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https://github.com/SheffieldML/GPy.git
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cross-terms
This commit is contained in:
Nicolo Fusi
parent
ddd3ece3ce
commit
19407293dc
5 changed files with 40 additions and 105 deletions
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@ -17,11 +17,11 @@ def BGPLVM(seed=default_seed):
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D = 4
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# generate GPLVM-like data
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X = np.random.rand(N, Q)
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k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
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k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
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K = k.K(X)
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Y = np.random.multivariate_normal(np.zeros(N), K, D).T
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k = GPy.kern.linear(Q, ARD=True) + GPy.kern.white(Q)
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k = GPy.kern.rbf(Q, ARD=True) + GPy.kern.linear(Q, ARD=True) + GPy.kern.rbf(Q, ARD=True) + GPy.kern.white(Q)
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# k = GPy.kern.rbf(Q) + GPy.kern.rbf(Q) + GPy.kern.white(Q)
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# k = GPy.kern.rbf(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
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# k = GPy.kern.rbf(Q, ARD = False) + GPy.kern.white(Q, 0.00001)
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@ -55,7 +55,8 @@ class bias(kernpart):
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target += self.variance
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def psi1(self, Z, mu, S, target):
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target += self.variance
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self._psi1 = self.variance
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target += self._psi1
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def psi2(self, Z, mu, S, target):
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target += self.variance**2
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130
GPy/kern/kern.py
130
GPy/kern/kern.py
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@ -316,32 +316,19 @@ class kern(parameterised):
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# compute the "cross" terms
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# TODO: input_slices needed
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crossterms = 0
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for p1, p2 in itertools.combinations(self.parts, 2):
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prod = np.multiply
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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':
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# target += p2.variance * (p1._psi1[:, :, None] + p1._psi1[:, None, :])
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# # linear X bias
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# elif p1.name == 'bias' and p2.name == 'linear':
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# tmp = np.zeros((mu.shape[0], Z.shape[0]))
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# p2.psi1(Z, mu, S, tmp)
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# target += p1.variance * (tmp[:, :, None] + tmp[:, None, :])
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# elif p2.name == 'bias' and p1.name == 'linear':
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# tmp = np.zeros((mu.shape[0], Z.shape[0]))
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# p1.psi1(Z, mu, S, tmp)
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# target += p2.variance * (tmp[:, :, None] + tmp[:, None, :])
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# # rbf X linear
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# elif p1.name == 'linear' and p2.name == 'rbf':
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# raise NotImplementedError # TODO
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# elif p2.name == 'linear' and p1.name == 'rbf':
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# raise NotImplementedError # TODO
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# else:
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# raise NotImplementedError, "psi2 cannot be computed for this kernel"
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# TODO psi1 this must be faster/better/precached/more nice
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tmp1 = np.zeros((mu.shape[0], Z.shape[0]))
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p1.psi1(Z, mu, S, tmp1)
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tmp2 = np.zeros((mu.shape[0], Z.shape[0]))
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p2.psi1(Z, mu, S, tmp2)
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prod = np.multiply(tmp1, tmp2)
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crossterms += prod[:,:,None] + prod[:, None, :]
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target += crossterms
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return target
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def dpsi2_dtheta(self, dL_dpsi2, Z, mu, S):
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@ -350,71 +337,34 @@ class kern(parameterised):
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# compute the "cross" terms
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# TODO: better looping, input_slices
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for i1, i2 in itertools.combinations(range(len(self.parts)), 2):
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for i1, i2 in itertools.permutations(range(len(self.parts)), 2):
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p1, p2 = self.parts[i1], self.parts[i2]
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# ipsl1, ipsl2 = self.input_slices[i1], self.input_slices[i2]
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ps1, ps2 = self.param_slices[i1], self.param_slices[i2]
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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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p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1.variance * 2., Z, mu, S, target[ps2])
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p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2._psi1 * 2., Z, mu, S, target[ps1])
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elif p2.name == 'bias' and p1.name == 'rbf':
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p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2.variance * 2., Z, mu, S, target[ps1])
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p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1._psi1 * 2., Z, mu, S, target[ps2])
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# linear X bias
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elif p1.name == 'bias' and p2.name == 'linear':
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p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1.variance * 2., Z, mu, S, target[ps2]) # [ps1])
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psi1 = np.zeros((mu.shape[0], Z.shape[0]))
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p2.psi1(Z, mu, S, psi1)
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p1.dpsi1_dtheta(dL_dpsi2.sum(1) * psi1 * 2., Z, mu, S, target[ps1])
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elif p2.name == 'bias' and p1.name == 'linear':
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p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2.variance * 2., Z, mu, S, target[ps1])
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psi1 = np.zeros((mu.shape[0], Z.shape[0]))
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p1.psi1(Z, mu, S, psi1)
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p2.dpsi1_dtheta(dL_dpsi2.sum(1) * psi1 * 2., Z, mu, S, target[ps2])
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# rbf X linear
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elif p1.name == 'linear' and p2.name == 'rbf':
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raise NotImplementedError # TODO
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elif p2.name == 'linear' and p1.name == 'rbf':
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raise NotImplementedError # TODO
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else:
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raise NotImplementedError, "psi2 cannot be computed for this kernel"
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tmp = np.zeros((mu.shape[0], Z.shape[0]))
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p1.psi1(Z, mu, S, tmp)
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p2.dpsi1_dtheta((tmp[:,None,:]*dL_dpsi2).sum(1)*2., Z, mu, S, target[ps2])
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return self._transform_gradients(target)
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def dpsi2_dZ(self, dL_dpsi2, Z, mu, S):
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target = np.zeros_like(Z)
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[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)]
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#target *= 2
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# compute the "cross" terms
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# TODO: we need input_slices here.
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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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p2.dpsi1_dX(dL_dpsi2.sum(1).T * p1.variance, Z, mu, S, target)
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elif p2.name == 'bias' and p1.name == 'rbf':
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p1.dpsi1_dZ(dL_dpsi2.sum(1).T * p2.variance, Z, mu, S, target)
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# linear X bias
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elif p1.name == 'bias' and p2.name == 'linear':
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p2.dpsi1_dZ(dL_dpsi2.sum(1).T * p1.variance, Z, mu, S, target)
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elif p2.name == 'bias' and p1.name == 'linear':
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p1.dpsi1_dZ(dL_dpsi2.sum(1).T * p2.variance, Z, mu, S, target)
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# rbf X linear
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elif p1.name == 'linear' and p2.name == 'rbf':
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raise NotImplementedError # TODO
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elif p2.name == 'linear' and p1.name == 'rbf':
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raise NotImplementedError # TODO
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else:
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raise NotImplementedError, "psi2 cannot be computed for this kernel"
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for p1, p2 in itertools.permutations(self.parts, 2):
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if p1.name == 'linear' and p2.name == 'linear':
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raise NotImplementedError("We don't handle linear/linear cross-terms")
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tmp = np.zeros((mu.shape[0], Z.shape[0]))
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p1.psi1(Z, mu, S, tmp)
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tmp2 = np.zeros_like(target)
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p2.dpsi1_dZ((tmp[:,None,:]*dL_dpsi2).sum(1).T, Z, mu, S, tmp2)
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target += tmp2
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return target * 2.
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return target * 2
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def dpsi2_dmuS(self, dL_dpsi2, Z, mu, S):
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target_mu, target_S = np.zeros((2, mu.shape[0], mu.shape[1]))
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@ -422,27 +372,13 @@ class kern(parameterised):
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# compute the "cross" terms
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# TODO: we need input_slices here.
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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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p2.dpsi1_dmuS(dL_dpsi2.sum(1).T * p1.variance * 2., Z, mu, S, target_mu, target_S)
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elif p2.name == 'bias' and p1.name == 'rbf':
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p1.dpsi1_dmuS(dL_dpsi2.sum(1).T * p2.variance * 2., Z, mu, S, target_mu, target_S)
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# linear X bias
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elif p1.name == 'bias' and p2.name == 'linear':
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p2.dpsi1_dmuS(dL_dpsi2.sum(1).T * p1.variance * 2., Z, mu, S, target_mu, target_S)
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elif p2.name == 'bias' and p1.name == 'linear':
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p1.dpsi1_dmuS(dL_dpsi2.sum(1).T * p2.variance * 2., Z, mu, S, target_mu, target_S)
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# rbf X linear
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elif p1.name == 'linear' and p2.name == 'rbf':
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raise NotImplementedError # TODO
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elif p2.name == 'linear' and p1.name == 'rbf':
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raise NotImplementedError # TODO
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else:
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raise NotImplementedError, "psi2 cannot be computed for this kernel"
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for p1, p2 in itertools.permutations(self.parts, 2):
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if p1.name == 'linear' and p2.name == 'linear':
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raise NotImplementedError("We don't handle linear/linear cross-terms")
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tmp = np.zeros((mu.shape[0], Z.shape[0]))
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p1.psi1(Z, mu, S, tmp)
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p2.dpsi1_dmuS((tmp[:,None,:]*dL_dpsi2).sum(1).T*2., Z, mu, S, target_mu, target_S)
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return target_mu, target_S
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@ -54,5 +54,3 @@ class kernpart(object):
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raise NotImplementedError
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def dK_dX(self,X,X2,target):
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raise NotImplementedError
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@ -18,6 +18,7 @@ class white(kernpart):
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self.Nparam = 1
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self.name = 'white'
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self._set_params(np.array([variance]).flatten())
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self._psi1 = 0 # TODO: more elegance here
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def _get_params(self):
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return self.variance
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@ -81,4 +82,3 @@ class white(kernpart):
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def dpsi2_dmuS(self,dL_dpsi2,Z,mu,S,target_mu,target_S):
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pass
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