mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-06-05 14:55:15 +02:00
Merge branch 'devel' of github.com:SheffieldML/GPy into devel
This commit is contained in:
Max Zwiessele
commit
b3fe82718a
7 changed files with 234 additions and 91 deletions
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@ -13,24 +13,30 @@ from numpy.linalg.linalg import LinAlgError
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import itertools
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from matplotlib.colors import colorConverter
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from matplotlib.figure import SubplotParams
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from GPy.inference.optimization import SCG
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class Bayesian_GPLVM(sparse_GP, GPLVM):
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"""
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Bayesian Gaussian Process Latent Variable Model
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:param Y: observed data
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:type Y: np.ndarray
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:param Y: observed data (np.ndarray) or GPy.likelihood
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:type Y: np.ndarray| GPy.likelihood instance
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:param Q: latent dimensionality
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:type Q: int
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:param init: initialisation method for the latent space
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:type init: 'PCA'|'random'
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"""
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def __init__(self, Y, Q, X=None, X_variance=None, init='PCA', M=10,
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def __init__(self, likelihood_or_Y, Q, X=None, X_variance=None, init='PCA', M=10,
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Z=None, kernel=None, oldpsave=10, _debug=False,
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**kwargs):
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if type(likelihood_or_Y) is np.ndarray:
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likelihood = Gaussian(likelihood_or_Y)
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else:
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likelihood = likelihood_or_Y
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if X == None:
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X = self.initialise_latent(init, Q, Y)
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X = self.initialise_latent(init, Q, likelihood.Y)
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if X_variance is None:
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X_variance = np.clip((np.ones_like(X) * 0.5) + .01 * np.random.randn(*X.shape), 0.001, 1)
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@ -56,7 +62,7 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
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self._savedpsiKmm = []
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self._savedABCD = []
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sparse_GP.__init__(self, X, Gaussian(Y), kernel, Z=Z, X_variance=X_variance, **kwargs)
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sparse_GP.__init__(self, X, likelihood, kernel, Z=Z, X_variance=X_variance, **kwargs)
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@property
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def oldps(self):
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@ -184,16 +190,46 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
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ax.plot(self.Z[:, input_1], self.Z[:, input_2], '^w')
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return ax
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def do_test_latents(self, Y):
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"""
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Compute the latent representation for a set of new points Y
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Notes:
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This will only work with a univariate Gaussian likelihood (for now)
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"""
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assert not self.likelihood.is_heteroscedastic
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N_test = Y.shape[0]
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Q = self.Z.shape[1]
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means = np.zeros((N_test,Q))
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covars = np.zeros((N_test,Q))
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dpsi0 = - 0.5 * self.D * self.likelihood.precision
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dpsi2 = self.dL_dpsi2[0][None,:,:] # TODO: this may change if we ignore het. likelihoods
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V = self.likelihood.precision*Y
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dpsi1 = np.dot(self.Cpsi1V,V.T)
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start = np.zeros(self.Q*2)
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for n,dpsi1_n in enumerate(dpsi1.T[:,:,None]):
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args = (self.kern,self.Z,dpsi0,dpsi1_n,dpsi2)
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xopt,fopt,neval,status = SCG(f=latent_cost, gradf=latent_grad, x=start, optargs=args, display = False)
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mu,log_S = xopt.reshape(2,1,-1)
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means[n] = mu[0].copy()
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covars[n] = np.exp(log_S[0]).copy()
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return means, covars
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def plot_X_1d(self, fig=None, axes=None, fig_num="LVM mu S 1d", colors=None):
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"""
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Plot latent space X in 1D:
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-if fig is given, create Q subplots in fig and plot in these
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-if axes is given plot Q 1D latent space plots of X into each `axis`
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-if neither fig nor axes is given create a figure with fig_num and plot in there
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colors:
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colors of different latent space dimensions Q
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"""
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import pylab
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@ -483,3 +519,63 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
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cidd = figs[0].canvas.mpl_connect('motion_notify_event', motion)
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return ax1, ax2, ax3, ax4, ax5 # , ax6, ax7
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def latent_cost_and_grad(mu_S, kern,Z, dL_dpsi0, dL_dpsi1, dL_dpsi2):
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"""
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objective function for fitting the latent variables for test points
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(negative log-likelihood: should be minimised!)
