mirror of
https://github.com/SheffieldML/GPy.git
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52ba8e4ba3
slices are now handles by special indexing kern parts, such as coregionalisation, independent_outputs. The old slicing functionality has been removed simply to clean up the code a little. Now that input_slices still exist (and will continue to be useful) in kern.py. They do need a little work though, for the psi-statistics
545 lines
25 KiB
Python
545 lines
25 KiB
Python
# 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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import pylab as pb
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from ..core.parameterised import parameterised
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from kernpart import kernpart
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import itertools
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from prod_orthogonal import prod_orthogonal
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from prod import prod
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class kern(parameterised):
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def __init__(self, D, parts=[], input_slices=None):
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"""
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This is the main kernel class for GPy. It handles multiple (additive) kernel functions, and keeps track of variaous things like which parameters live where.
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The technical code for kernels is divided into _parts_ (see e.g. rbf.py). This obnject contains a list of parts, which are computed additively. For multiplication, special _prod_ parts are used.
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:param D: The dimensioality of the kernel's input space
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:type D: int
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:param parts: the 'parts' (PD functions) of the kernel
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:type parts: list of kernpart objects
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:param input_slices: the slices on the inputs which apply to each kernel
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:type input_slices: list of slice objects, or list of bools
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"""
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self.parts = parts
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self.Nparts = len(parts)
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self.Nparam = sum([p.Nparam for p in self.parts])
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self.D = D
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# deal with input_slices
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if input_slices is None:
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self.input_slices = [slice(None) for p in self.parts]
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else:
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assert len(input_slices) == len(self.parts)
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self.input_slices = [sl if type(sl) is slice else slice(None) for sl in input_slices]
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for p in self.parts:
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assert isinstance(p, kernpart), "bad kernel part"
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self.compute_param_slices()
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parameterised.__init__(self)
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def plot_ARD(self, ax=None):
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"""
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If an ARD kernel is present, it bar-plots the ARD parameters
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"""
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if ax is None:
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ax = pb.gca()
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for p in self.parts:
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if hasattr(p, 'ARD') and p.ARD:
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ax.set_title('ARD parameters, %s kernel' % p.name)
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if p.name == 'linear':
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ard_params = p.variances
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else:
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ard_params = 1. / p.lengthscale
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ax.bar(np.arange(len(ard_params)) - 0.4, ard_params)
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ax.set_xticks(np.arange(len(ard_params)))
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ax.set_xticklabels([r"${}$".format(i + 1) for i in range(len(ard_params))])
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return ax
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def _transform_gradients(self, g):
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x = self._get_params()
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g[self.constrained_positive_indices] = g[self.constrained_positive_indices] * x[self.constrained_positive_indices]
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g[self.constrained_negative_indices] = g[self.constrained_negative_indices] * x[self.constrained_negative_indices]
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[np.put(g, i, g[i] * (x[i] - l) * (h - x[i]) / (h - l)) for i, l, h in zip(self.constrained_bounded_indices, self.constrained_bounded_lowers, self.constrained_bounded_uppers)]
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[np.put(g, i, v) for i, v in [(t[0], np.sum(g[t])) for t in self.tied_indices]]
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if len(self.tied_indices) or len(self.constrained_fixed_indices):
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to_remove = np.hstack((self.constrained_fixed_indices + [t[1:] for t in self.tied_indices]))
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return np.delete(g, to_remove)
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else:
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return g
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def compute_param_slices(self):
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"""create a set of slices that can index the parameters of each part"""
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self.param_slices = []
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count = 0
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for p in self.parts:
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self.param_slices.append(slice(count, count + p.Nparam))
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count += p.Nparam
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def __add__(self, other):
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assert self.D == other.D
