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60 lines
2.2 KiB
Python
60 lines
2.2 KiB
Python
# Copyright (c) 2013, 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 ..core.mapping import Mapping
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import GPy
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class Kernel(Mapping):
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"""
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Mapping based on a kernel/covariance function.
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.. math::
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f(\mathbf{x}*) = \mathbf{A}\mathbf{k}(\mathbf{X}, \mathbf{x}^*) + \mathbf{b}
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:param X: input observations containing :math:`\mathbf{X}`
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:type X: ndarray
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:param output_dim: dimension of output.
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:type output_dim: int
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:param kernel: a GPy kernel, defaults to GPy.kern.rbf
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:type kernel: GPy.kern.kern
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"""
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def __init__(self, X, output_dim=1, kernel=None):
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Mapping.__init__(self, input_dim=X.shape[1], output_dim=output_dim)
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if kernel is None:
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kernel = GPy.kern.rbf(self.input_dim)
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self.kern = kernel
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self.X = X
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self.num_data = X.shape[0]
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self.num_params = self.output_dim*(self.num_data + 1)
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self.A = np.array((self.num_data, self.output_dim))
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self.bias = np.array(self.output_dim)
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self.randomize()
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self.name = 'kernel'
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def _get_param_names(self):
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return sum([['A_%i_%i' % (n, d) for d in range(self.output_dim)] for n in range(self.num_data)], []) + ['bias_%i' % d for d in range(self.output_dim)]
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def _get_params(self):
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return np.hstack((self.A.flatten(), self.bias))
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def _set_params(self, x):
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self.A = x[:self.num_data * self.output_dim].reshape(self.num_data, self.output_dim).copy()
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self.bias = x[self.num_data*self.output_dim:].copy()
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def randomize(self):
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self.A = np.random.randn(self.num_data, self.output_dim)/np.sqrt(self.num_data+1)
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self.bias = np.random.randn(self.output_dim)/np.sqrt(self.num_data+1)
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def f(self, X):
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return np.dot(self.kern.K(X, self.X),self.A) + self.bias
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def df_dtheta(self, dL_df, X):
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self._df_dA = (dL_df[:, :, None]*self.kern.K(X, self.X)[:, None, :]).sum(0).T
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self._df_dbias = (dL_df.sum(0))
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return np.hstack((self._df_dA.flatten(), self._df_dbias))
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def df_dX(self, dL_df, X):
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return self.kern.gradients_X((dL_df[:, None, :]*self.A[None, :, :]).sum(2), X, self.X)
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