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https://github.com/SheffieldML/GPy.git
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400 lines
12 KiB
Python
400 lines
12 KiB
Python
# Copyright (c) 2012, GPy authors (see AUTHORS.txt).
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# Licensed under the BSD 3-clause license (see LICENSE.txt)
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import numpy as np
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import pylab as pb
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from matplotlib import pyplot as plt, pyplot
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import GPy
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from GPy.models.Bayesian_GPLVM import Bayesian_GPLVM
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from GPy.util.datasets import simulation_BGPLVM
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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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M = 3
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Q = 2
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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 = 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) + 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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m = GPy.models.Bayesian_GPLVM(Y, Q, kernel=k, M=M)
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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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# pb.figure()
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# m.plot()
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# pb.title('PCA initialisation')
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# pb.figure()
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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.ensure_default_constraints()
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m.randomize()
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m.checkgrad(verbose=1)
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return m
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def GPLVM_oil_100(optimize=True):
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data = GPy.util.datasets.oil_100()
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# create simple GP model
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kernel = GPy.kern.rbf(6, ARD=True) + GPy.kern.bias(6)
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m = GPy.models.GPLVM(data['X'], 6, kernel=kernel)
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m.data_labels = data['Y'].argmax(axis=1)
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# optimize
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m.ensure_default_constraints()
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if optimize:
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m.optimize('scg', messages=1)
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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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return m
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def BGPLVM_oil(optimize=True, N=100, Q=10, M=15, max_f_eval=300):
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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) + GPy.kern.white(Q, 0.001)
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m = GPy.models.Bayesian_GPLVM(data['X'][:N], Q, kernel=kernel, M=M)
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m.data_labels = data['Y'][:N].argmax(axis=1)
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# optimize
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if optimize:
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m.constrain_fixed('noise', 0.05)
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m.ensure_default_constraints()
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m.optimize('scg', messages=1, max_f_eval=max(80, max_f_eval))
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m.unconstrain('noise')
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m.constrain_positive('noise')
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m.optimize('scg', messages=1, max_f_eval=max(0, max_f_eval - 80))
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else:
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m.ensure_default_constraints()
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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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pb.figure()
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pb.bar(np.arange(m.kern.D), 1. / m.input_sensitivity())
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return m
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def oil_100():
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data = GPy.util.datasets.oil_100()
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m = GPy.models.GPLVM(data['X'], 2)
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# optimize
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m.ensure_default_constraints()
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m.optimize(messages=1, max_iters=2)
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# plot
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print(m)
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# m.plot_latent(labels=data['Y'].argmax(axis=1))
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return m
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def _simulate_sincos(D1, D2, D3, N, M, Q, plot_sim=False):
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x = np.linspace(0, 4 * np.pi, N)[:, None]
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s1 = np.vectorize(lambda x: np.sin(x))
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s2 = np.vectorize(lambda x: np.cos(x))
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s3 = np.vectorize(lambda x:-np.exp(-np.cos(2 * x)))
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sS = np.vectorize(lambda x: np.sin(2 * x))
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s1 = s1(x)
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s2 = s2(x)
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s3 = s3(x)
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sS = sS(x)
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# s1 -= s1.mean()
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# s2 -= s2.mean()
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# s3 -= s3.mean()
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# sS -= sS.mean()
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# s1 /= .5 * (np.abs(s1).max() - np.abs(s1).min())
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# s2 /= .5 * (np.abs(s2).max() - np.abs(s2).min())
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# s3 /= .5 * (np.abs(s3).max() - np.abs(s3).min())
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# sS /= .5 * (np.abs(sS).max() - np.abs(sS).min())
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S1 = np.hstack([s1, sS])
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S2 = np.hstack([s2, sS])
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S3 = np.hstack([s3, sS])
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Y1 = S1.dot(np.random.randn(S1.shape[1], D1))
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Y2 = S2.dot(np.random.randn(S2.shape[1], D2))
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Y3 = S3.dot(np.random.randn(S3.shape[1], D3))
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Y1 += .2 * np.random.randn(*Y1.shape)
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Y2 += .2 * np.random.randn(*Y2.shape)
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Y3 += .2 * 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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Y3 -= Y3.mean(0)
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Y1 /= Y1.std(0)
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Y2 /= Y2.std(0)
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Y3 /= Y3.std(0)
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slist = [s1, s2, s3, sS]
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Ylist = [Y1, Y2, Y3]
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if plot_sim:
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import pylab
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import itertools
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fig = pylab.figure("MRD Simulation", figsize=(8, 6))
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fig.clf()
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ax = fig.add_subplot(2, 1, 1)
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labls = sorted(filter(lambda x: x.startswith("s"), locals()))
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for S, lab in itertools.izip(slist, labls):
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ax.plot(S, label=lab)
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ax.legend()
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for i, Y in enumerate(Ylist):
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ax = fig.add_subplot(2, len(Ylist), len(Ylist) + 1 + i)
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ax.imshow(Y)
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ax.set_title("Y{}".format(i + 1))
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pylab.draw()
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pylab.tight_layout()
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return slist, [S1, S2, S3], Ylist
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def bgplvm_simulation_matlab_compare():
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sim_data = simulation_BGPLVM()
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Y = sim_data['Y']
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S = sim_data['S']
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mu = sim_data['mu']
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M, [_, Q] = 20, mu.shape
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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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k = kern.linear(Q, ARD=True) + kern.bias(Q, np.exp(-2)) + kern.white(Q, np.exp(-2))
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m = Bayesian_GPLVM(Y, Q, init="PCA", M=M, kernel=k,
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# X=mu,
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# X_variance=S,
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_debug=True)
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m.ensure_default_constraints()
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m['noise'] = .01 # Y.var() / 100.
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m['linear_variance'] = .01
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return m
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def bgplvm_simulation(burnin='scg', plot_sim=False,
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max_burnin=100, true_X=False,
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do_opt=True,
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max_f_eval=1000):
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D1, D2, D3, N, M, Q = 10, 8, 8, 250, 10, 6
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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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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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# k = kern.white(Q, .00001) + kern.bias(Q)
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m = Bayesian_GPLVM(Y, Q, init="PCA", M=M, kernel=k, _debug=True)
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# m.set('noise',)
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m.ensure_default_constraints()
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m['noise'] = Y.var() / 100.
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m['linear_variance'] = .001
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# m.auto_scale_factor = True
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# m.scale_factor = 1.
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if burnin:
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print "initializing beta"
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cstr = "noise"
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m.unconstrain(cstr); m.constrain_fixed(cstr, Y.var() / 70.)
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m.optimize(burnin, messages=1, max_f_eval=max_burnin)
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print "releasing beta"
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cstr = "noise"
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m.unconstrain(cstr); m.constrain_positive(cstr)
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if true_X:
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true_X = np.hstack((slist[0], slist[3], 0. * np.ones((N, Q - 2))))
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m.set('X_\d', true_X)
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m.constrain_fixed("X_\d")
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cstr = 'X_variance'
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# m.unconstrain(cstr), m.constrain_fixed(cstr, .0001)
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m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-7, .1)
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# cstr = 'X_variance'
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# m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-3, 1.)
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# m['X_var'] = np.ones(N * Q) * .5 + np.random.randn(N * Q) * .01
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# cstr = "iip"
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# m.unconstrain(cstr); m.constrain_fixed(cstr)
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# cstr = 'variance'
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# m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-10, 1.)
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# cstr = 'X_\d'
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# m.unconstrain(cstr), m.constrain_bounded(cstr, -10., 10.)
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#
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# cstr = 'noise'
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# m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-5, 1.)
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#
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# cstr = 'white'
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# m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-6, 1.)
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#
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# cstr = 'linear_variance'
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# m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-10, 10.)
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# cstr = 'variance'
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# m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-10, 10.)
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# np.seterr(all='call')
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# def ipdbonerr(errtype, flags):
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# import ipdb; ipdb.set_trace()
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# np.seterrcall(ipdbonerr)
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if do_opt and burnin:
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try:
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m.optimize(burnin, messages=1, max_f_eval=max_f_eval)
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except:
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pass
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finally:
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return m
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return m
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def mrd_simulation(plot_sim=False):
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# num = 2
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# ard1 = np.array([1., 1, 0, 0], dtype=float)
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# ard2 = np.array([0., 1, 1, 0], dtype=float)
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# ard1[ard1 == 0] = 1E-10
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# ard2[ard2 == 0] = 1E-10
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# ard1i = 1. / ard1
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# ard2i = 1. / ard2
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# k = GPy.kern.rbf(Q, ARD=True, lengthscale=ard1i) + GPy.kern.bias(Q, 0) + GPy.kern.white(Q, 0.0001)
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# Y1 = np.random.multivariate_normal(np.zeros(N), k.K(X), D1).T
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# Y1 -= Y1.mean(0)
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#
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# k = GPy.kern.rbf(Q, ARD=True, lengthscale=ard2i) + GPy.kern.bias(Q, 0) + GPy.kern.white(Q, 0.0001)
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# Y2 = np.random.multivariate_normal(np.zeros(N), k.K(X), D2).T
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# Y2 -= Y2.mean(0)
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# make_params = lambda ard: np.hstack([[1], ard, [1, .3]])
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D1, D2, D3, N, M, Q = 2000, 34, 8, 500, 3, 6
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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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from GPy import kern
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reload(mrd); reload(kern)
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# k = kern.rbf(2, ARD=True) + kern.bias(2) + kern.white(2)
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# Y1 = np.random.multivariate_normal(np.zeros(N), k.K(S1), D1).T
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# Y2 = np.random.multivariate_normal(np.zeros(N), k.K(S2), D2).T
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# Y3 = np.random.multivariate_normal(np.zeros(N), k.K(S3), D3).T
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Ylist = Ylist[0:2]
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# k = kern.rbf(Q, ARD=True) + kern.bias(Q) + kern.white(Q)
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k = kern.linear(Q, ARD=True) + kern.bias(Q, .01) + kern.white(Q, .001)
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m = mrd.MRD(*Ylist, Q=Q, M=M, kernel=k, initx="concat", initz='permute', _debug=False)
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for i, Y in enumerate(Ylist):
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m.set('{}_noise'.format(i + 1), Y.var() / 100.)
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m.ensure_default_constraints()
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m.auto_scale_factor = True
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# cstr = 'variance'
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# m.unconstrain(cstr), m.constrain_bounded(cstr, 1e-12, 1.)
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#
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# cstr = 'linear_variance'
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# m.unconstrain(cstr), m.constrain_positive(cstr)
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# print "initializing beta"
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# cstr = "noise"
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# m.unconstrain(cstr); m.constrain_fixed(cstr)
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# m.optimize('scg', messages=1, max_f_eval=100)
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# print "releasing beta"
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# cstr = "noise"
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# m.unconstrain(cstr); m.constrain_positive(cstr)
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np.seterr(all='call')
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def ipdbonerr(errtype, flags):
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import ipdb; ipdb.set_trace()
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np.seterrcall(ipdbonerr)
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return m # , mtest
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def mrd_silhouette():
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pass
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def brendan_faces():
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data = GPy.util.datasets.brendan_faces()
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Y = data['Y'][0:-1:10, :]
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m = GPy.models.GPLVM(data['Y'], 2)
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# optimize
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m.ensure_default_constraints()
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m.optimize(messages=1, max_f_eval=10000)
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ax = m.plot_latent()
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y = m.likelihood.Y[0, :]
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data_show = GPy.util.visualize.image_show(y[None, :], dimensions=(20, 28), transpose=True, invert=False, scale=False)
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lvm_visualizer = GPy.util.visualize.lvm(m, data_show, ax)
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raw_input('Press enter to finish')
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plt.close('all')
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return m
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def stick():
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data = GPy.util.datasets.stick()
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m = GPy.models.GPLVM(data['Y'], 2)
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# optimize
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m.ensure_default_constraints()
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m.optimize(messages=1, max_f_eval=10000)
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ax = m.plot_latent()
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y = m.likelihood.Y[0, :]
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data_show = GPy.util.visualize.stick_show(y[None, :], connect=data['connect'])
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lvm_visualizer = GPy.util.visualize.lvm(m, data_show, ax)
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raw_input('Press enter to finish')
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plt.close('all')
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return m
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# def BGPLVM_oil():
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# data = GPy.util.datasets.oil()
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# Y, X = data['Y'], data['X']
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# X -= X.mean(axis=0)
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# X /= X.std(axis=0)
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#
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# Q = 10
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# M = 30
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#
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# kernel = GPy.kern.rbf(Q, ARD=True) + GPy.kern.bias(Q) + GPy.kern.white(Q)
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# m = GPy.models.Bayesian_GPLVM(X, Q, kernel=kernel, M=M)
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# # m.scale_factor = 100.0
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# m.constrain_positive('(white|noise|bias|X_variance|rbf_variance|rbf_length)')
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# from sklearn import cluster
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# km = cluster.KMeans(M, verbose=10)
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# Z = km.fit(m.X).cluster_centers_
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# # Z = GPy.util.misc.kmm_init(m.X, M)
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# m.set('iip', Z)
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# m.set('bias', 1e-4)
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# # optimize
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# # m.ensure_default_constraints()
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#
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# import pdb; pdb.set_trace()
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# m.optimize('tnc', messages=1)
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# print m
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# m.plot_latent(labels=data['Y'].argmax(axis=1))
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# return m
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