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newkern = kern(self.D, self.parts + other.parts, self.input_slices + other.input_slices)
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# transfer constraints:
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newkern.constrained_positive_indices = np.hstack((self.constrained_positive_indices, self.Nparam + other.constrained_positive_indices))
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newkern.constrained_negative_indices = np.hstack((self.constrained_negative_indices, self.Nparam + other.constrained_negative_indices))
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newkern.constrained_bounded_indices = self.constrained_bounded_indices + [self.Nparam + x for x in other.constrained_bounded_indices]
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newkern.constrained_bounded_lowers = self.constrained_bounded_lowers + other.constrained_bounded_lowers
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newkern.constrained_bounded_uppers = self.constrained_bounded_uppers + other.constrained_bounded_uppers
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newkern.constrained_fixed_indices = self.constrained_fixed_indices + [self.Nparam + x for x in other.constrained_fixed_indices]
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newkern.constrained_fixed_values = self.constrained_fixed_values + other.constrained_fixed_values
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newkern.tied_indices = self.tied_indices + [self.Nparam + x for x in other.tied_indices]
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return newkern
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def add(self, other):
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"""
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Add another kernel to this one. Both kernels are defined on the same _space_
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:param other: the other kernel to be added
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:type other: GPy.kern
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"""
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return self + other
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def add_orthogonal(self, other):
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"""
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Add another kernel to this one. Both kernels are defined on separate spaces
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:param other: the other kernel to be added
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:type other: GPy.kern
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"""
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# deal with input slices
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D = self.D + other.D
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self_input_slices = [slice(*sl.indices(self.D)) for sl in self.input_slices]
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other_input_indices = [sl.indices(other.D) for sl in other.input_slices]
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other_input_slices = [slice(i[0] + self.D, i[1] + self.D, i[2]) for i in other_input_indices]
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newkern = kern(D, self.parts + other.parts, self_input_slices + other_input_slices)
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# transfer constraints:
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newkern.constrained_positive_indices = np.hstack((self.constrained_positive_indices, self.Nparam + other.constrained_positive_indices))
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newkern.constrained_negative_indices = np.hstack((self.constrained_negative_indices, self.Nparam + other.constrained_negative_indices))
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newkern.constrained_bounded_indices = self.constrained_bounded_indices + [self.Nparam + x for x in other.constrained_bounded_indices]
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newkern.constrained_bounded_lowers = self.constrained_bounded_lowers + other.constrained_bounded_lowers
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newkern.constrained_bounded_uppers = self.constrained_bounded_uppers + other.constrained_bounded_uppers
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newkern.constrained_fixed_indices = self.constrained_fixed_indices + [self.Nparam + x for x in other.constrained_fixed_indices]
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newkern.constrained_fixed_values = self.constrained_fixed_values + other.constrained_fixed_values
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newkern.tied_indices = self.tied_indices + [self.Nparam + x for x in other.tied_indices]
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return newkern
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def __mul__(self, other):
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"""
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Shortcut for `prod_orthogonal`. Note that `+` assumes that we sum 2 kernels defines on the same space whereas `*` assumes that the kernels are defined on different subspaces.
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"""
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return self.prod(other)
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def prod(self, other):
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"""
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multiply two kernels defined on the same spaces.
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:param other: the other kernel to be added
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:type other: GPy.kern
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"""
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K1 = self.copy()
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K2 = other.copy()
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newkernparts = [prod(k1, k2) for k1, k2 in itertools.product(K1.parts, K2.parts)]
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slices = []
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for sl1, sl2 in itertools.product(K1.input_slices, K2.input_slices):
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s1, s2 = [False] * K1.D, [False] * K2.D
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s1[sl1], s2[sl2] = [True], [True]
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slices += [s1 + s2]
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newkern = kern(K1.D, newkernparts, slices)
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newkern._follow_constrains(K1, K2)
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return newkern
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def prod_orthogonal(self, other):
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"""
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multiply two kernels. Both kernels are defined on separate spaces.