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"""
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mu,log_S = mu_S.reshape(2,1,-1)
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S = np.exp(log_S)
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psi0 = kern.psi0(Z,mu,S)
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psi1 = kern.psi1(Z,mu,S)
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psi2 = kern.psi2(Z,mu,S)
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lik = dL_dpsi0*psi0 + np.dot(dL_dpsi1.flatten(),psi1.flatten()) + np.dot(dL_dpsi2.flatten(),psi2.flatten()) - 0.5*np.sum(np.square(mu) + S) + 0.5*np.sum(log_S)
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mu0, S0 = kern.dpsi0_dmuS(dL_dpsi0,Z,mu,S)
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mu1, S1 = kern.dpsi1_dmuS(dL_dpsi1,Z,mu,S)
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mu2, S2 = kern.dpsi2_dmuS(dL_dpsi2,Z,mu,S)
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dmu = mu0 + mu1 + mu2 - mu
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#dS = S0 + S1 + S2 -0.5 + .5/S
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dlnS = S*(S0 + S1 + S2 -0.5) + .5
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return -lik,-np.hstack((dmu.flatten(),dlnS.flatten()))
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def latent_cost(mu_S, kern,Z, dL_dpsi0, dL_dpsi1, dL_dpsi2):
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"""
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objective function for fitting the latent variables (negative log-likelihood: should be minimised!)
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This is the same as latent_cost_and_grad but only for the objective
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"""
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mu,log_S = mu_S.reshape(2,1,-1)
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S = np.exp(log_S)
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psi0 = kern.psi0(Z,mu,S)
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psi1 = kern.psi1(Z,mu,S)
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psi2 = kern.psi2(Z,mu,S)
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lik = dL_dpsi0*psi0 + np.dot(dL_dpsi1.flatten(),psi1.flatten()) + np.dot(dL_dpsi2.flatten(),psi2.flatten()) - 0.5*np.sum(np.square(mu) + S) + 0.5*np.sum(log_S)
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return -float(lik)
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def latent_grad(mu_S, kern,Z, dL_dpsi0, dL_dpsi1, dL_dpsi2):
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"""
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This is the same as latent_cost_and_grad but only for the grad
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"""
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mu,log_S = mu_S.reshape(2,1,-1)
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S = np.exp(log_S)
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mu0, S0 = kern.dpsi0_dmuS(dL_dpsi0,Z,mu,S)
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mu1, S1 = kern.dpsi1_dmuS(dL_dpsi1,Z,mu,S)
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mu2, S2 = kern.dpsi2_dmuS(dL_dpsi2,Z,mu,S)
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dmu = mu0 + mu1 + mu2 - mu
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#dS = S0 + S1 + S2 -0.5 + .5/S
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dlnS = S*(S0 + S1 + S2 -0.5) + .5
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return -np.hstack((dmu.flatten(),dlnS.flatten()))
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@ -173,7 +173,7 @@ class GP(model):
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"""
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# normalize X values
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Xnew = (Xnew.copy() - self._Xmean) / self._Xstd
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mu, var = self._raw_predict(Xnew, which_parts, full_cov)
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mu, var = self._raw_predict(Xnew, which_parts=which_parts, full_cov=full_cov)
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# now push through likelihood
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mean, var, _025pm, _975pm = self.likelihood.predictive_values(mu, var, full_cov)
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@ -15,11 +15,11 @@ import pylab
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class MRD(model):
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"""
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Do MRD on given Datasets in Ylist.
