances is not None:
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variances = np.asarray(variances)
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assert variances.size == self.input_dim, "bad number of variances, need one ARD variance per input_dim"
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else:
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variances = np.ones(self.input_dim)
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self.variances = Param('variances', variances, Logexp())
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self.add_parameter(self.variances)
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# @Cache_this(limit=2)
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def K(self, X, X2=None):
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tmp = self._product(X, X2)
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return (self.variances*tmp).sum(axis=-1)
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# @Cache_this(limit=2)
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def _product(self, X, X2=None):
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if X2 is None:
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X2 = X
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X_X2 = X[:,None,:]-X2[None,:,:]
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tmp = np.abs(X_X2**3)/6+np.einsum('nq,mq->nmq',X,X2)*(self.interval[1]-self.interval[0]) \
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-(X[:,None,:]+X2[None,:,:])*(self.interval[1]*self.interval[1]-self.interval[0]*self.interval[0])/2+(self.interval[1]**3-self.interval[0]**3)/3.
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return tmp
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def Kdiag(self, X):
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tmp = np.square(X)*(self.interval[1]-self.interval[0]) \
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-X*(self.interval[1]*self.interval[1]-self.interval[0]*self.interval[0])+(self.interval[1]**3-self.interval[0]**3)/3
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return (self.variances*tmp).sum(axis=-1)
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def update_gradients_full(self, dL_dK, X, X2=None):
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dK_dvar = self._product(X, X2)
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if self.ARD:
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self.variances.gradient[:] = np.einsum('nmq,nm->q',dK_dvar,dL_dK)
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else:
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self.variances.gradient[:] = np.einsum('nmq,nm->',dK_dvar,dL_dK)
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def update_gradients_diag(self, dL_dKdiag, X):
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tmp = np.square(X)*(self.interval[1]-self.interval[0]) \
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-X*(self.interval[1]*self.interval[1]-self.interval[0]*self.interval[0])+(self.interval[1]**3-self.interval[0]**3)/3
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if self.ARD:
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self.variances.gradient[:] = np.einsum('nq,n->q',tmp,dL_dKdiag)
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else:
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self.variances.gradient[:] = np.einsum('nq,n->',tmp,dL_dKdiag)
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def gradients_X(self, dL_dK, X, X2=None):
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XX = self._product(X, X2)
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if X2 is None:
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Xp = (self.variances*(X-self.delta))*(XX>0)
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else:
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Xp = (self.variances*(X2-self.delta))*(XX>0)
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if X2 is None:
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return np.einsum('nmq,nm->nq',Xp,dL_dK)+np.einsum('mnq,nm->mq',Xp,dL_dK)
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else:
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return np.einsum('nmq,nm->nq',Xp,dL_dK)
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def gradients_X_diag(self, dL_dKdiag, X):
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return 2.*self.variances*dL_dKdiag[:,None]*(X-self.delta)
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def input_sensitivity(self):
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return np.ones(self.input_dim) * self.variances
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