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:param other: the other kernel to be added
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:type other: GPy.kern
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"""
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K1 = self.copy()
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K2 = other.copy()
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newkernparts = [prod_orthogonal(k1, k2) for k1, k2 in itertools.product(K1.parts, K2.parts)]
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slices = []
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for sl1, sl2 in itertools.product(K1.input_slices, K2.input_slices):
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s1, s2 = [False] * K1.D, [False] * K2.D
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s1[sl1], s2[sl2] = [True], [True]
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slices += [s1 + s2]
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newkern = kern(K1.D + K2.D, newkernparts, slices)
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newkern._follow_constrains(K1, K2)
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return newkern
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def _follow_constrains(self, K1, K2):
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# Build the array that allows to go from the initial indices of the param to the new ones
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K1_param = []
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n = 0
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for k1 in K1.parts:
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K1_param += [range(n, n + k1.Nparam)]
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n += k1.Nparam
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n = 0
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K2_param = []
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for k2 in K2.parts:
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K2_param += [range(K1.Nparam + n, K1.Nparam + n + k2.Nparam)]
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n += k2.Nparam
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index_param = []
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for p1 in K1_param:
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for p2 in K2_param:
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index_param += p1 + p2
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index_param = np.array(index_param)
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# Get the ties and constrains of the kernels before the multiplication
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prev_ties = K1.tied_indices + [arr + K1.Nparam for arr in K2.tied_indices]
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prev_constr_pos = np.append(K1.constrained_positive_indices, K1.Nparam + K2.constrained_positive_indices)
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prev_constr_neg = np.append(K1.constrained_negative_indices, K1.Nparam + K2.constrained_negative_indices)
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prev_constr_fix = K1.constrained_fixed_indices + [arr + K1.Nparam for arr in K2.constrained_fixed_indices]
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prev_constr_fix_values = K1.constrained_fixed_values + K2.constrained_fixed_values
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prev_constr_bou = K1.constrained_bounded_indices + [arr + K1.Nparam for arr in K2.constrained_bounded_indices]
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prev_constr_bou_low = K1.constrained_bounded_lowers + K2.constrained_bounded_lowers
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prev_constr_bou_upp = K1.constrained_bounded_uppers + K2.constrained_bounded_uppers
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# follow the previous ties
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for arr in prev_ties:
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for j in arr:
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index_param[np.where(index_param == j)[0]] = arr[0]
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# ties and constrains
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for i in range(K1.Nparam + K2.Nparam):
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index = np.where(index_param == i)[0]
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if index.size > 1:
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self.tie_params(index)
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for i in prev_constr_pos:
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self.constrain_positive(np.where(index_param == i)[0])
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for i in prev_constr_neg:
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self.constrain_neg(np.where(index_param == i)[0])
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for j, i in enumerate(prev_constr_fix):
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self.constrain_fixed(np.where(index_param == i)[0], prev_constr_fix_values[j])
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for j, i in enumerate(prev_constr_bou):
