mirror of
https://github.com/SheffieldML/GPy.git
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[classification] sparse gp classification and dtc update
This commit is contained in:
Max Zwiessele
parent
4ea5ebaa68
commit
1d354f5cce
14 changed files with 208 additions and 369 deletions
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@ -4,6 +4,7 @@ import numpy as np
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from ...util.linalg import pdinv,jitchol,DSYR,tdot,dtrtrs, dpotrs
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from .posterior import Posterior
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from . import LatentFunctionInference
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from ...util import diag
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log_2_pi = np.log(2*np.pi)
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class EP(LatentFunctionInference):
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@ -41,7 +42,6 @@ class EP(LatentFunctionInference):
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K = kern.K(X)
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if self._ep_approximation is None:
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#if we don't yet have the results of runnign EP, run EP and store the computed factors in self._ep_approximation
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mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation = self.expectation_propagation(K, Y, likelihood, Y_metadata)
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else:
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@ -69,6 +69,7 @@ class EP(LatentFunctionInference):
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#Initial values - Posterior distribution parameters: q(f|X,Y) = N(f|mu,Sigma)
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mu = np.zeros(num_data)
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Sigma = K.copy()
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diag.add(Sigma, 1e-7)
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#Initial values - Marginal moments
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Z_hat = np.empty(num_data,dtype=np.float64)
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@ -79,14 +80,14 @@ class EP(LatentFunctionInference):
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if self.old_mutilde is None:
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tau_tilde, mu_tilde, v_tilde = np.zeros((3, num_data))
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else:
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assert old_mutilde.size == num_data, "data size mis-match: did you change the data? try resetting!"
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assert self.old_mutilde.size == num_data, "data size mis-match: did you change the data? try resetting!"
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mu_tilde, v_tilde = self.old_mutilde, self.old_vtilde
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tau_tilde = v_tilde/mu_tilde
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#Approximation
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tau_diff = self.epsilon + 1.
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v_diff = self.epsilon + 1.
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iterations = 0
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iterations = 0
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while (tau_diff > self.epsilon) or (v_diff > self.epsilon):
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update_order = np.random.permutation(num_data)
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for i in update_order:
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@ -3,27 +3,18 @@
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import numpy as np
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from ...util import diag
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from ...util.linalg import mdot, jitchol, backsub_both_sides, tdot, dtrtrs, dtrtri, dpotri, dpotrs, symmetrify, DSYR
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from ...core.parameterization.variational import VariationalPosterior
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from . import LatentFunctionInference
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from .posterior import Posterior
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from ...util.linalg import jitchol, dtrtrs, dtrtri, DSYR
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from ...core.parameterization.observable_array import ObsAr
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from . import VarDTC
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log_2_pi = np.log(2*np.pi)
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class EPDTC(LatentFunctionInference):
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class EPDTC(VarDTC):
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const_jitter = 1e-6
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def __init__(self, epsilon=1e-6, eta=1., delta=1., limit=1):
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from ...util.caching import Cacher
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self.limit = limit
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self.get_trYYT = Cacher(self._get_trYYT, limit)
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self.get_YYTfactor = Cacher(self._get_YYTfactor, limit)
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super(EPDTC, self).__init__(limit=limit)
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self.epsilon, self.eta, self.delta = epsilon, eta, delta
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self.reset()
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def set_limit(self, limit):
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self.get_trYYT.limit = limit
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self.get_YYTfactor.limit = limit
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def on_optimization_start(self):
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self._ep_approximation = None
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@ -31,212 +22,74 @@ class EPDTC(LatentFunctionInference):
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# TODO: update approximation in the end as well? Maybe even with a switch?
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pass
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def _get_trYYT(self, Y):
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return np.sum(np.square(Y))
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def __getstate__(self):
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# has to be overridden, as Cacher objects cannot be pickled.
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return self.limit
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def __setstate__(self, state):
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# has to be overridden, as Cacher objects cannot be pickled.
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self.limit = state
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from ...util.caching import Cacher
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self.get_trYYT = Cacher(self._get_trYYT, self.limit)
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self.get_YYTfactor = Cacher(self._get_YYTfactor, self.limit)
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def _get_YYTfactor(self, Y):
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"""
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find a matrix L which satisfies LLT = YYT.
