mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-05-24 14:15:14 +02:00
Merge branch 'devel' of github.com:SheffieldML/GPy into devel
This commit is contained in:
Nicolo Fusi
commit
fa523c3fce
7 changed files with 105 additions and 41 deletions
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@ -96,7 +96,8 @@ class GP(GPBase):
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model for a new variable Y* = v_tilde/tau_tilde, with a covariance
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matrix K* = K + diag(1./tau_tilde) plus a normalization term.
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"""
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return - 0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) - 0.5 * self.output_dim * self.K_logdet + self._model_fit_term() + self.likelihood.Z
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return (-0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) -
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0.5 * self.output_dim * self.K_logdet + self._model_fit_term() + self.likelihood.Z)
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def _log_likelihood_gradients(self):
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@ -108,7 +108,7 @@ class SparseGP(GPBase):
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self.B = np.eye(self.num_inducing) + self.A
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self.LB = jitchol(self.B)
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#VVT_factor is a matrix such that tdot(VVT_factor) = VVT...this is for efficiency!
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# VVT_factor is a matrix such that tdot(VVT_factor) = VVT...this is for efficiency!
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self.psi1Vf = np.dot(self.psi1.T, self.likelihood.VVT_factor)
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# back substutue C into psi1Vf
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@ -163,7 +163,7 @@ class SparseGP(GPBase):
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def log_likelihood(self):
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""" Compute the (lower bound on the) log marginal likelihood """
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if self.likelihood.is_heteroscedastic:
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A = -0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.likelihood.V*self.likelihood.Y)
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A = -0.5 * self.num_data * self.output_dim * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.likelihood.V * self.likelihood.Y)
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B = -0.5 * self.output_dim * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A))
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else:
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A = -0.5 * self.num_data * self.output_dim * (np.log(2.*np.pi) - np.log(self.likelihood.precision)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
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@ -246,7 +246,7 @@ class SparseGP(GPBase):
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Kmmi_LmiBLmi = backsub_both_sides(self.Lm, np.eye(self.num_inducing) - Bi)
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if self.Cpsi1V is None:
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psi1V = np.dot(self.psi1.T,self.likelihood.V)
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psi1V = np.dot(self.psi1.T, self.likelihood.V)
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tmp, _ = dtrtrs(self.Lm, np.asfortranarray(psi1V), lower=1, trans=0)
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tmp, _ = dpotrs(self.LB, tmp, lower=1)
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self.Cpsi1V, _ = dtrtrs(self.Lm, tmp, lower=1, trans=1)
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@ -7,26 +7,29 @@ from matplotlib import pyplot as plt, cm
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import GPy
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from GPy.core.transformations import logexp
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from GPy.models.bayesian_gplvm import BayesianGPLVM
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from GPy.likelihoods.gaussian import Gaussian
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default_seed = np.random.seed(123344)
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def BGPLVM(seed=default_seed):
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N = 10
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num_inducing = 3
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Q = 2
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D = 4
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Q = 5
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D = 10
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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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lengthscales = np.random.rand(Q)
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k = GPy.kern.rbf(Q, .5, lengthscales, ARD=True) + GPy.kern.white(Q, 0.01)
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K = k.K(X)
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Y = np.random.multivariate_normal(np.zeros(N), K, Q).T
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lik = Gaussian(Y, normalize=True)
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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_inv(Q, ARD=True) + GPy.kern.bias(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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m = GPy.models.BayesianGPLVM(Y, Q, kernel=k, num_inducing=num_inducing)
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m = GPy.models.BayesianGPLVM(lik, Q, kernel=k, num_inducing=num_inducing)
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m.lengthscales = lengthscales
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# m.constrain_positive('(rbf|bias|noise|white|S)')
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# m.constrain_fixed('S', 1)
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@ -37,8 +40,8 @@ def BGPLVM(seed=default_seed):
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# m.optimize(messages = 1)
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# m.plot()
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# pb.title('After optimisation')
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m.randomize()
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m.checkgrad(verbose=1)
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# m.randomize()
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# m.checkgrad(verbose=1)
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return m
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@ -70,16 +73,16 @@ def sparseGPLVM_oil(optimize=True, N=100, Q=6, num_inducing=15, max_iters=50):
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# create simple GP model
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kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q)
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m = GPy.models.SparseGPLVM(Y, Q, kernel=kernel, num_inducing = num_inducing)
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m = GPy.models.SparseGPLVM(Y, Q, kernel=kernel, num_inducing=num_inducing)
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m.data_labels = data['Y'].argmax(axis=1)
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# optimize
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if optimize:
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m.optimize('scg', messages=1, max_iters = max_iters)
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m.optimize('scg', messages=1, max_iters=max_iters)
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# plot
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print(m)
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#m.plot_latent(labels=m.data_labels)
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# m.plot_latent(labels=m.data_labels)
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return m
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def swiss_roll(optimize=True, N=1000, num_inducing=15, Q=4, sigma=.2, plot=False):
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@ -136,12 +139,13 @@ def swiss_roll(optimize=True, N=1000, num_inducing=15, Q=4, sigma=.2, plot=False
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m.optimize('scg', messages=1)
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return m
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def BGPLVM_oil(optimize=True, N=200, Q=10, num_inducing=15, max_iters=50, plot=False, **k):
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def BGPLVM_oil(optimize=True, N=200, Q=10, num_inducing=15, max_iters=150, plot=False, **k):
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np.random.seed(0)
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data = GPy.util.datasets.oil()
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# create simple GP model
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kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2))
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kernel = GPy.kern.rbf_inv(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2))
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kernel += GPy.kern.rbf_inv(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2))
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Y = data['X'][:N]
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Yn = Y - Y.mean(0)
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Yn /= Yn.std(0)
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@ -150,14 +154,14 @@ def BGPLVM_oil(optimize=True, N=200, Q=10, num_inducing=15, max_iters=50, plot=F
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m.data_labels = data['Y'][:N].argmax(axis=1)
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# m.constrain('variance|leng', logexp_clipped())
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m['.*lengt'] = 1. # m.X.var(0).max() / m.X.var(0)
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# m['.*lengt'] = m.X.var(0).max() / m.X.var(0)
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m['noise'] = Yn.var() / 100.
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# optimize
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if optimize:
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m.constrain_fixed('noise')
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m.optimize('scg', messages=1, max_iters=100, gtol=.05)
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m.optimize('scg', messages=1, max_iters=200, gtol=.05)
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m.constrain_positive('noise')
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m.optimize('scg', messages=1, max_iters=max_iters, gtol=.05)
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@ -208,7 +212,7 @@ def _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim=False):
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Y1 += .3 * np.random.randn(*Y1.shape)
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Y2 += .2 * np.random.randn(*Y2.shape)
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Y3 += .1 * np.random.randn(*Y3.shape)
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Y3 += .25 * np.random.randn(*Y3.shape)
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Y1 -= Y1.mean(0)
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Y2 -= Y2.mean(0)
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@ -263,16 +267,16 @@ def bgplvm_simulation_matlab_compare():
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def bgplvm_simulation(optimize='scg',
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plot=True,
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max_iters=2e4):
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max_iters=2e4,
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plot_sim=False):
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# from GPy.core.transformations import logexp_clipped
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D1, D2, D3, N, num_inducing, Q = 15, 8, 8, 100, 3, 5
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slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot)
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D1, D2, D3, N, num_inducing, Q = 15, 5, 8, 300, 30, 6
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slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, num_inducing, Q, plot_sim)
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from GPy.models import mrd
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from GPy import kern
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reload(mrd); reload(kern)
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Y = Ylist[0]
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k = kern.linear(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2)) # + kern.bias(Q)
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@ -280,7 +284,6 @@ def bgplvm_simulation(optimize='scg',
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# m.constrain('variance|noise', logexp_clipped())
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m['noise'] = Y.var() / 100.
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m['linear_variance'] = .01
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if optimize:
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print "Optimizing model:"
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@ -346,7 +349,7 @@ def brendan_faces():
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def stick_play(range=None, frame_rate=15):
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data = GPy.util.datasets.stick()
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# optimize
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if range==None:
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if range == None:
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Y = data['Y'].copy()
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else:
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Y = data['Y'][range[0]:range[1], :].copy()
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@ -374,10 +377,10 @@ def stick_bgplvm(model=None):
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data = GPy.util.datasets.stick()
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Q = 6
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kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q, np.exp(-2)) + GPy.kern.white(Q, np.exp(-2))
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m = BayesianGPLVM(data['Y'], Q, init="PCA", num_inducing=20,kernel=kernel)
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m = BayesianGPLVM(data['Y'], Q, init="PCA", num_inducing=20, kernel=kernel)
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# optimize
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m.ensure_default_constraints()
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m.optimize(messages=1, max_f_eval=3000,xtol=1e-300,ftol=1e-300)
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m.optimize(messages=1, max_f_eval=3000, xtol=1e-300, ftol=1e-300)
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m._set_params(m._get_params())
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plt.clf, (latent_axes, sense_axes) = plt.subplots(1, 2)
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plt.sca(latent_axes)
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@ -66,12 +66,26 @@ class kern(Parameterized):
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Parameterized.setstate(self, state)
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def plot_ARD(self, fignum=None, ax=None, title=None):
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"""If an ARD kernel is present, it bar-plots the ARD parameters"""
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def plot_ARD(self, fignum=None, ax=None, title='', legend=False):
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"""If an ARD kernel is present, it bar-plots the ARD parameters,
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:param fignum: figure number of the plot
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:param ax: matplotlib axis to plot on
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:param title:
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title of the plot,
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pass '' to not print a title
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pass None for a generic title
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"""
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if ax is None:
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fig = pb.figure(fignum)
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ax = fig.add_subplot(111)
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from GPy.util import Tango
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from matplotlib.textpath import TextPath
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Tango.reset()
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xticklabels = []
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bars = []
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x0 = 0
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for p in self.parts:
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c = Tango.nextMedium()
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if hasattr(p, 'ARD') and p.ARD:
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if title is None:
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ax.set_title('ARD parameters, %s kernel' % p.name)
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@ -82,10 +96,32 @@ class kern(Parameterized):
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else:
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ard_params = 1. / p.lengthscale
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x = np.arange(len(ard_params))
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ax.bar(x - 0.4, ard_params)
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ax.set_xticks(x)
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ax.set_xticklabels([r"${}$".format(i) for i in x])
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x = np.arange(x0, x0 + len(ard_params))
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bars.append(ax.bar(x, ard_params, align='center', color=c, edgecolor='k', linewidth=1.2, label=p.name))
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xticklabels.extend([r"$\mathrm{{{name}}}\ {x}$".format(name=p.name, x=i) for i in np.arange(len(ard_params))])
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x0 += len(ard_params)
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x = np.arange(x0)
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for bar in bars:
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for patch, num in zip(bar.patches, np.arange(len(bar.patches))):
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height = patch.get_height()
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xi = patch.get_x() + patch.get_width() / 2.
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va = 'top'
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c = 'w'
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t = TextPath((0, 0), "${xi}$".format(xi=xi), rotation=0, usetex=True, ha='center')
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if patch.get_extents().height <= t.get_extents().height + 2:
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va = 'bottom'
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c = 'k'
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ax.text(xi, height, "${xi}$".format(xi=int(num)), color=c, rotation=0, ha='center', va=va)
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# for xi, t in zip(x, xticklabels):
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# ax.text(xi, maxi / 2, t, rotation=90, ha='center', va='center')
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# ax.set_xticklabels(xticklabels, rotation=17)
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ax.set_xticks([])
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ax.set_xlim(-.5, x0 - .5)
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if title is '':
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ax.legend(bbox_to_anchor=(0., 1.02, 1., .102), loc=3,
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ncol=len(bars), mode="expand", borderaxespad=0.)
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else:
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ax.legend()
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return ax
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def _transform_gradients(self, g):
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@ -361,6 +397,7 @@ class kern(Parameterized):
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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.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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@ -115,8 +115,8 @@ class BayesianGPLVM(SparseGP, GPLVM):
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self.dbound_dZtheta = SparseGP._log_likelihood_gradients(self)
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return np.hstack((self.dbound_dmuS.flatten(), self.dbound_dZtheta))
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def plot_latent(self, *args, **kwargs):
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return plot_latent.plot_latent(self, *args, **kwargs)
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def plot_latent(self, plot_inducing=True, *args, **kwargs):
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return plot_latent.plot_latent(self, plot_inducing=plot_inducing, *args, **kwargs)
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def do_test_latents(self, Y):
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"""
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@ -36,10 +36,10 @@ class GPLVM(GP):
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self.ensure_default_constraints()
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def initialise_latent(self, init, input_dim, Y):
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Xr = np.random.randn(Y.shape[0], input_dim)
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if init == 'PCA':
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return PCA(Y, input_dim)[0]
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else:
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return np.random.randn(Y.shape[0], input_dim)
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Xr[:, :Y.shape[1]] = PCA(Y, input_dim)[0]
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return Xr
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def getstate(self):
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return GP.getstate(self)
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@ -23,7 +23,7 @@ class GradientTests(unittest.TestCase):
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self.X2D = np.random.uniform(-3., 3., (40, 2))
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self.Y2D = np.sin(self.X2D[:, 0:1]) * np.sin(self.X2D[:, 1:2]) + np.random.randn(40, 1) * 0.05
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def check_model_with_white(self, kern, model_type='GPRegression', dimension=1):
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def check_model_with_white(self, kern, model_type='GPRegression', dimension=1, uncertain_inputs=False):
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# Get the correct gradients
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if dimension == 1:
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X = self.X1D
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@ -36,6 +36,9 @@ class GradientTests(unittest.TestCase):
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noise = GPy.kern.white(dimension)
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kern = kern + noise
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if uncertain_inputs:
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m = model_fit(X, Y, kernel=kern, X_variance=np.random.rand(X.shape[0], X.shape[1]))
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else:
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m = model_fit(X, Y, kernel=kern)
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m.randomize()
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# contrain all parameters to be positive
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@ -141,6 +144,26 @@ class GradientTests(unittest.TestCase):
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rbf = GPy.kern.rbf(2)
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self.check_model_with_white(rbf, model_type='SparseGPRegression', dimension=2)
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def test_SparseGPRegression_rbf_linear_white_kern_1D(self):
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''' Testing the sparse GP regression with rbf and white kernel on 2d data '''
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rbflin = GPy.kern.rbf(1) + GPy.kern.linear(1)
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self.check_model_with_white(rbflin, model_type='SparseGPRegression', dimension=1)
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def test_SparseGPRegression_rbf_linear_white_kern_2D(self):
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''' Testing the sparse GP regression with rbf and white kernel on 2d data '''
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rbflin = GPy.kern.rbf(2) + GPy.kern.linear(2)
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self.check_model_with_white(rbflin, model_type='SparseGPRegression', dimension=2)
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def test_SparseGPRegression_rbf_linear_white_kern_2D_uncertain_inputs(self):
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''' Testing the sparse GP regression with rbf, linear and white kernel on 2d data with uncertain inputs'''
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rbflin = GPy.kern.rbf(2) + GPy.kern.linear(2)
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self.check_model_with_white(rbflin, model_type='SparseGPRegression', dimension=2, uncertain_inputs=1)
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def test_SparseGPRegression_rbf_linear_white_kern_1D_uncertain_inputs(self):
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''' Testing the sparse GP regression with rbf, linear and white kernel on 1d data with uncertain inputs'''
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rbflin = GPy.kern.rbf(1) + GPy.kern.linear(1)
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self.check_model_with_white(rbflin, model_type='SparseGPRegression', dimension=1, uncertain_inputs=1)
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def test_GPLVM_rbf_bias_white_kern_2D(self):
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""" Testing GPLVM with rbf + bias and white kernel """
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N, input_dim, D = 50, 1, 2
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|
|
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Add table
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Reference in a new issue