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self.constrain_bounded(np.where(index_param == i)[0], prev_constr_bou_low[j], prev_constr_bou_upp[j])
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def _get_params(self):
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return np.hstack([p._get_params() for p in self.parts])
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def _set_params(self, x):
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[p._set_params(x[s]) for p, s in zip(self.parts, self.param_slices)]
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def _get_param_names(self):
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# this is a bit nasty: we wat to distinguish between parts with the same name by appending a count
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part_names = np.array([k.name for k in self.parts], dtype=np.str)
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counts = [np.sum(part_names == ni) for i, ni in enumerate(part_names)]
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cum_counts = [np.sum(part_names[i:] == ni) for i, ni in enumerate(part_names)]
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names = [name + '_' + str(cum_count) if count > 1 else name for name, count, cum_count in zip(part_names, counts, cum_counts)]
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return sum([[name + '_' + n for n in k._get_param_names()] for name, k in zip(names, self.parts)], [])
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def K(self, X, X2=None, which_parts='all'):
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if which_parts=='all':
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which_parts = [True]*self.Nparts
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assert X.shape[1] == self.D
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if X2 is None:
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target = np.zeros((X.shape[0], X.shape[0]))
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[p.K(X[:, i_s], None, target=target) for p, i_s, part_i_used in zip(self.parts, self.input_slices, which_parts) if part_i_used]
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else:
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target = np.zeros((X.shape[0], X2.shape[0]))
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[p.K(X[:, i_s], X2[:,i_s], target=target) for p, i_s, part_i_used in zip(self.parts, self.input_slices, which_parts) if part_i_used]
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return target
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def dK_dtheta(self, dL_dK, X, X2=None):
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"""
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:param dL_dK: An array of dL_dK derivaties, dL_dK
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:type dL_dK: Np.ndarray (N x M)
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:param X: Observed data inputs
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:type X: np.ndarray (N x D)
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:param X2: Observed dara inputs (optional, defaults to X)
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:type X2: np.ndarray (M x D)
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"""
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assert X.shape[1] == self.D
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target = np.zeros(self.Nparam)
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if X2 is None:
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[p.dK_dtheta(dL_dK, X[:, i_s], None, target[ps]) for p, i_s, ps, in zip(self.parts, self.input_slices, self.param_slices)]
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else:
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[p.dK_dtheta(dL_dK, X[:, i_s], X2[:, i_s], target[ps]) for p, i_s, ps, in zip(self.parts, self.input_slices, self.param_slices)]
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return self._transform_gradients(target)
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def dK_dX(self, dL_dK, X, X2=None):
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if X2 is None:
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X2 = X
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target = np.zeros_like(X)
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if X2 is None:
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[p.dK_dX(dL_dK, X[:, i_s], None, target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)]
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else:
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[p.dK_dX(dL_dK, X[:, i_s], X2[:, i_s], target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)]
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return target
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def Kdiag(self, X, which_parts='all'):
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if which_parts=='all':
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which_parts = [True]*self.Nparts
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assert X.shape[1] == self.D
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target = np.zeros(X.shape[0])
