mirror of
https://github.com/SheffieldML/GPy.git
synced 2026-05-21 14:05:14 +02:00
Merge branch 'devel' of github.com:SheffieldML/GPy into devel
This commit is contained in:
Ricardo
commit
afcb30dfbe
12 changed files with 186 additions and 202 deletions
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@ -39,8 +39,8 @@ class logexp(transformation):
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return '(+ve)'
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class logexp_clipped(transformation):
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max_bound = 1e300
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min_bound = 1e-10
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max_bound = 1e250
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min_bound = 1e-9
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log_max_bound = np.log(max_bound)
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log_min_bound = np.log(min_bound)
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def __init__(self, lower=1e-6):
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@ -49,11 +49,13 @@ class logexp_clipped(transformation):
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def f(self, x):
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exp = np.exp(np.clip(x, self.log_min_bound, self.log_max_bound))
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f = np.log(1. + exp)
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if np.isnan(f).any():
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import ipdb;ipdb.set_trace()
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return f
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def finv(self, f):
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return np.log(np.exp(np.clip(f, self.min_bound, self.max_bound)) - 1.)
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def gradfactor(self, f):
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ef = np.exp(f)
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ef = np.exp(f) # np.clip(f, self.min_bound, self.max_bound))
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gf = (ef - 1.) / ef
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return np.where(f < self.lower, 0, gf)
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def initialize(self, f):
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@ -9,8 +9,8 @@ import pylab as pb
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import numpy as np
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import GPy
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default_seed=10000
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def crescent_data(seed=default_seed): #FIXME
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default_seed = 10000
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def crescent_data(seed=default_seed): # FIXME
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"""Run a Gaussian process classification on the crescent data. The demonstration calls the basic GP classification model and uses EP to approximate the likelihood.
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:param model_type: type of model to fit ['Full', 'FITC', 'DTC'].
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@ -27,10 +27,10 @@ def crescent_data(seed=default_seed): #FIXME
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# Likelihood object
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distribution = GPy.likelihoods.likelihood_functions.probit()
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likelihood = GPy.likelihoods.EP(data['Y'],distribution)
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likelihood = GPy.likelihoods.EP(data['Y'], distribution)
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m = GPy.models.GP(data['X'],likelihood,kernel)
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m = GPy.models.GP(data['X'], likelihood, kernel)
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m.ensure_default_constraints()
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m.update_likelihood_approximation()
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@ -54,10 +54,10 @@ def oil():
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# Likelihood object
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distribution = GPy.likelihoods.likelihood_functions.probit()
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likelihood = GPy.likelihoods.EP(data['Y'][:, 0:1],distribution)
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likelihood = GPy.likelihoods.EP(data['Y'][:, 0:1], distribution)
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# Create GP model
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m = GPy.models.GP(data['X'],likelihood=likelihood,kernel=kernel)
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m = GPy.models.GP(data['X'], likelihood=likelihood, kernel=kernel)
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# Contrain all parameters to be positive
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m.constrain_positive('')
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@ -85,17 +85,17 @@ def toy_linear_1d_classification(seed=default_seed):
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# Likelihood object
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distribution = GPy.likelihoods.likelihood_functions.probit()
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likelihood = GPy.likelihoods.EP(Y,distribution)
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likelihood = GPy.likelihoods.EP(Y, distribution)
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# Model definition
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m = GPy.models.GP(data['X'],likelihood=likelihood,kernel=kernel)
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m = GPy.models.GP(data['X'], likelihood=likelihood, kernel=kernel)
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m.ensure_default_constraints()
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# Optimize
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m.update_likelihood_approximation()
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# Parameters optimization:
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m.optimize()
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#m.pseudo_EM() #FIXME
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# m.pseudo_EM() #FIXME
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# Plot
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pb.subplot(211)
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@ -121,20 +121,20 @@ def sparse_toy_linear_1d_classification(seed=default_seed):
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# Likelihood object
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distribution = GPy.likelihoods.likelihood_functions.probit()
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likelihood = GPy.likelihoods.EP(Y,distribution)
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likelihood = GPy.likelihoods.EP(Y, distribution)
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Z = np.random.uniform(data['X'].min(),data['X'].max(),(10,1))
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Z = np.random.uniform(data['X'].min(), data['X'].max(), (10, 1))
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# Model definition
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m = GPy.models.sparse_GP(data['X'],likelihood=likelihood,kernel=kernel,Z=Z,normalize_X=False)
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m.set('len',2.)
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m = GPy.models.sparse_GP(data['X'], likelihood=likelihood, kernel=kernel, Z=Z, normalize_X=False)
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m.set('len', 2.)
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m.ensure_default_constraints()
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# Optimize
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m.update_likelihood_approximation()
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# Parameters optimization:
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m.optimize()
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#m.EPEM() #FIXME
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# m.EPEM() #FIXME
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# Plot
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pb.subplot(211)
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@ -162,15 +162,15 @@ def sparse_crescent_data(inducing=10, seed=default_seed):
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# Likelihood object
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distribution = GPy.likelihoods.likelihood_functions.probit()
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likelihood = GPy.likelihoods.EP(data['Y'],distribution)
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likelihood = GPy.likelihoods.EP(data['Y'], distribution)
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sample = np.random.randint(0,data['X'].shape[0],inducing)
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Z = data['X'][sample,:]
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sample = np.random.randint(0, data['X'].shape[0], inducing)
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Z = data['X'][sample, :]
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# create sparse GP EP model
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m = GPy.models.sparse_GP(data['X'],likelihood=likelihood,kernel=kernel,Z=Z)
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m = GPy.models.sparse_GP(data['X'], likelihood=likelihood, kernel=kernel, Z=Z)
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m.ensure_default_constraints()
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m.set('len',10.)
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m.set('len', 10.)
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m.update_likelihood_approximation()
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@ -17,11 +17,11 @@ def BGPLVM(seed=default_seed):
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D = 4
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# generate GPLVM-like data
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X = np.random.rand(N, Q)
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k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
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k = GPy.kern.rbf(Q) + GPy.kern.white(Q, 0.00001)
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K = k.K(X)
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Y = np.random.multivariate_normal(np.zeros(N), K, D).T
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k = GPy.kern.linear(Q, ARD=True) + GPy.kern.white(Q)
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k = GPy.kern.rbf(Q, ARD=True) + GPy.kern.linear(Q, ARD=True) + GPy.kern.rbf(Q, ARD=True) + GPy.kern.white(Q)
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# k = GPy.kern.rbf(Q) + GPy.kern.rbf(Q) + GPy.kern.white(Q)
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# k = GPy.kern.rbf(Q) + GPy.kern.bias(Q) + GPy.kern.white(Q, 0.00001)
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# k = GPy.kern.rbf(Q, ARD = False) + GPy.kern.white(Q, 0.00001)
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@ -273,8 +273,8 @@ def bgplvm_simulation(optimize='scg',
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pylab.figure(); pylab.axis(); m.kern.plot_ARD()
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return m
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def mrd_simulation(plot_sim=False):
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D1, D2, D3, N, M, Q = 150, 250, 300, 700, 3, 7
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def mrd_simulation(optimize=True, plot_sim=False):
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D1, D2, D3, N, M, Q = 150, 250, 30, 300, 3, 7
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slist, Slist, Ylist = _simulate_sincos(D1, D2, D3, N, M, Q, plot_sim)
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from GPy.models import mrd
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@ -292,6 +292,13 @@ def mrd_simulation(plot_sim=False):
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m.constrain('variance|noise', logexp_clipped())
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m.ensure_default_constraints()
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# DEBUG
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np.seterr("raise")
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if optimize:
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print "Optimizing Model:"
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m.optimize('scg', messages=1, max_iters=3e3)
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return m
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def brendan_faces():
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@ -39,6 +39,9 @@ def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=500, display=True, xto
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function_eval number of fn evaluations
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status: string describing convergence status
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"""
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print " SCG"
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print ' {0:{mi}s} {1:11s} {2:11s} {3:11s}'.format("I", "F", "Scale", "|g|", mi=len(str(maxiters)))
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if xtol is None:
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xtol = 1e-6
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if ftol is None:
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@ -46,18 +49,18 @@ def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=500, display=True, xto
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if gtol is None:
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gtol = 1e-5
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sigma0 = 1.0e-4
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fold = f(x, *optargs) # Initial function value.
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fold = f(x, *optargs) # Initial function value.
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function_eval = 1
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fnow = fold
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gradnew = gradf(x, *optargs) # Initial gradient.
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gradnew = gradf(x, *optargs) # Initial gradient.
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current_grad = np.dot(gradnew, gradnew)
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gradold = gradnew.copy()
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d = -gradnew # Initial search direction.
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success = True # Force calculation of directional derivs.
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nsuccess = 0 # nsuccess counts number of successes.
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beta = 1.0 # Initial scale parameter.
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betamin = 1.0e-15 # Lower bound on scale.
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betamax = 1.0e100 # Upper bound on scale.
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d = -gradnew # Initial search direction.
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success = True # Force calculation of directional derivs.
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nsuccess = 0 # nsuccess counts number of successes.
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beta = 1.0 # Initial scale parameter.
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betamin = 1.0e-15 # Lower bound on scale.
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betamax = 1.0e100 # Upper bound on scale.
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status = "Not converged"
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flog = [fold]
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@ -107,12 +110,12 @@ def SCG(f, gradf, x, optargs=(), maxiters=500, max_f_eval=500, display=True, xto
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fnow = fold
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# Store relevant variables
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flog.append(fnow) # Current function value
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flog.append(fnow) # Current function value
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iteration += 1
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if display:
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print '\r',
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print 'Iter: {0:>0{mi}g} Obj:{1:> 12e} Scale:{2:> 12e} |g|:{3:> 12e}'.format(iteration, float(fnow), float(beta), float(current_grad), mi=len(str(maxiters))),
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print '{0:>0{mi}g} {1:> 12e} {2:> 12e} {3:> 12e}'.format(iteration, float(fnow), float(beta), float(current_grad), mi=len(str(maxiters))),
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# print 'Iteration:', iteration, ' Objective:', fnow, ' Scale:', beta, '\r',
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sys.stdout.flush()
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@ -18,7 +18,7 @@ class opt_SGD(Optimizer):
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"""
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def __init__(self, start, iterations = 10, learning_rate = 1e-4, momentum = 0.9, model = None, messages = False, batch_size = 1, self_paced = False, center = True, iteration_file = None, **kwargs):
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def __init__(self, start, iterations = 10, learning_rate = 1e-4, momentum = 0.9, model = None, messages = False, batch_size = 1, self_paced = False, center = True, iteration_file = None, learning_rate_adaptation=None, **kwargs):
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self.opt_name = "Stochastic Gradient Descent"
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self.model = model
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@ -33,6 +33,13 @@ class opt_SGD(Optimizer):
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self.center = center
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self.param_traces = [('noise',[])]
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self.iteration_file = iteration_file
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self.learning_rate_adaptation = learning_rate_adaptation
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if self.learning_rate_adaptation != None:
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if self.learning_rate_adaptation == 'annealing':
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self.learning_rate_0 = self.learning_rate
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else:
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self.learning_rate_0 = self.learning_rate.mean()
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# if len([p for p in self.model.kern.parts if p.name == 'bias']) == 1:
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# self.param_traces.append(('bias',[]))
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# if len([p for p in self.model.kern.parts if p.name == 'linear']) == 1:
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@ -204,6 +211,7 @@ class opt_SGD(Optimizer):
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ci = self.shift_constraints(j)
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f, fp = f_fp(self.x_opt[j])
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step[j] = self.momentum * step[j] + self.learning_rate[j] * fp
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self.x_opt[j] -= step[j]
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self.restore_constraints(ci)
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@ -216,9 +224,53 @@ class opt_SGD(Optimizer):
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return f, step, self.model.N
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def adapt_learning_rate(self, t):
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if self.learning_rate_adaptation == 'adagrad':
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if t > 5:
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g = np.array(self.grads)
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l2_g = np.sqrt(np.square(g).sum(0))
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self.learning_rate = 0.001/l2_g
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else:
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self.learning_rate = np.zeros_like(self.learning_rate)
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elif self.learning_rate_adaptation == 'annealing':
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self.learning_rate = self.learning_rate_0/(1+float(t+1)/10)
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elif self.learning_rate_adaptation == 'semi_pesky':
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if self.model.__class__.__name__ == 'Bayesian_GPLVM':
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if t == 0:
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N = self.model.N
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Q = self.model.Q
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M = self.model.M
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iip_pos = np.arange(2*N*Q,2*N*Q+M*Q)
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mu_pos = np.arange(0,N*Q)
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S_pos = np.arange(N*Q,2*N*Q)
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self.vbparam_dict = {'iip': [iip_pos],
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'mu': [mu_pos],
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'S': [S_pos]}
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for k in self.vbparam_dict.keys():
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hbar_t = 0.0
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tau_t = 1000.0
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gbar_t = 0.0
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self.vbparam_dict[k].append(hbar_t)
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self.vbparam_dict[k].append(tau_t)
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self.vbparam_dict[k].append(gbar_t)
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g_t = self.model.grads
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for k in self.vbparam_dict.keys():
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pos, hbar_t, tau_t, gbar_t = self.vbparam_dict[k]
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gbar_t = (1-1/tau_t)*gbar_t + 1/tau_t * g_t[pos]
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hbar_t = (1-1/tau_t)*hbar_t + 1/tau_t * np.dot(g_t[pos].T, g_t[pos])
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self.learning_rate[pos] = np.dot(gbar_t.T, gbar_t) / hbar_t
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tau_t = tau_t*(1-self.learning_rate[pos]) + 1
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self.vbparam_dict[k] = [pos, hbar_t, tau_t, gbar_t]
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def opt(self, f_fp=None, f=None, fp=None):
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self.x_opt = self.model._get_params_transformed()
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self.model.grads = np.zeros_like(self.x_opt)
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self.grads = []
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X, Y = self.model.X.copy(), self.model.likelihood.Y.copy()
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@ -235,6 +287,7 @@ class opt_SGD(Optimizer):
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step = np.zeros_like(num_params)
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for it in range(self.iterations):
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self.model.grads = np.zeros_like(self.x_opt) # TODO this is ugly
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if it == 0 or self.self_paced is False:
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features = np.random.permutation(Y.shape[1])
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@ -272,16 +325,17 @@ class opt_SGD(Optimizer):
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sys.stdout.write(status)
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sys.stdout.flush()
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self.param_traces['noise'].append(noise)
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NLL.append(f)
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self.fopt_trace.append(f)
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NLL.append(f)
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self.fopt_trace.append(NLL[-1])
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# fig = plt.figure('traces')
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# plt.clf()
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# plt.plot(self.param_traces['noise'])
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# for k in self.param_traces.keys():
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# self.param_traces[k].append(self.model.get(k)[0])
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self.grads.append(self.model.grads.tolist())
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self.adapt_learning_rate(it)
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# should really be a sum(), but earlier samples in the iteration will have a very crappy ll
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self.f_opt = np.mean(NLL)
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self.model.N = N
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@ -293,7 +347,7 @@ class opt_SGD(Optimizer):
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sigma = self.model.likelihood._variance
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self.model.likelihood._variance = None # invalidate cache
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self.model.likelihood._set_params(sigma)
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self.trace.append(self.f_opt)
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if self.iteration_file is not None:
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f = open(self.iteration_file + "iteration%d.pickle" % it, 'w')
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@ -303,6 +357,6 @@ class opt_SGD(Optimizer):
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if self.messages != 0:
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sys.stdout.write('\r' + ' '*len(status)*2 + ' \r')
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status = "SGD Iteration: {0: 3d}/{1: 3d} f: {2: 2.3f}\n".format(it+1, self.iterations, self.f_opt)
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status = "SGD Iteration: {0: 3d}/{1: 3d} f: {2: 2.3f} max eta: {3: 1.5f}\n".format(it+1, self.iterations, self.f_opt, self.learning_rate.max())
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sys.stdout.write(status)
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sys.stdout.flush()
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@ -55,8 +55,9 @@ class bias(kernpart):
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target += self.variance
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def psi1(self, Z, mu, S, target):
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target += self.variance
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self._psi1 = self.variance
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target += self._psi1
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def psi2(self, Z, mu, S, target):
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target += self.variance**2
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130
GPy/kern/kern.py
130
GPy/kern/kern.py
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@ -315,31 +315,20 @@ class kern(parameterised):
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# compute the "cross" terms
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# TODO: input_slices needed
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crossterms = 0
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for p1, p2 in itertools.combinations(self.parts, 2):
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# white doesn;t combine with anything
|
||||
if p1.name == 'white' or p2.name == 'white':
|
||||
pass
|
||||
# rbf X bias
|
||||
elif p1.name == 'bias' and p2.name == 'rbf':
|
||||
target += p1.variance * (p2._psi1[:, :, None] + p2._psi1[:, None, :])
|
||||
elif p2.name == 'bias' and p1.name == 'rbf':
|
||||
target += p2.variance * (p1._psi1[:, :, None] + p1._psi1[:, None, :])
|
||||
# linear X bias
|
||||
elif p1.name == 'bias' and p2.name == 'linear':
|
||||
tmp = np.zeros((mu.shape[0], Z.shape[0]))
|
||||
p2.psi1(Z, mu, S, tmp)
|
||||
target += p1.variance * (tmp[:, :, None] + tmp[:, None, :])
|
||||
elif p2.name == 'bias' and p1.name == 'linear':
|
||||
tmp = np.zeros((mu.shape[0], Z.shape[0]))
|
||||
p1.psi1(Z, mu, S, tmp)
|
||||
target += p2.variance * (tmp[:, :, None] + tmp[:, None, :])
|
||||
# rbf X linear
|
||||
elif p1.name == 'linear' and p2.name == 'rbf':
|
||||
raise NotImplementedError # TODO
|
||||
elif p2.name == 'linear' and p1.name == 'rbf':
|
||||
raise NotImplementedError # TODO
|
||||
else:
|
||||
raise NotImplementedError, "psi2 cannot be computed for this kernel"
|
||||
|
||||
# TODO psi1 this must be faster/better/precached/more nice
|
||||
tmp1 = np.zeros((mu.shape[0], Z.shape[0]))
|
||||
p1.psi1(Z, mu, S, tmp1)
|
||||
tmp2 = np.zeros((mu.shape[0], Z.shape[0]))
|
||||
p2.psi1(Z, mu, S, tmp2)
|
||||
|
||||
prod = np.multiply(tmp1, tmp2)
|
||||
crossterms += prod[:,:,None] + prod[:, None, :]
|
||||
|
||||
target += crossterms
|
||||
return target
|
||||
|
||||
def dpsi2_dtheta(self, dL_dpsi2, Z, mu, S):
|
||||
|
|
@ -348,71 +337,34 @@ class kern(parameterised):
|
|||
|
||||
# compute the "cross" terms
|
||||
# TODO: better looping, input_slices
|
||||
for i1, i2 in itertools.combinations(range(len(self.parts)), 2):
|
||||
for i1, i2 in itertools.permutations(range(len(self.parts)), 2):
|
||||
p1, p2 = self.parts[i1], self.parts[i2]
|
||||
# ipsl1, ipsl2 = self.input_slices[i1], self.input_slices[i2]
|
||||
ps1, ps2 = self.param_slices[i1], self.param_slices[i2]
|
||||
|
||||
# white doesn;t combine with anything
|
||||
if p1.name == 'white' or p2.name == 'white':
|
||||
pass
|
||||
# rbf X bias
|
||||
elif p1.name == 'bias' and p2.name == 'rbf':
|
||||
p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1.variance * 2., Z, mu, S, target[ps2])
|
||||
p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2._psi1 * 2., Z, mu, S, target[ps1])
|
||||
elif p2.name == 'bias' and p1.name == 'rbf':
|
||||
p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2.variance * 2., Z, mu, S, target[ps1])
|
||||
p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1._psi1 * 2., Z, mu, S, target[ps2])
|
||||
# linear X bias
|
||||
elif p1.name == 'bias' and p2.name == 'linear':
|
||||
p2.dpsi1_dtheta(dL_dpsi2.sum(1) * p1.variance * 2., Z, mu, S, target[ps2]) # [ps1])
|
||||
psi1 = np.zeros((mu.shape[0], Z.shape[0]))
|
||||
p2.psi1(Z, mu, S, psi1)
|
||||
p1.dpsi1_dtheta(dL_dpsi2.sum(1) * psi1 * 2., Z, mu, S, target[ps1])
|
||||
elif p2.name == 'bias' and p1.name == 'linear':
|
||||
p1.dpsi1_dtheta(dL_dpsi2.sum(1) * p2.variance * 2., Z, mu, S, target[ps1])
|
||||
psi1 = np.zeros((mu.shape[0], Z.shape[0]))
|
||||
p1.psi1(Z, mu, S, psi1)
|
||||
p2.dpsi1_dtheta(dL_dpsi2.sum(1) * psi1 * 2., Z, mu, S, target[ps2])
|
||||
# rbf X linear
|
||||
elif p1.name == 'linear' and p2.name == 'rbf':
|
||||
raise NotImplementedError # TODO
|
||||
elif p2.name == 'linear' and p1.name == 'rbf':
|
||||
raise NotImplementedError # TODO
|
||||
else:
|
||||
raise NotImplementedError, "psi2 cannot be computed for this kernel"
|
||||
tmp = np.zeros((mu.shape[0], Z.shape[0]))
|
||||
p1.psi1(Z, mu, S, tmp)
|
||||
p2.dpsi1_dtheta((tmp[:,None,:]*dL_dpsi2).sum(1)*2., Z, mu, S, target[ps2])
|
||||
|
||||
return self._transform_gradients(target)
|
||||
|
||||
def dpsi2_dZ(self, dL_dpsi2, Z, mu, S):
|
||||
target = np.zeros_like(Z)
|
||||
[p.dpsi2_dZ(dL_dpsi2, Z[:, i_s], mu[:, i_s], S[:, i_s], target[:, i_s]) for p, i_s in zip(self.parts, self.input_slices)]
|
||||
#target *= 2
|
||||
|
||||
# compute the "cross" terms
|
||||
# TODO: we need input_slices here.
|
||||
for p1, p2 in itertools.combinations(self.parts, 2):
|
||||
# white doesn;t combine with anything
|
||||
if p1.name == 'white' or p2.name == 'white':
|
||||
pass
|
||||
# rbf X bias
|
||||
elif p1.name == 'bias' and p2.name == 'rbf':
|
||||
p2.dpsi1_dX(dL_dpsi2.sum(1).T * p1.variance, Z, mu, S, target)
|
||||
elif p2.name == 'bias' and p1.name == 'rbf':
|
||||
p1.dpsi1_dZ(dL_dpsi2.sum(1).T * p2.variance, Z, mu, S, target)
|
||||
# linear X bias
|
||||
elif p1.name == 'bias' and p2.name == 'linear':
|
||||
p2.dpsi1_dZ(dL_dpsi2.sum(1).T * p1.variance, Z, mu, S, target)
|
||||
elif p2.name == 'bias' and p1.name == 'linear':
|
||||
p1.dpsi1_dZ(dL_dpsi2.sum(1).T * p2.variance, Z, mu, S, target)
|
||||
# rbf X linear
|
||||
elif p1.name == 'linear' and p2.name == 'rbf':
|
||||
raise NotImplementedError # TODO
|
||||
elif p2.name == 'linear' and p1.name == 'rbf':
|
||||
raise NotImplementedError # TODO
|
||||
else:
|
||||
raise NotImplementedError, "psi2 cannot be computed for this kernel"
|
||||
for p1, p2 in itertools.permutations(self.parts, 2):
|
||||
if p1.name == 'linear' and p2.name == 'linear':
|
||||
raise NotImplementedError("We don't handle linear/linear cross-terms")
|
||||
tmp = np.zeros((mu.shape[0], Z.shape[0]))
|
||||
p1.psi1(Z, mu, S, tmp)
|
||||
tmp2 = np.zeros_like(target)
|
||||
p2.dpsi1_dZ((tmp[:,None,:]*dL_dpsi2).sum(1).T, Z, mu, S, tmp2)
|
||||
target += tmp2
|
||||
|
||||
return target * 2.
|
||||
return target * 2
|
||||
|
||||
def dpsi2_dmuS(self, dL_dpsi2, Z, mu, S):
|
||||
target_mu, target_S = np.zeros((2, mu.shape[0], mu.shape[1]))
|
||||
|
|
@ -420,27 +372,13 @@ class kern(parameterised):
|
|||
|
||||
# compute the "cross" terms
|
||||
# TODO: we need input_slices here.
|
||||
for p1, p2 in itertools.combinations(self.parts, 2):
|
||||
# white doesn;t combine with anything
|
||||
if p1.name == 'white' or p2.name == 'white':
|
||||
pass
|
||||
# rbf X bias
|
||||
elif p1.name == 'bias' and p2.name == 'rbf':
|
||||
p2.dpsi1_dmuS(dL_dpsi2.sum(1).T * p1.variance * 2., Z, mu, S, target_mu, target_S)
|
||||
elif p2.name == 'bias' and p1.name == 'rbf':
|
||||
p1.dpsi1_dmuS(dL_dpsi2.sum(1).T * p2.variance * 2., Z, mu, S, target_mu, target_S)
|
||||
# linear X bias
|
||||
elif p1.name == 'bias' and p2.name == 'linear':
|
||||
p2.dpsi1_dmuS(dL_dpsi2.sum(1).T * p1.variance * 2., Z, mu, S, target_mu, target_S)
|
||||
elif p2.name == 'bias' and p1.name == 'linear':
|
||||
p1.dpsi1_dmuS(dL_dpsi2.sum(1).T * p2.variance * 2., Z, mu, S, target_mu, target_S)
|
||||
# rbf X linear
|
||||
elif p1.name == 'linear' and p2.name == 'rbf':
|
||||
raise NotImplementedError # TODO
|
||||
elif p2.name == 'linear' and p1.name == 'rbf':
|
||||
raise NotImplementedError # TODO
|
||||
else:
|
||||
raise NotImplementedError, "psi2 cannot be computed for this kernel"
|
||||
for p1, p2 in itertools.permutations(self.parts, 2):
|
||||
if p1.name == 'linear' and p2.name == 'linear':
|
||||
raise NotImplementedError("We don't handle linear/linear cross-terms")
|
||||
|
||||
tmp = np.zeros((mu.shape[0], Z.shape[0]))
|
||||
p1.psi1(Z, mu, S, tmp)
|
||||
p2.dpsi1_dmuS((tmp[:,None,:]*dL_dpsi2).sum(1).T*2., Z, mu, S, target_mu, target_S)
|
||||
|
||||
return target_mu, target_S
|
||||
|
||||
|
|
|
|||
|
|
@ -54,5 +54,3 @@ class kernpart(object):
|
|||
raise NotImplementedError
|
||||
def dK_dX(self,X,X2,target):
|
||||
raise NotImplementedError
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -18,7 +18,8 @@ class white(kernpart):
|
|||
self.Nparam = 1
|
||||
self.name = 'white'
|
||||
self._set_params(np.array([variance]).flatten())
|
||||
|
||||
self._psi1 = 0 # TODO: more elegance here
|
||||
|
||||
def _get_params(self):
|
||||
return self.variance
|
||||
|
||||
|
|
@ -81,4 +82,3 @@ class white(kernpart):
|
|||
|
||||
def dpsi2_dmuS(self,dL_dpsi2,Z,mu,S,target_mu,target_S):
|
||||
pass
|
||||
|
||||
|
|
|
|||
|
|
@ -171,9 +171,6 @@ class Bayesian_GPLVM(sparse_GP, GPLVM):
|
|||
self.dbound_dZtheta = sparse_GP._log_likelihood_gradients(self)
|
||||
return np.hstack((self.dbound_dmuS.flatten(), self.dbound_dZtheta))
|
||||
|
||||
def _log_likelihood_normal_gradients(self):
|
||||
Si, _, _, _ = pdinv(self.X_variance)
|
||||
|
||||
def plot_latent(self, which_indices=None, *args, **kwargs):
|
||||
|
||||
if which_indices is None:
|
||||
|
|
|
|||
|
|
@ -16,9 +16,9 @@ class sparse_GP(GP):
|
|||
:param X: inputs
|
||||
:type X: np.ndarray (N x Q)
|
||||
:param likelihood: a likelihood instance, containing the observed data
|
||||
:type likelihood: GPy.likelihood.(Gaussian | EP)
|
||||
:param kernel : the kernel/covariance function. See link kernels
|
||||
:type kernel: a GPy kernel
|
||||
:type likelihood: GPy.likelihood.(Gaussian | EP | Laplace)
|
||||
:param kernel : the kernel (covariance function). See link kernels
|
||||
:type kernel: a GPy.kern.kern instance
|
||||
:param X_variance: The uncertainty in the measurements of X (Gaussian variance)
|
||||
:type X_variance: np.ndarray (N x Q) | None
|
||||
:param Z: inducing inputs (optional, see note)
|
||||
|
|
@ -30,8 +30,6 @@ class sparse_GP(GP):
|
|||
"""
|
||||
|
||||
def __init__(self, X, likelihood, kernel, Z, X_variance=None, normalize_X=False):
|
||||
# self.scale_factor = 100.0 # a scaling factor to help keep the algorithm stable
|
||||
# self.auto_scale_factor = False
|
||||
self.Z = Z
|
||||
self.M = Z.shape[0]
|
||||
self.likelihood = likelihood
|
||||
|
|
@ -63,49 +61,29 @@ class sparse_GP(GP):
|
|||
self.psi2 = None
|
||||
|
||||
def _computations(self):
|
||||
# sf = self.scale_factor
|
||||
# sf2 = sf ** 2
|
||||
|
||||
# factor Kmm
|
||||
self.Lm = jitchol(self.Kmm)
|
||||
|
||||
# The rather complex computations of self.A
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
assert self.likelihood.D == 1 # TODO: what if the likelihood is heterscedatic and there are multiple independent outputs?
|
||||
if self.has_uncertain_inputs:
|
||||
# psi2_beta_scaled = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.N, 1, 1) / sf2)).sum(0)
|
||||
psi2_beta_scaled = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.N, 1, 1))).sum(0)
|
||||
evals, evecs = linalg.eigh(psi2_beta_scaled)
|
||||
clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable
|
||||
if not np.allclose(evals, clipped_evals):
|
||||
print "Warning: clipping posterior eigenvalues"
|
||||
tmp = evecs * np.sqrt(clipped_evals)
|
||||
tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
|
||||
self.A = tdot(tmp)
|
||||
if self.has_uncertain_inputs:
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
psi2_beta = (self.psi2 * (self.likelihood.precision.flatten().reshape(self.N, 1, 1))).sum(0)
|
||||
else:
|
||||
# tmp = self.psi1 * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.N)) / sf)
|
||||
tmp = self.psi1 * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.N)))
|
||||
tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
|
||||
self.A = tdot(tmp)
|
||||
psi2_beta = self.psi2.sum(0) * self.likelihood.precision
|
||||
evals, evecs = linalg.eigh(psi2_beta)
|
||||
clipped_evals = np.clip(evals, 0., 1e6) # TODO: make clipping configurable
|
||||
tmp = evecs * np.sqrt(clipped_evals)
|
||||
else:
|
||||
if self.has_uncertain_inputs:
|
||||
# psi2_beta_scaled = (self.psi2 * (self.likelihood.precision / sf2)).sum(0)
|
||||
psi2_beta_scaled = (self.psi2 * (self.likelihood.precision)).sum(0)
|
||||
evals, evecs = linalg.eigh(psi2_beta_scaled)
|
||||
clipped_evals = np.clip(evals, 0., 1e15) # TODO: make clipping configurable
|
||||
if not np.allclose(evals, clipped_evals):
|
||||
print "Warning: clipping posterior eigenvalues"
|
||||
tmp = evecs * np.sqrt(clipped_evals)
|
||||
tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
|
||||
self.A = tdot(tmp)
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
tmp = self.psi1 * (np.sqrt(self.likelihood.precision.flatten().reshape(1, self.N)))
|
||||
else:
|
||||
# tmp = self.psi1 * (np.sqrt(self.likelihood.precision) / sf)
|
||||
tmp = self.psi1 * (np.sqrt(self.likelihood.precision))
|
||||
tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
|
||||
self.A = tdot(tmp)
|
||||
tmp, _ = linalg.lapack.flapack.dtrtrs(self.Lm, np.asfortranarray(tmp), lower=1)
|
||||
self.A = tdot(tmp)
|
||||
|
||||
|
||||
# factor B
|
||||
# self.B = np.eye(self.M) / sf2 + self.A
|
||||
self.B = np.eye(self.M) + self.A
|
||||
self.LB = jitchol(self.B)
|
||||
|
||||
|
|
@ -121,8 +99,6 @@ class sparse_GP(GP):
|
|||
# Compute dL_dKmm
|
||||
tmp = tdot(self._LBi_Lmi_psi1V)
|
||||
self.DBi_plus_BiPBi = backsub_both_sides(self.LB, self.D * np.eye(self.M) + tmp)
|
||||
# tmp = -0.5 * self.DBi_plus_BiPBi / sf2
|
||||
# tmp += -0.5 * self.B * sf2 * self.D
|
||||
tmp = -0.5 * self.DBi_plus_BiPBi
|
||||
tmp += -0.5 * self.B * self.D
|
||||
tmp += self.D * np.eye(self.M)
|
||||
|
|
@ -132,6 +108,7 @@ class sparse_GP(GP):
|
|||
self.dL_dpsi0 = -0.5 * self.D * (self.likelihood.precision * np.ones([self.N, 1])).flatten()
|
||||
self.dL_dpsi1 = np.dot(self.Cpsi1V, self.likelihood.V.T)
|
||||
dL_dpsi2_beta = 0.5 * backsub_both_sides(self.Lm, self.D * np.eye(self.M) - self.DBi_plus_BiPBi)
|
||||
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
if self.has_uncertain_inputs:
|
||||
self.dL_dpsi2 = self.likelihood.precision.flatten()[:, None, None] * dL_dpsi2_beta[None, :, :]
|
||||
|
|
@ -158,7 +135,6 @@ class sparse_GP(GP):
|
|||
else:
|
||||
# likelihood is not heterscedatic
|
||||
self.partial_for_likelihood = -0.5 * self.N * self.D * self.likelihood.precision + 0.5 * self.likelihood.trYYT * self.likelihood.precision ** 2
|
||||
# self.partial_for_likelihood += 0.5 * self.D * (self.psi0.sum() * self.likelihood.precision ** 2 - np.trace(self.A) * self.likelihood.precision * sf2)
|
||||
self.partial_for_likelihood += 0.5 * self.D * (self.psi0.sum() * self.likelihood.precision ** 2 - np.trace(self.A) * self.likelihood.precision)
|
||||
self.partial_for_likelihood += self.likelihood.precision * (0.5 * np.sum(self.A * self.DBi_plus_BiPBi) - np.sum(np.square(self._LBi_Lmi_psi1V)))
|
||||
|
||||
|
|
@ -166,16 +142,12 @@ class sparse_GP(GP):
|
|||
|
||||
def log_likelihood(self):
|
||||
""" Compute the (lower bound on the) log marginal likelihood """
|
||||
# sf2 = self.scale_factor ** 2
|
||||
if self.likelihood.is_heteroscedastic:
|
||||
A = -0.5 * self.N * self.D * np.log(2.*np.pi) + 0.5 * np.sum(np.log(self.likelihood.precision)) - 0.5 * np.sum(self.likelihood.V * self.likelihood.Y)
|
||||
# B = -0.5 * self.D * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A) * sf2)
|
||||
B = -0.5 * self.D * (np.sum(self.likelihood.precision.flatten() * self.psi0) - np.trace(self.A))
|
||||
else:
|
||||
A = -0.5 * self.N * self.D * (np.log(2.*np.pi) - np.log(self.likelihood.precision)) - 0.5 * self.likelihood.precision * self.likelihood.trYYT
|
||||
# B = -0.5 * self.D * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A) * sf2)
|
||||
B = -0.5 * self.D * (np.sum(self.likelihood.precision * self.psi0) - np.trace(self.A))
|
||||
# C = -self.D * (np.sum(np.log(np.diag(self.LB))) + 0.5 * self.M * np.log(sf2))
|
||||
C = -self.D * (np.sum(np.log(np.diag(self.LB)))) # + 0.5 * self.M * np.log(sf2))
|
||||
D = 0.5 * np.sum(np.square(self._LBi_Lmi_psi1V))
|
||||
return A + B + C + D
|
||||
|
|
@ -185,14 +157,6 @@ class sparse_GP(GP):
|
|||
self.kern._set_params(p[self.Z.size:self.Z.size + self.kern.Nparam])
|
||||
self.likelihood._set_params(p[self.Z.size + self.kern.Nparam:])
|
||||
self._compute_kernel_matrices()
|
||||
# if self.auto_scale_factor:
|
||||
# self.scale_factor = np.sqrt(self.psi2.sum(0).mean()*self.likelihood.precision)
|
||||
# if self.auto_scale_factor:
|
||||
# if self.likelihood.is_heteroscedastic:
|
||||
# self.scale_factor = max(100,np.sqrt(self.psi2_beta_scaled.sum(0).mean()))
|
||||
# else:
|
||||
# self.scale_factor = np.sqrt(self.psi2.sum(0).mean()*self.likelihood.precision)
|
||||
# self.scale_factor = 100.
|
||||
self._computations()
|
||||
|
||||
def _get_params(self):
|
||||
|
|
@ -205,7 +169,7 @@ class sparse_GP(GP):
|
|||
"""
|
||||
Approximates a non-gaussian likelihood using Expectation Propagation
|
||||
|
||||
For a Gaussian (or direct: TODO) likelihood, no iteration is required:
|
||||
For a Gaussian likelihood, no iteration is required:
|
||||
this function does nothing
|
||||
"""
|
||||
if self.has_uncertain_inputs:
|
||||
|
|
|
|||
|
|
@ -236,7 +236,7 @@ def tdot(*args, **kwargs):
|
|||
else:
|
||||
return tdot_numpy(*args,**kwargs)
|
||||
|
||||
def DSYR(A,x,alpha=1.):
|
||||
def DSYR_blas(A,x,alpha=1.):
|
||||
"""
|
||||
Performs a symmetric rank-1 update operation:
|
||||
A <- A + alpha * np.dot(x,x.T)
|
||||
|
|
@ -258,6 +258,26 @@ def DSYR(A,x,alpha=1.):
|
|||
x_, byref(INCX), A_, byref(LDA))
|
||||
symmetrify(A,upper=True)
|
||||
|
||||
def DSYR_numpy(A,x,alpha=1.):
|
||||
"""
|
||||
Performs a symmetric rank-1 update operation:
|
||||
A <- A + alpha * np.dot(x,x.T)
|
||||
|
||||
Arguments
|
||||
---------
|
||||
:param A: Symmetric NxN np.array
|
||||
:param x: Nx1 np.array
|
||||
:param alpha: scalar
|
||||
"""
|
||||
A += alpha*np.dot(x[:,None],x[None,:])
|
||||
|
||||
|
||||
def DSYR(*args, **kwargs):
|
||||
if _blas_available:
|
||||
return DSYR_blas(*args,**kwargs)
|
||||
else:
|
||||
return DSYR_numpy(*args,**kwargs)
|
||||
|
||||
def symmetrify(A,upper=False):
|
||||
"""
|
||||
Take the square matrix A and make it symmetrical by copting elements from the lower half to the upper
|
||||
|
|
|
|||
Loading…
Add table
Add a link
Reference in a new issue