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Note that L may have fewer columns than Y.
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"""
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N, D = Y.shape
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if (N>=D):
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return Y
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else:
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return jitchol(tdot(Y))
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def get_VVTfactor(self, Y, prec):
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return Y * prec # TODO chache this, and make it effective
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def reset(self):
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self.old_mutilde, self.old_vtilde = None, None
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self._ep_approximation = None
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def inference(self, kern, X, Z, likelihood, Y, mean_function=None, Y_metadata=None):
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assert mean_function is None, "inference with a mean function not implemented"
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num_data, output_dim = Y.shape
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assert output_dim ==1, "ep in 1D only (for now!)"
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def inference(self, kern, X, Z, likelihood, Y, mean_function=None, Y_metadata=None, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None):
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assert Y.shape[1]==1, "ep in 1D only (for now!)"
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Kmm = kern.K(Z)
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Kmn = kern.K(Z,X)
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if psi1 is None:
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try:
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Kmn = kern.K(Z, X)
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except TypeError:
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Kmn = kern.psi1(Z, X).T
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else:
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Kmn = psi1.T
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if self._ep_approximation is None:
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mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation = self.expectation_propagation(Kmm, Kmn, Y, likelihood, Y_metadata)
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else:
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mu, Sigma, mu_tilde, tau_tilde, Z_hat = self._ep_approximation
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if isinstance(X, VariationalPosterior):
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uncertain_inputs = True
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psi0 = kern.psi0(Z, X)
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psi1 = Kmn.T#kern.psi1(Z, X)
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psi2 = kern.psi2(Z, X)
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else:
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uncertain_inputs = False
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psi0 = kern.Kdiag(X)
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psi1 = Kmn.T#kern.K(X, Z)
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psi2 = None
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#see whether we're using variational uncertain inputs
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_, output_dim = Y.shape
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#see whether we've got a different noise variance for each datum
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#beta = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), 1e-6)
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beta = tau_tilde
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VVT_factor = beta[:,None]*mu_tilde[:,None]
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trYYT = self.get_trYYT(mu_tilde[:,None])
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# do the inference:
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het_noise = beta.size > 1
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num_inducing = Z.shape[0]
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num_data = Y.shape[0]
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# kernel computations, using BGPLVM notation
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Kmm = kern.K(Z).copy()
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diag.add(Kmm, self.const_jitter)
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Lm = jitchol(Kmm)
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# The rather complex computations of A
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if uncertain_inputs:
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if het_noise:
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psi2_beta = psi2 * (beta.flatten().reshape(num_data, 1, 1)).sum(0)
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else:
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psi2_beta = psi2.sum(0) * beta
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LmInv = dtrtri(Lm)
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A = LmInv.dot(psi2_beta.dot(LmInv.T))
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else:
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if het_noise:
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tmp = psi1 * (np.sqrt(beta.reshape(num_data, 1)))
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else:
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tmp = psi1 * (np.sqrt(beta))
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tmp, _ = dtrtrs(Lm, tmp.T, lower=1)
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A = tdot(tmp) #print A.sum()
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# factor B
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B = np.eye(num_inducing) + A
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LB = jitchol(B)
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psi1Vf = np.dot(psi1.T, VVT_factor)
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# back substutue C into psi1Vf
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tmp, _ = dtrtrs(Lm, psi1Vf, lower=1, trans=0)
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_LBi_Lmi_psi1Vf, _ = dtrtrs(LB, tmp, lower=1, trans=0)
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tmp, _ = dtrtrs(LB, _LBi_Lmi_psi1Vf, lower=1, trans=1)
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Cpsi1Vf, _ = dtrtrs(Lm, tmp, lower=1, trans=1)
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# data fit and derivative of L w.r.t. Kmm
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delit = tdot(_LBi_Lmi_psi1Vf)
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data_fit = np.trace(delit)
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DBi_plus_BiPBi = backsub_both_sides(LB, output_dim * np.eye(num_inducing) + delit)
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delit = -0.5 * DBi_plus_BiPBi
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delit += -0.5 * B * output_dim
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delit += output_dim * np.eye(num_inducing)
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# Compute dL_dKmm