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[p.Kdiag(X[:, i_s], target=target) for p, i_s in zip(self.parts, self.input_slices)]
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return target
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def dKdiag_dtheta(self, dL_dKdiag, X):
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assert X.shape[1] == self.D
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assert dL_dKdiag.size == X.shape[0]
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target = np.zeros(self.Nparam)
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[p.dKdiag_dtheta(dL_dKdiag, X[:, i_s], target[ps]) for p, i_s, ps in zip(self.parts, self.input_slices, self.param_slices)]
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return self._transform_gradients(target)
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def dKdiag_dX(self, dL_dKdiag, X):
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assert X.shape[1] == self.D
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target = np.zeros_like(X)
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[p.dKdiag_dX(dL_dKdiag, X[:, i_s], target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)]
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return target
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def psi0(self, Z, mu, S):
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target = np.zeros(mu.shape[0])
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[p.psi0(Z[:,i_s], mu[:,i_s], S[:,i_s], target) for p, i_s in zip(self.parts, self.input_slices)]
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return target
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def dpsi0_dtheta(self, dL_dpsi0, Z, mu, S):
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target = np.zeros(self.Nparam)
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[p.dpsi0_dtheta(dL_dpsi0, Z[:,i_s], mu[:,i_s], S[:,i_s], target[ps]) for p, ps, i_s in zip(self.parts, self.param_slices, self.input_slices)]
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return self._transform_gradients(target)
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def dpsi0_dmuS(self, dL_dpsi0, Z, mu, S):
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target_mu, target_S = np.zeros_like(mu), np.zeros_like(S)
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[p.dpsi0_dmuS(dL_dpsi0, Z[:,i_s], mu[:,i_s], S[:,i_s], target_mu[:,i_s], target_S[:,i_s]) for p, i_s in zip(self.parts, self.input_slices)]
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return target_mu, target_S
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def psi1(self, Z, mu, S):
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target = np.zeros((mu.shape[0], Z.shape[0]))
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[p.psi1(Z[:,i_s], mu[:,i_s], S[:,i_s], target) for p, i_s in zip(self.parts, self.input_slices)]
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return target
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def dpsi1_dtheta(self, dL_dpsi1, Z, mu, S):
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target = np.zeros((self.Nparam))
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[p.dpsi1_dtheta(dL_dpsi1, Z[:, i_s], mu[:, i_s], S[:, i_s], target[ps]) for p, ps, i_s in zip(self.parts, self.param_slices, self.input_slices)]
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return self._transform_gradients(target)
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def dpsi1_dZ(self, dL_dpsi1, Z, mu, S):
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target = np.zeros_like(Z)
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[p.dpsi1_dZ(dL_dpsi1, Z[:, i_s], mu[:, i_s], S[:, i_s], target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)]
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return target
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def dpsi1_dmuS(self, dL_dpsi1, Z, mu, S):
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"""return shapes are N,M,Q"""
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target_mu, target_S = np.zeros((2, mu.shape[0], mu.shape[1]))
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[p.dpsi1_dmuS(dL_dpsi1, Z[:, i_s], mu[:, i_s], S[:, i_s], target_mu[:, i_s], target_S[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)]
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return target_mu, target_S
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def psi2(self, Z, mu, S):
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"""
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:param Z: np.ndarray of inducing inputs (M x Q)
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:param mu, S: np.ndarrays of means and variances (each N x Q)
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:returns psi2: np.ndarray (N,M,M)
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"""
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target = np.zeros((mu.shape[0], Z.shape[0], Z.shape[0]))
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[p.psi2(Z[:, i_s], mu[:, i_s], S[:, i_s], target) for p, i_s in zip(self.parts, self.input_slices)]
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# compute the "cross" terms
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#TODO: input_slices needed
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for p1, p2 in itertools.combinations(self.parts, 2):
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# white doesn;t combine with anything
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if p1.name == 'white' or p2.name == 'white':
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pass
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# rbf X bias
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elif p1.name == 'bias' and p2.name == 'rbf':
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target += p1.variance * (p2._psi1[:, :, None] + p2._psi1[:, None, :])
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elif p2.name == 'bias' and p1.name == 'rbf':
|
|
target += p2.variance * (p1._psi1[:, :, None] + p1._psi1[:, None, :])
|
|
# linear X bias
|
|
elif p1.name == 'bias' and p2.name == 'linear':
|
|
tmp = np.zeros((mu.shape[0], Z.shape[0]))
|
|
p2.psi1(Z, mu, S, tmp)
|
|
target += p1.variance * (tmp[:, :, None] + tmp[:, None, :])
|
|
elif p2.name == 'bias' and p1.name == 'linear':
|
|
tmp = np.zeros((mu.shape[0], Z.shape[0]))
|
|
p1.psi1(Z, mu, S, tmp)
|
|
target += p2.variance * (tmp[:, :, None] + tmp[:, None, :])
|
|
# rbf X linear
|
|
elif p1.name == 'linear' and p2.name == 'rbf':
|
|
raise NotImplementedError # TODO
|
|
elif p2.name == 'linear' and p1.name == 'rbf':
|
|
raise NotImplementedError # TODO
|
|
else:
|
|
raise NotImplementedError, "psi2 cannot be computed for this kernel"
|
|
return target
|
|
|
|
def dpsi2_dtheta(self, dL_dpsi2, Z, mu, S):
|
|
target = np.zeros(self.Nparam)
|
|
[p.dpsi2_dtheta(dL_dpsi2, Z[:, i_s], mu[:, i_s], S[:, i_s], target[ps]) for p, i_s, ps in zip(self.parts, self.input_slices, self.param_slices)]
|
|
|
|
# compute the "cross" terms
|
|
# TODO: better looping, input_slices
|
|
for i1, i2 in itertools.combinations(range(len(self.parts)), 2):
|
|
p1, p2 = self.parts[i1], self.parts[i2]
|
|
# ipsl1, ipsl2 = self.input_slices[i1], self.input_slices[i2]
|
|
ps1, ps2 = self.param_slices[i1], self.param_slices[i2]
|
|
|
|
# white doesn;t combine with anything
|
|
if p1.name == 'white' or p2.name == 'white':
|
|
pass
|
|
# rbf X bias
|
|
elif p1.name == 'bias' and p2.name == 'rbf':
|
|
p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1.variance * 2., Z, mu, S, target[ps2])
|
|
p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2._psi1 * 2., Z, mu, S, target[ps1])
|
|
elif p2.name == 'bias' and p1.name == 'rbf':
|
|
p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2.variance * 2., Z, mu, S, target[ps1])
|
|
p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1._psi1 * 2., Z, mu, S, target[ps2])
|
|
# linear X bias
|
|
elif p1.name == 'bias' and p2.name == 'linear':
|
|
p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1.variance * 2., Z, mu, S, target[ps2]) # [ps1])
|
|
psi1 = np.zeros((mu.shape[0], Z.shape[0]))
|
|
p2.psi1(Z, mu, S, psi1)
|
|
p1.dpsi1_dtheta(dL_dpsi2.sum(1) * psi1 * 2., Z, mu, S, target[ps1])
|
|
elif p2.name == 'bias' and p1.name == 'linear':
|
|
p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2.variance * 2., Z, mu, S, target[ps1])
|
|
psi1 = np.zeros((mu.shape[0], Z.shape[0]))
|
|
p1.psi1(Z, mu, S, psi1)
|
|
p2.dpsi1_dtheta(dL_dpsi2.sum(1) * psi1 * 2., Z, mu, S, target[ps2])
|
|
# rbf X linear
|
|
elif p1.name == 'linear' and p2.name == 'rbf':
|
|
raise NotImplementedError # TODO
|
|
elif p2.name == 'linear' and p1.name == 'rbf':
|
|
raise NotImplementedError # TODO
|
|
else:
|
|
raise NotImplementedError, "psi2 cannot be computed for this kernel"
|
|
|
|
return self._transform_gradients(target)
|
|
|
|
def dpsi2_dZ(self, dL_dpsi2, Z, mu, S):
|
|
target = np.zeros_like(Z)
|
|
[p.dpsi2_dZ(dL_dpsi2, Z[:, i_s], mu[:, i_s], S[:, i_s], target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)]
|
|
|
|
# compute the "cross" terms
|
|
#TODO: we need input_slices here.
|
|
for p1, p2 in itertools.combinations(self.parts, 2):
|
|
# white doesn;t combine with anything
|
|
if p1.name == 'white' or p2.name == 'white':
|
|
pass
|
|
# rbf X bias
|
|
elif p1.name == 'bias' and p2.name == 'rbf':
|
|
p2.dpsi1_dX(dL_dpsi2.sum(1).T * p1.variance, Z, mu, S, target)
|
|
elif p2.name == 'bias' and p1.name == 'rbf':
|
|
p1.dpsi1_dZ(dL_dpsi2.sum(1).T * p2.variance, Z, mu, S, target)
|
|
# linear X bias
|
|
elif p1.name == 'bias' and p2.name == 'linear':
|
|
p2.dpsi1_dZ(dL_dpsi2.sum(1).T * p1.variance, Z, mu, S, target)
|
|
elif p2.name == 'bias' and p1.name == 'linear':
|
|
p1.dpsi1_dZ(dL_dpsi2.sum(1).T * p2.variance, Z, mu, S, target)
|
|
# rbf X linear
|
|
elif p1.name == 'linear' and p2.name == 'rbf':
|
|
raise NotImplementedError # TODO
|
|
elif p2.name == 'linear' and p1.name == 'rbf':
|
|
raise NotImplementedError # TODO
|
|
else:
|
|
raise NotImplementedError, "psi2 cannot be computed for this kernel"
|
|
|
|
return target * 2.
|
|
|
|
def dpsi2_dmuS(self, dL_dpsi2, Z, mu, S):
|
|
target_mu, target_S = np.zeros((2, mu.shape[0], mu.shape[1]))
|
|
[p.dpsi2_dmuS(dL_dpsi2, Z[:, i_s], mu[:, i_s], S[:, i_s], target_mu[:, i_s], target_S[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)]
|
|
|
|
# compute the "cross" terms
|
|
#TODO: we need input_slices here.
|
|
for p1, p2 in itertools.combinations(self.parts, 2):
|
|
# white doesn;t combine with anything
|
|
if p1.name == 'white' or p2.name == 'white':
|
|
pass
|
|
# rbf X bias
|
|
elif p1.name == 'bias' and p2.name == 'rbf':
|
|
p2.dpsi1_dmuS(dL_dpsi2.sum(1).T * p1.variance * 2., Z, mu, S, target_mu, target_S)
|
|
elif p2.name == 'bias' and p1.name == 'rbf':
|
|
p1.dpsi1_dmuS(dL_dpsi2.sum(1).T * p2.variance * 2., Z, mu, S, target_mu, target_S)
|
|
# linear X bias
|
|
elif p1.name == 'bias' and p2.name == 'linear':
|
|
p2.dpsi1_dmuS(dL_dpsi2.sum(1).T * p1.variance * 2., Z, mu, S, target_mu, target_S)
|
|
elif p2.name == 'bias' and p1.name == 'linear':
|
|
p1.dpsi1_dmuS(dL_dpsi2.sum(1).T * p2.variance * 2., Z, mu, S, target_mu, target_S)
|
|
# rbf X linear
|
|
elif p1.name == 'linear' and p2.name == 'rbf':
|
|
raise NotImplementedError # TODO
|
|
elif p2.name == 'linear' and p1.name == 'rbf':
|
|
raise NotImplementedError # TODO
|
|
else:
|
|
raise NotImplementedError, "psi2 cannot be computed for this kernel"
|
|
|
|
return target_mu, target_S
|
|
|
|
def plot(self, x=None, plot_limits=None, which_functions='all', resolution=None, *args, **kwargs):
|
|
if which_functions == 'all':
|
|
which_functions = [True] * self.Nparts
|
|
if self.D == 1:
|
|
if x is None:
|
|
x = np.zeros((1, 1))
|
|
else:
|
|
x = np.asarray(x)
|
|
assert x.size == 1, "The size of the fixed variable x is not 1"
|
|
x = x.reshape((1, 1))
|
|
|
|
if plot_limits == None:
|
|
xmin, xmax = (x - 5).flatten(), (x + 5).flatten()
|
|
elif len(plot_limits) == 2:
|
|
xmin, xmax = plot_limits
|
|
else:
|
|
raise ValueError, "Bad limits for plotting"
|
|
|
|
Xnew = np.linspace(xmin, xmax, resolution or 201)[:, None]
|
|
Kx = self.K(Xnew, x, slices2=which_functions)
|
|
pb.plot(Xnew, Kx, *args, **kwargs)
|
|
pb.xlim(xmin, xmax)
|
|
pb.xlabel("x")
|
|
pb.ylabel("k(x,%0.1f)" % x)
|
|
|
|
elif self.D == 2:
|
|
if x is None:
|
|
x = np.zeros((1, 2))
|
|
else:
|
|
x = np.asarray(x)
|
|
assert x.size == 2, "The size of the fixed variable x is not 2"
|
|
x = x.reshape((1, 2))
|
|
|
|
if plot_limits == None:
|
|
xmin, xmax = (x - 5).flatten(), (x + 5).flatten()
|
|
elif len(plot_limits) == 2:
|
|
xmin, xmax = plot_limits
|
|
else:
|
|
raise ValueError, "Bad limits for plotting"
|
|
|
|
resolution = resolution or 51
|
|
xx, yy = np.mgrid[xmin[0]:xmax[0]:1j * resolution, xmin[1]:xmax[1]:1j * resolution]
|
|
xg = np.linspace(xmin[0], xmax[0], resolution)
|
|
yg = np.linspace(xmin[1], xmax[1], resolution)
|
|
Xnew = np.vstack((xx.flatten(), yy.flatten())).T
|
|
Kx = self.K(Xnew, x, slices2=which_functions)
|
|
Kx = Kx.reshape(resolution, resolution).T
|
|
pb.contour(xg, yg, Kx, vmin=Kx.min(), vmax=Kx.max(), cmap=pb.cm.jet, *args, **kwargs)
|
|
pb.xlim(xmin[0], xmax[0])
|
|
pb.ylim(xmin[1], xmax[1])
|
|
pb.xlabel("x1")
|
|
pb.ylabel("x2")
|
|
pb.title("k(x1,x2 ; %0.1f,%0.1f)" % (x[0, 0], x[0, 1]))
|
|
else:
|
|
raise NotImplementedError, "Cannot plot a kernel with more than two input dimensions"
|