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All Ys in Ylist are in [N x Dn], where Dn can be different per Yn,
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All Ys in likelihood_list are in [N x Dn], where Dn can be different per Yn,
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N must be shared across datasets though.
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:param Ylist...: observed datasets
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:type Ylist: [np.ndarray]
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:param likelihood_list...: likelihoods of observed datasets
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:type likelihood_list: [GPy.likelihood]
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:param names: names for different gplvm models
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:type names: [str]
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:param Q: latent dimensionality (will raise
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@ -41,8 +41,41 @@ class MRD(model):
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:param kernel:
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kernel to use
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"""
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def __init__(self,likelihood_list,Q,M=10,names=None,kernels=None,initX='PCA',initz='permute',_debug=False, **kwargs):
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if names is None:
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self.names = ["{}".format(i + 1) for i in range(len(likelihood_list))]
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def __init__(self, *Ylist, **kwargs):
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#sort out the kernels
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if kernels is None:
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kernels = [None]*len(likelihood_list)
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elif isinstance(kernels,kern.kern):
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kernels = [kernels.copy() for i in range(len(likelihood_list))]
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else:
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assert len(kernels)==len(likelihood_list), "need one kernel per output"
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assert all([isinstance(k, kern.kern) for k in kernels]), "invalid kernel object detected!"
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self.Q = Q
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self.M = M
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self.N = self.gref.N
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self.NQ = self.N * self.Q
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self.MQ = self.M * self.Q
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self._init = True
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X = self._init_X(initx, likelihood_list)
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Z = self._init_Z(initz, X)
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self.bgplvms = [Bayesian_GPLVM(l, k, X=X, Z=Z, M=self.M, **kwargs) for l,k in zip(likelihood_list,kernels)]
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del self._init
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self.gref = self.bgplvms[0]
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nparams = numpy.array([0] + [sparse_GP._get_params(g).size - g.Z.size for g in self.bgplvms])
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self.nparams = nparams.cumsum()
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model.__init__(self) # @UndefinedVariable
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def __init__(self, *likelihood_list, **kwargs):
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if kwargs.has_key("_debug"):
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self._debug = kwargs['_debug']
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del kwargs['_debug']
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@ -52,7 +85,7 @@ class MRD(model):
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self.names = kwargs['names']
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del kwargs['names']
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else:
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self.names = ["{}".format(i + 1) for i in range(len(Ylist))]
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self.names = ["{}".format(i + 1) for i in range(len(likelihood_list))]
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if kwargs.has_key('kernel'):
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kernel = kwargs['kernel']
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k = lambda: kernel.copy()
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@ -80,9 +113,10 @@ class MRD(model):
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self.M = 10
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self._init = True
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X = self._init_X(initx, Ylist)
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X = self._init_X(initx, likelihood_list)
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Z = self._init_Z(initz, X)
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self.bgplvms = [Bayesian_GPLVM(Y, kernel=k(), X=X, Z=Z, M=self.M, **kwargs) for Y in Ylist]
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self.bgplvms = [Bayesian_GPLVM(Y, kernel=k(), X=X, Z=Z, M=self.M, **kwargs) for Y in likelihood_list]
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del self._init
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self.gref = self.bgplvms[0]
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@ -126,11 +160,11 @@ class MRD(model):
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if not self._init:
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raise AttributeError("bgplvm list not initialized")
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@property
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def Ylist(self):
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def likelihood_list(self):
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return [g.likelihood.Y for g in self.bgplvms]
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@Ylist.setter
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def Ylist(self, Ylist):
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for g, Y in itertools.izip(self.bgplvms, Ylist):
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@likelihood_list.setter
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def likelihood_list(self, likelihood_list):
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for g, Y in itertools.izip(self.bgplvms, likelihood_list):
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g.likelihood.Y = Y
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@property
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@ -152,7 +186,7 @@ class MRD(model):
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def randomize(self, initx='concat', initz='permute', *args, **kw):
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super(MRD, self).randomize(*args, **kw)
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self._init_X(initx, self.Ylist)
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self._init_X(initx, self.likelihood_list)
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self._init_Z(initz, self.X)
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def _get_param_names(self):
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@ -225,6 +259,10 @@ class MRD(model):
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# g._computations()
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def update_likelihood_approximation(self):#TODO: object oriented vs script base
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for bgplvm in self.bgplvms:
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bgplvm.update_likelihood_approximation()
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def log_likelihood(self):
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ll = -self.gref.KL_divergence()
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for g in self.bgplvms:
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@ -246,17 +284,18 @@ class MRD(model):
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partial=g.partial_for_likelihood)]) \
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for g in self.bgplvms])))
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def _init_X(self, init='PCA', Ylist=None):
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if Ylist is None:
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Ylist = self.Ylist
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def _init_X(self, init='PCA', likelihood_list=None):
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if likelihood_list is None:
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likelihood_list = self.likelihood_list
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if init in "PCA_single":
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X = numpy.zeros((Ylist[0].shape[0], self.Q))
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for qs, Y in itertools.izip(numpy.array_split(numpy.arange(self.Q), len(Ylist)), Ylist):
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X[:, qs] = PCA(Y, len(qs))[0]
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X = numpy.zeros((likelihood_list[0].Y.shape[0], self.Q))
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for qs, Y in itertools.izip(numpy.array_split(numpy.arange(self.Q), len(likelihood_list)), likelihood_list):
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X[:, qs] = PCA(Y.Y, len(qs))[0]
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elif init in "PCA_concat":
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X = PCA(numpy.hstack(Ylist), self.Q)[0]
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X = PCA(numpy.hstack([l.Y for l in likelihood_list]), self.Q)[0]
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#X = PCA(numpy.hstack(likelihood_list), self.Q)[0]
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else: # init == 'random':
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X = numpy.random.randn(Ylist[0].shape[0], self.Q)
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X = numpy.random.randn(likelihood_list[0].Y.shape[0], self.Q)
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self.X = X
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return X
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@ -294,8 +333,8 @@ class MRD(model):
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fig = self._handle_plotting(fig_num, axes, lambda i, g, ax: ax.imshow(g.X))
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return fig
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def plot_predict(self, fig_num="MRD Predictions", axes=None):
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fig = self._handle_plotting(fig_num, axes, lambda i, g, ax: ax.imshow(g.predict(g.X)[0]))
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def plot_predict(self, fig_num="MRD Predictions", axes=None, **kwargs):
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fig = self._handle_plotting(fig_num, axes, lambda i, g, ax: ax.imshow(g.predict(g.X)[0],**kwargs))
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return fig
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def plot_scales(self, fig_num="MRD Scales", axes=None, *args, **kwargs):
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@ -8,6 +8,7 @@ from ..util.plot import gpplot
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from .. import kern