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dL_dKmm = backsub_both_sides(Lm, delit)
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# derivatives of L w.r.t. psi
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dL_dpsi0, dL_dpsi1, dL_dpsi2 = _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm,
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VVT_factor, Cpsi1Vf, DBi_plus_BiPBi,
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psi1, het_noise, uncertain_inputs)
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# log marginal likelihood
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log_marginal = _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise,
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psi0, A, LB, trYYT, data_fit, VVT_factor)
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#put the gradients in the right places
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dL_dR = _compute_dL_dR(likelihood,
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het_noise, uncertain_inputs, LB,
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_LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A,
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psi0, psi1, beta,
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data_fit, num_data, output_dim, trYYT, mu_tilde[:,None])
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dL_dthetaL = 0#likelihood.exact_inference_gradients(dL_dR,Y_metadata)
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if uncertain_inputs:
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grad_dict = {'dL_dKmm': dL_dKmm,
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'dL_dpsi0':dL_dpsi0,
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'dL_dpsi1':dL_dpsi1,
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'dL_dpsi2':dL_dpsi2,
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'dL_dthetaL':dL_dthetaL}
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else:
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grad_dict = {'dL_dKmm': dL_dKmm,
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'dL_dKdiag':dL_dpsi0,
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'dL_dKnm':dL_dpsi1,
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'dL_dthetaL':dL_dthetaL}
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#get sufficient things for posterior prediction
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#TODO: do we really want to do this in the loop?
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if VVT_factor.shape[1] == Y.shape[1]:
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woodbury_vector = Cpsi1Vf # == Cpsi1V
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else:
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print('foobar')
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psi1V = np.dot(mu_tilde[:,None].T*beta, psi1).T
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tmp, _ = dtrtrs(Lm, psi1V, lower=1, trans=0)
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tmp, _ = dpotrs(LB, tmp, lower=1)
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woodbury_vector, _ = dtrtrs(Lm, tmp, lower=1, trans=1)
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Bi, _ = dpotri(LB, lower=1)
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symmetrify(Bi)
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Bi = -dpotri(LB, lower=1)[0]
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diag.add(Bi, 1)
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woodbury_inv = backsub_both_sides(Lm, Bi)
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#construct a posterior object
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post = Posterior(woodbury_inv=woodbury_inv, woodbury_vector=woodbury_vector, K=Kmm, mean=None, cov=None, K_chol=Lm)
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return post, log_marginal, grad_dict
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return super(EPDTC, self).inference(kern, X, Z, likelihood, mu_tilde,
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mean_function=mean_function,
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Y_metadata=Y_metadata,
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beta=tau_tilde,
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Lm=Lm, dL_dKmm=dL_dKmm,
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psi0=psi0, psi1=psi1, psi2=psi2)
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def expectation_propagation(self, Kmm, Kmn, Y, likelihood, Y_metadata):
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num_data, output_dim = Y.shape
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assert output_dim == 1, "This EP methods only works for 1D outputs"
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num_data, data_dim = Y.shape
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assert data_dim == 1, "This EP methods only works for 1D outputs"
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LLT0 = Kmm.copy()
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#diag.add(LLT0, 1e-8)
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KmnKnm = np.dot(Kmn,Kmn.T)
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Lm = jitchol(Kmm)
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Lmi = dtrtrs(Lm,np.eye(Lm.shape[0]))[0] #chol_inv(Lm)
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Lm = jitchol(LLT0)
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Lmi = dtrtri(Lm)
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Kmmi = np.dot(Lmi.T,Lmi)
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KmmiKmn = np.dot(Kmmi,Kmn)
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Qnn_diag = np.sum(Kmn*KmmiKmn,-2)
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LLT0 = Kmm.copy()
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#Initial values - Posterior distribution parameters: q(f|X,Y) = N(f|mu,Sigma)
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mu = np.zeros(num_data)
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LLT = Kmm.copy() #Sigma = K.copy()
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Sigma_diag = Qnn_diag.copy()
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Sigma_diag = Qnn_diag.copy() + 1e-8
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#Initial values - Marginal moments
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Z_hat = np.empty(num_data,dtype=np.float64)
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mu_hat = np.empty(num_data,dtype=np.float64)
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sigma2_hat = np.empty(num_data,dtype=np.float64)
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Z_hat = np.zeros(num_data,dtype=np.float64)
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mu_hat = np.zeros(num_data,dtype=np.float64)
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sigma2_hat = np.zeros(num_data,dtype=np.float64)
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#initial values - Gaussian factors
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if self.old_mutilde is None:
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tau_tilde, mu_tilde, v_tilde = np.zeros((3, num_data))
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else:
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assert old_mutilde.size == num_data, "data size mis-match: did you change the data? try resetting!"
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assert self.old_mutilde.size == num_data, "data size mis-match: did you change the data? try resetting!"
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mu_tilde, v_tilde = self.old_mutilde, self.old_vtilde
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tau_tilde = v_tilde/mu_tilde
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#Approximation
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tau_diff = self.epsilon + 1.
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v_diff = self.epsilon + 1.
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iterations = 0
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iterations = 0
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tau_tilde_old = 0.
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v_tilde_old = 0.
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update_order = np.random.permutation(num_data)
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while (tau_diff > self.epsilon) or (v_diff > self.epsilon):
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update_order = np.random.permutation(num_data)
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for i in update_order:
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#Cavity distribution parameters
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tau_cav = 1./Sigma_diag[i] - self.eta*tau_tilde[i]
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@ -252,7 +105,7 @@ class EPDTC(LatentFunctionInference):
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#DSYR(Sigma, Sigma[:,i].copy(), -delta_tau/(1.+ delta_tau*Sigma[i,i]))
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DSYR(LLT,Kmn[:,i].copy(),delta_tau)
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L = jitchol(LLT)
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L = jitchol(LLT+np.eye(LLT.shape[0])*1e-7)
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V,info = dtrtrs(L,Kmn,lower=1)
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Sigma_diag = np.sum(V*V,-2)
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@ -262,9 +115,10 @@ class EPDTC(LatentFunctionInference):
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#(re) compute Sigma and mu using full Cholesky decompy
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LLT = LLT0 + np.dot(Kmn*tau_tilde[None,:],Kmn.T)
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#diag.add(LLT, 1e-8)
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L = jitchol(LLT)
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V,info = dtrtrs(L,Kmn,lower=1)
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V2,info = dtrtrs(L.T,V,lower=0)
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V, _ = dtrtrs(L,Kmn,lower=1)
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V2, _ = dtrtrs(L.T,V,lower=0)
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#Sigma_diag = np.sum(V*V,-2)
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#Knmv_tilde = np.dot(Kmn,v_tilde)
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#mu = np.dot(V2.T,Knmv_tilde)
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@ -272,81 +126,17 @@ class EPDTC(LatentFunctionInference):
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mu = np.dot(Sigma,v_tilde)
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#monitor convergence
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if iterations>0:
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tau_diff = np.mean(np.square(tau_tilde-tau_tilde_old))
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v_diff = np.mean(np.square(v_tilde-v_tilde_old))
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#if iterations>0:
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tau_diff = np.mean(np.square(tau_tilde-tau_tilde_old))
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v_diff = np.mean(np.square(v_tilde-v_tilde_old))
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tau_tilde_old = tau_tilde.copy()
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v_tilde_old = v_tilde.copy()
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# Only to while loop once:?
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tau_diff = 0
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v_diff = 0
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iterations += 1
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mu_tilde = v_tilde/tau_tilde
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return mu, Sigma, mu_tilde, tau_tilde, Z_hat
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def _compute_dL_dpsi(num_inducing, num_data, output_dim, beta, Lm, VVT_factor, Cpsi1Vf, DBi_plus_BiPBi, psi1, het_noise, uncertain_inputs):
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dL_dpsi0 = -0.5 * output_dim * (beta[:,None] * np.ones([num_data, 1])).flatten()
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dL_dpsi1 = np.dot(VVT_factor, Cpsi1Vf.T)
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dL_dpsi2_beta = 0.5 * backsub_both_sides(Lm, output_dim * np.eye(num_inducing) - DBi_plus_BiPBi)
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if het_noise:
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if uncertain_inputs:
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dL_dpsi2 = beta[:, None, None] * dL_dpsi2_beta[None, :, :]
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else:
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dL_dpsi1 += 2.*np.dot(dL_dpsi2_beta, (psi1 * beta.reshape(num_data, 1)).T).T
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dL_dpsi2 = None
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else:
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dL_dpsi2 = beta * dL_dpsi2_beta
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if uncertain_inputs:
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# repeat for each of the N psi_2 matrices
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dL_dpsi2 = np.repeat(dL_dpsi2[None, :, :], num_data, axis=0)
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else:
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# subsume back into psi1 (==Kmn)
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dL_dpsi1 += 2.*np.dot(psi1, dL_dpsi2)
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dL_dpsi2 = None
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return dL_dpsi0, dL_dpsi1, dL_dpsi2
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def _compute_dL_dR(likelihood, het_noise, uncertain_inputs, LB, _LBi_Lmi_psi1Vf, DBi_plus_BiPBi, Lm, A, psi0, psi1, beta, data_fit, num_data, output_dim, trYYT, Y):
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# the partial derivative vector for the likelihood
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if likelihood.size == 0:
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# save computation here.
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dL_dR = None
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elif het_noise:
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if uncertain_inputs:
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raise NotImplementedError("heteroscedatic derivates with uncertain inputs not implemented")
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else:
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#from ...util.linalg import chol_inv
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#LBi = chol_inv(LB)
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||||
LBi, _ = dtrtrs(LB,np.eye(LB.shape[0]))
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||||
Lmi_psi1, nil = dtrtrs(Lm, psi1.T, lower=1, trans=0)
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_LBi_Lmi_psi1, _ = dtrtrs(LB, Lmi_psi1, lower=1, trans=0)
|
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|
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dL_dR = -0.5 * beta + 0.5 * (beta*Y)**2
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dL_dR += 0.5 * output_dim * (psi0 - np.sum(Lmi_psi1**2,0))[:,None] * beta**2
|
||||
|
||||
dL_dR += 0.5*np.sum(mdot(LBi.T,LBi,Lmi_psi1)*Lmi_psi1,0)[:,None]*beta**2
|
||||
|
||||
dL_dR += -np.dot(_LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T * Y * beta**2
|
||||
dL_dR += 0.5*np.dot(_LBi_Lmi_psi1Vf.T,_LBi_Lmi_psi1).T**2 * beta**2
|
||||
else:
|
||||
# likelihood is not heteroscedatic
|
||||
dL_dR = -0.5 * num_data * output_dim * beta + 0.5 * trYYT * beta ** 2
|
||||
dL_dR += 0.5 * output_dim * (psi0.sum() * beta ** 2 - np.trace(A) * beta)
|
||||
dL_dR += beta * (0.5 * np.sum(A * DBi_plus_BiPBi) - data_fit)
|
||||
return dL_dR
|
||||
|
||||
def _compute_log_marginal_likelihood(likelihood, num_data, output_dim, beta, het_noise, psi0, A, LB, trYYT, data_fit,Y):
|
||||
#compute log marginal likelihood
|
||||
if het_noise:
|
||||
lik_1 = -0.5 * num_data * output_dim * np.log(2. * np.pi) + 0.5 * np.sum(np.log(beta)) - 0.5 * np.sum(beta * np.square(Y).sum(axis=-1))
|
||||
lik_2 = -0.5 * output_dim * (np.sum(beta.flatten() * psi0) - np.trace(A))
|
||||
else:
|
||||
lik_1 = -0.5 * num_data * output_dim * (np.log(2. * np.pi) - np.log(beta)) - 0.5 * beta * trYYT
|
||||
lik_2 = -0.5 * output_dim * (np.sum(beta * psi0) - np.trace(A))
|
||||
lik_3 = -output_dim * (np.sum(np.log(np.diag(LB))))
|
||||
lik_4 = 0.5 * data_fit
|
||||
log_marginal = lik_1 + lik_2 + lik_3 + lik_4
|
||||
return log_marginal
|
||||
return mu, Sigma, ObsAr(mu_tilde[:,None]), tau_tilde, Z_hat
|
||||
|
|
|
|||
|
|
@ -64,31 +64,30 @@ class VarDTC(LatentFunctionInference):
|
|||
def get_VVTfactor(self, Y, prec):
|
||||
return Y * prec # TODO chache this, and make it effective
|
||||
|
||||
def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None):
|
||||
def inference(self, kern, X, Z, likelihood, Y, Y_metadata=None, mean_function=None, beta=None, Lm=None, dL_dKmm=None, psi0=None, psi1=None, psi2=None):
|
||||
assert mean_function is None, "inference with a mean function not implemented"
|
||||
|
||||
num_data, output_dim = Y.shape
|
||||
num_inducing = Z.shape[0]
|
||||
|
||||
_, output_dim = Y.shape
|
||||
uncertain_inputs = isinstance(X, VariationalPosterior)
|
||||
|
||||
#see whether we've got a different noise variance for each datum
|
||||
beta = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), 1e-6)
|
||||
# VVT_factor is a matrix such that tdot(VVT_factor) = VVT...this is for efficiency!
|
||||
#self.YYTfactor = self.get_YYTfactor(Y)
|
||||
#VVT_factor = self.get_VVTfactor(self.YYTfactor, beta)
|
||||
het_noise = beta.size > 1
|
||||
if beta is None:
|
||||
#assume Gaussian likelihood
|
||||
beta = 1./np.fmax(likelihood.gaussian_variance(Y_metadata), self.const_jitter)
|
||||
|
||||
if beta.ndim == 1:
|
||||
beta = beta[:, None]
|
||||
het_noise = beta.size > 1
|
||||
|
||||
VVT_factor = beta*Y
|
||||
#VVT_factor = beta*Y
|
||||
trYYT = self.get_trYYT(Y)
|
||||
|
||||
# do the inference:
|
||||
num_inducing = Z.shape[0]
|
||||
num_data = Y.shape[0]
|
||||
# kernel computations, using BGPLVM notation
|
||||
|
||||
Kmm = kern.K(Z).copy()
|
||||
diag.add(Kmm, self.const_jitter)
|
||||
if Lm is None:
|
||||
Kmm = kern.K(Z).copy()
|
||||
diag.add(Kmm, self.const_jitter)
|
||||
Lm = jitchol(Kmm)
|
||||
|
||||
# The rather complex computations of A, and the psi stats
|
||||
|
|
@ -99,15 +98,16 @@ class VarDTC(LatentFunctionInference):
|
|||
psi1 = kern.psi1(Z, X)
|
||||
if het_noise:
|
||||
if psi2 is None:
|
||||
assert len(psi2.shape) == 3 # Need to have not summed out N
|
||||
#FIXME: Need testing
|
||||
psi2_beta = np.sum([psi2[X[i:i+1,:], :, :] * beta_i for i,beta_i in enumerate(beta)],0)
|
||||
psi2_beta = (kern.psi2n(Z, X) * beta[:, :, None]).sum(0)
|
||||
else:
|
||||
psi2_beta = np.sum([kern.psi2(Z,X[i:i+1,:]) * beta_i for i,beta_i in enumerate(beta)],0)
|
||||
psi2_beta = (psi2 * beta[:, :, None]).sum(0)
|
||||
else:
|
||||
if psi2 is None:
|
||||
psi2 = kern.psi2(Z,X)
|
||||
psi2_beta = psi2 * beta
|
||||
psi2_beta = kern.psi2(Z,X) * beta
|
||||
elif psi2.ndim == 3:
|
||||
psi2_beta = psi2.sum(0) * beta
|
||||
else:
|
||||
psi2_beta = psi2 * beta
|
||||
LmInv = dtrtri(Lm)
|
||||
A = LmInv.dot(psi2_beta.dot(LmInv.T))
|
||||
else:
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue