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run_reg_toy.py
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run_reg_toy.py
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# import matplotlib
# matplotlib.use('Agg')
import numpy as np
import matplotlib as mpl
# mpl.use('pgf')
def figsize(scale, ratio=None):
fig_width_pt = 397.4849 # Get this from LaTeX using \the\textwidth
inches_per_pt = 1.0/72.27 # Convert pt to inch
golden_mean = (np.sqrt(5.0)-1.0)/4 # Aesthetic ratio (you could change this)
if ratio is not None:
golden_mean = ratio
fig_width = fig_width_pt*inches_per_pt*scale # width in inches
fig_height = fig_width*golden_mean # height in inches
fig_size = [fig_width,fig_height]
return fig_size
pgf_with_latex = { # setup matplotlib to use latex for output
"pgf.texsystem": "pdflatex", # change this if using xetex or lautex
"text.usetex": True, # use LaTeX to write all text
"font.family": "serif",
# blank entries should cause plots to inherit fonts from the document
"font.serif": [],
"font.sans-serif": [],
"font.monospace": [],
"axes.labelsize": 10, # LaTeX default is 10pt font.
"font.size": 10,
"legend.fontsize": 8, # Make the legend/label fonts a little smaller
"xtick.labelsize": 8,
"ytick.labelsize": 8,
"figure.figsize": figsize(0.9), # default fig size of 0.9 textwidth
"pgf.preamble": [
# use utf8 fonts becasue your computer can handle it :)
r"\usepackage[utf8x]{inputenc}",
# plots will be generated using this preamble
r"\usepackage[T1]{fontenc}",
# plots will be generated using this preamble
r"\usepackage{amsmath}",
]
}
mpl.rcParams.update(pgf_with_latex)
grey = '#808080'
mpl.rcParams['axes.linewidth'] = 0.3
mpl.rcParams['axes.edgecolor'] = grey
mpl.rcParams['xtick.color'] = grey
mpl.rcParams['ytick.color'] = grey
mpl.rcParams['axes.labelcolor'] = "black"
import gpflow
import osgpr
import sgpr
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
def init_Z(cur_Z, new_X, use_old_Z=True, first_batch=True):
if use_old_Z:
Z = np.copy(cur_Z)
else:
M = cur_Z.shape[0]
M_old = int(0.7 * M)
M_new = M - M_old
old_Z = cur_Z[np.random.permutation(M)[0:M_old], :]
new_Z = new_X[np.random.permutation(new_X.shape[0])[0:M_new], :]
Z = np.vstack((old_Z, new_Z))
return Z
def plot_model(model, ax, cur_x, cur_y, pred_x, seen_x=None, seen_y=None):
mx, vx = model.predict_f(pred_x)
Zopt = model.inducing_variable.Z.numpy()
mu, Su = model.predict_f(Zopt, full_cov=True)
if len(Su.shape) == 3:
Su = Su[0, :, :]
vx = vx[:, 0]
ax.plot(cur_x, cur_y, 'kx', mew=1, alpha=0.8)
if seen_x is not None:
ax.plot(seen_x, seen_y, 'kx', mew=1, alpha=0.2)
ax.plot(pred_x, mx, 'b', lw=2)
ax.fill_between(
pred_x[:, 0], mx[:, 0] - 2*np.sqrt(vx),
mx[:, 0] + 2*np.sqrt(vx),
color='b', alpha=0.3)
ax.plot(Zopt, mu, 'ro', mew=1)
ax.set_ylim([-2.4, 2])
ax.set_xlim([np.min(pred_x), np.max(pred_x)])
plt.subplots_adjust(hspace = .08)
ax.set_ylabel('y')
ax.yaxis.set_ticks(np.arange(-2, 3, 1))
ax.yaxis.set_major_formatter(ticker.FormatStrFormatter('%0.1f'))
return mu, Su, Zopt
def get_data(shuffle):
X = np.loadtxt('../data/reg_toy_x.txt', delimiter=',')
y = np.loadtxt('../data/reg_toy_y.txt', delimiter=',')
X = X.reshape(X.shape[0], 1)
y = y.reshape((y.shape[0], 1))
N = y.shape[0]
gap = N//3
X[:gap, :] = X[:gap, :] - 1
X[2*gap:3*gap, :] = X[2*gap:3*gap, :] + 1
if shuffle:
idxs = np.random.permutation(N)
X = X[idxs, :]
y = y[idxs, :]
return X, y
def optimize(model, **options):
gpflow.optimizers.Scipy().minimize(
model.training_loss, model.trainable_variables,
options=options)
def plot_PEP_optimized(M, alpha, use_old_Z, shuffle):
fig, axs = plt.subplots(4, 1, figsize=figsize(1, ratio=12.0/19.0), sharey=True, sharex=True)
X, y = get_data(shuffle)
N = X.shape[0]
gap = N//3
# get the first portion and call sparse GP regression
X1 = X[:gap, :]
y1 = y[:gap, :]
seen_x = None
seen_y = None
# Z1 = np.random.rand(M, 1)*L
Z1 = X1[np.random.permutation(X1.shape[0])[0:M], :]
model1 = sgpr.SGPR_PEP((X1, y1), gpflow.kernels.RBF(variance=1.0, lengthscales=0.8), Z=Z1, alpha=alpha)
model1.likelihood.variance.assign(0.001)
optimize(model1, disp=1)
# plot prediction
xx = np.linspace(-2, 12, 100)[:,None]
mu1, Su1, Zopt = plot_model(model1, axs[0], X1, y1, xx, seen_x, seen_y)
# now call online method on the second portion of the data
X2 = X[gap:2*gap, :]
y2 = y[gap:2*gap, :]
seen_x = X[:gap, :]
seen_y = y[:gap, :]
Kaa1 = model1.kernel(model1.inducing_variable.Z)
Zinit = init_Z(Zopt, X2, use_old_Z)
model2 = osgpr.OSGPR_PEP((X2, y2), gpflow.kernels.RBF(variance=model1.kernel.variance, lengthscales=model1.kernel.lengthscales), mu1, Su1, Kaa1,
Zopt, Zinit, alpha)
model2.likelihood.variance.assign(model1.likelihood.variance)
optimize(model2, disp=1)
# plot prediction
mu2, Su2, Zopt = plot_model(model2, axs[1], X2, y2, xx, seen_x, seen_y)
# now call online method on the third portion of the data
X3 = X[2*gap:3*gap, :]
y3 = y[2*gap:3*gap, :]
seen_x = np.vstack((seen_x, X2))
seen_y = np.vstack((seen_y, y2))
Kaa2 = model2.kernel(model2.inducing_variable.Z)
Zinit = init_Z(Zopt, X3, use_old_Z)
model3 = osgpr.OSGPR_PEP((X3, y3), gpflow.kernels.RBF(variance=model2.kernel.variance, lengthscales=model2.kernel.lengthscales), mu2, Su2, Kaa2,
Zopt, Zinit, alpha)
model3.likelihood.variance.assign(model2.likelihood.variance)
optimize(model3, disp=1)
mu3, Su3, Zopt = plot_model(model3, axs[2], X3, y3, xx, seen_x, seen_y)
axs[2].set_xlabel('x')
Z4 = X[np.random.permutation(X.shape[0])[0:M], :]
model4 = sgpr.SGPR_PEP((X, y), gpflow.kernels.RBF(variance=1.0, lengthscales=0.8), Z=Z4, alpha=alpha)
model4.likelihood.variance.assign(0.001)
optimize(model4, disp=1)
# plot prediction
xx = np.linspace(-2, 12, 100)[:,None]
mu4, Su4, Zopt = plot_model(model4, axs[3], X, y, xx, None, None)
axs[3].set_xlabel('x')
fig.savefig('../tmp/reg_PEP_alpha_%.3f_M_%d_iid_%r.png' % (alpha, M, shuffle), bbox_inches='tight')
def plot_VFE_optimized(M, use_old_Z, shuffle):
fig, axs = plt.subplots(4, 1, figsize=figsize(1, ratio=12.0/19.0), sharey=True, sharex=True)
X, y = get_data(shuffle)
N = X.shape[0]
gap = N//3
# get the first portion and call sparse GP regression
X1 = X[:gap, :]
y1 = y[:gap, :]
seen_x = None
seen_y = None
# Z1 = np.random.rand(M, 1)*L
Z1 = X1[np.random.permutation(X1.shape[0])[0:M], :]
model1 = gpflow.models.SGPR((X1, y1), gpflow.kernels.RBF(variance=1.0, lengthscales=0.8), inducing_variable=Z1, noise_variance=0.001)
optimize(model1, disp=1)
# plot prediction
xx = np.linspace(-2, 12, 100)[:,None]
mu1, Su1, Zopt = plot_model(model1, axs[0], X1, y1, xx, seen_x, seen_y)
# now call online method on the second portion of the data
X2 = X[gap:2*gap, :]
y2 = y[gap:2*gap, :]
seen_x = X[:gap, :]
seen_y = y[:gap, :]
Kaa1 = model1.kernel(model1.inducing_variable.Z)
Zinit = init_Z(Zopt, X2, use_old_Z)
model2 = osgpr.OSGPR_VFE((X2, y2), gpflow.kernels.RBF(variance=model1.kernel.variance, lengthscales=model1.kernel.lengthscales), mu1, Su1, Kaa1,
Zopt, Zinit)
model2.likelihood.variance.assign(model1.likelihood.variance)
optimize(model2, disp=1)
# plot prediction
mu2, Su2, Zopt = plot_model(model2, axs[1], X2, y2, xx, seen_x, seen_y)
# now call online method on the third portion of the data
X3 = X[2*gap:3*gap, :]
y3 = y[2*gap:3*gap, :]
seen_x = np.vstack((seen_x, X2))
seen_y = np.vstack((seen_y, y2))
Kaa2 = model2.kernel(model2.inducing_variable.Z)
Zinit = init_Z(Zopt, X3, use_old_Z)
model3 = osgpr.OSGPR_VFE((X3, y3), gpflow.kernels.RBF(variance=model2.kernel.variance, lengthscales=model2.kernel.lengthscales), mu2, Su2, Kaa2,
Zopt, Zinit)
model3.likelihood.variance.assign(model2.likelihood.variance)
optimize(model3, disp=1)
mu3, Su3, Zopt = plot_model(model3, axs[2], X3, y3, xx, seen_x, seen_y)
Z4 = X[np.random.permutation(X.shape[0])[0:M], :]
model4 = gpflow.models.SGPR((X, y), gpflow.kernels.RBF(variance=1.0, lengthscales=0.8), inducing_variable=Z4, noise_variance=0.001)
optimize(model4, disp=1)
# plot prediction
xx = np.linspace(-2, 12, 100)[:,None]
mu4, Su4, Zopt4 = plot_model(model4, axs[3], X, y, xx, None, None)
axs[3].set_xlabel('x')
fig.savefig('../tmp/reg_VFE_M_%d_iid_%r.png' % (M, shuffle), bbox_inches='tight')
if __name__ == '__main__':
use_old_Z = False
alpha = 0.5
seed = 10
shuffle = False
np.random.seed(seed)
plot_PEP_optimized(10, alpha, use_old_Z, shuffle)
np.random.seed(seed)
plot_VFE_optimized(10, use_old_Z, shuffle)