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from GP import GP
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from scipy import linalg
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from ..likelihoods import Gaussian
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class sparse_GP(GP):
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"""
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@ -172,19 +173,19 @@ class sparse_GP(GP):
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For a Gaussian likelihood, no iteration is required:
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this function does nothing
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"""
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if self.has_uncertain_inputs:
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Lmi = chol_inv(self.Lm)
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Kmmi = tdot(Lmi.T)
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diag_tr_psi2Kmmi = np.array([np.trace(psi2_Kmmi) for psi2_Kmmi in np.dot(self.psi2,Kmmi)])
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self.likelihood.fit_FITC(self.Kmm,self.psi1,diag_tr_psi2Kmmi) #This uses the fit_FITC code, but does not perfomr a FITC-EP.#TODO solve potential confusion
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#raise NotImplementedError, "EP approximation not implemented for uncertain inputs"
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else:
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self.likelihood.fit_DTC(self.Kmm, self.psi1)
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# self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
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self._set_params(self._get_params()) # update the GP
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if not isinstance(self.likelihood,Gaussian): #Updates not needed for Gaussian likelihood
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self.likelihood.restart() #TODO check consistency with pseudo_EP
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if self.has_uncertain_inputs:
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Lmi = chol_inv(self.Lm)
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Kmmi = tdot(Lmi.T)
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diag_tr_psi2Kmmi = np.array([np.trace(psi2_Kmmi) for psi2_Kmmi in np.dot(self.psi2,Kmmi)])
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self.likelihood.fit_FITC(self.Kmm,self.psi1,diag_tr_psi2Kmmi) #This uses the fit_FITC code, but does not perfomr a FITC-EP.#TODO solve potential confusion
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#raise NotImplementedError, "EP approximation not implemented for uncertain inputs"
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else:
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self.likelihood.fit_DTC(self.Kmm, self.psi1)
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# self.likelihood.fit_FITC(self.Kmm,self.psi1,self.psi0)
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self._set_params(self._get_params()) # update the GP
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def _log_likelihood_gradients(self):
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return np.hstack((self.dL_dZ().flatten(), self.dL_dtheta(), self.likelihood._gradients(partial=self.partial_for_likelihood)))
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@ -216,20 +217,33 @@ class sparse_GP(GP):
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dL_dZ += self.kern.dK_dX(self.dL_dpsi1, self.Z, self.X)
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return dL_dZ
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def _raw_predict(self, Xnew, which_parts='all', full_cov=False):
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def _raw_predict(self, Xnew, X_variance_new=None, which_parts='all', full_cov=False):
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"""Internal helper function for making predictions, does not account for normalization"""
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Bi, _ = linalg.lapack.flapack.dpotri(self.LB, lower=0) # WTH? this lower switch should be 1, but that doesn't work!
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symmetrify(Bi)
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Kmmi_LmiBLmi = backsub_both_sides(self.Lm, np.eye(self.M) - Bi)
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||||
Kx = self.kern.K(self.Z, Xnew, which_parts=which_parts)
|
||||
mu = np.dot(Kx.T, self.Cpsi1V) # / self.scale_factor)
|
||||
if full_cov:
|
||||
Kxx = self.kern.K(Xnew, which_parts=which_parts)
|
||||
var = Kxx - mdot(Kx.T, Kmmi_LmiBLmi, Kx) # NOTE this won't work for plotting
|
||||
if X_variance_new is None:
|
||||
Kx = self.kern.K(self.Z, Xnew, which_parts=which_parts)
|
||||
mu = np.dot(Kx.T, self.Cpsi1V)
|
||||
if full_cov:
|
||||
Kxx = self.kern.K(Xnew, which_parts=which_parts)
|
||||
var = Kxx - mdot(Kx.T, Kmmi_LmiBLmi, Kx) # NOTE this won't work for plotting
|
||||
else:
|
||||
Kxx = self.kern.Kdiag(Xnew, which_parts=which_parts)
|
||||
var = Kxx - np.sum(Kx * np.dot(Kmmi_LmiBLmi, Kx), 0)
|
||||
else:
|
||||
Kxx = self.kern.Kdiag(Xnew, which_parts=which_parts)
|
||||
var = Kxx - np.sum(Kx * np.dot(Kmmi_LmiBLmi, Kx), 0)
|
||||
# assert which_parts=='all', "swithching out parts of variational kernels is not implemented"
|
||||
Kx = self.kern.psi1(self.Z, Xnew, X_variance_new)#, which_parts=which_parts) TODO: which_parts
|
||||
mu = np.dot(Kx, self.Cpsi1V)
|
||||
if full_cov:
|
||||
raise NotImplementedError, "TODO"
|
||||
else:
|
||||
Kxx = self.kern.psi0(self.Z,Xnew,X_variance_new)
|
||||
psi2 = self.kern.psi2(self.Z,Xnew,X_variance_new)
|
||||
var = Kxx - np.sum(np.sum(psi2*Kmmi_LmiBLmi[None,:,:],1),1)
|
||||
|
||||
return mu, var[:, None]
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue