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regression.py
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regression.py
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#
# This file is part of the RGP distribution (https://github.com/smidmatej/RGP).
# Copyright (c) 2023 Smid Matej.
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, version 3.
#
# This program is distributed in the hope that it will be useful, but
# WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <http://www.gnu.org/licenses/>.
#
# Core
import numpy as np
from RGP import RBF, RGP
# Plotting
import matplotlib.pyplot as plt
from matplotlib import animation
from matplotlib import gridspec
from matplotlib.collections import PolyCollection
# Cosmetic
import seaborn as sns
from tqdm import tqdm
def main():
# ----- The basis vectors -----
X_ = np.arange(-10,10,1).reshape(-1,1)
y_ = np.random.normal(0, 0, size=X_.shape)
# ----- The true function we are trying to approximate -----
X_query = np.arange(-10,10,0.2).reshape(-1,1)
y_true = np.sin(X_query)
# ----- The training data -----
n_training = 50
X_t = np.random.uniform(-10,10, size=(n_training,1))
X_t = np.sort(X_t, axis=0)
# Put half of the data at the end in reverse order
X_t = np.concatenate((X_t[::2], np.flip(X_t[::2])), axis=0)
sample_noise = 0.1
y_t = np.sin(X_t) + np.random.normal(0, sample_noise, size=X_t.shape)
rgp = RGP(X_, y_)
mean_training = [None] * (X_t.shape[0]+1)
cov_training = [None] * (X_t.shape[0]+1)
g_ = [None] * (X_t.shape[0]+1)
mean_training[0], cov_training[0] = rgp.predict(X_query, cov=True)
g_[0] = rgp.mu_g_t # Current estimate of g at X
print('Training model recursively...')
pbar = tqdm(total=X_t.shape[0])
for t in range(X_t.shape[0]):
rgp.regress(X_t[t,:], y_t[t,:])
mean_training[t+1], cov_training[t+1] = rgp.predict(X_query, cov=True)
g_[t+1] = rgp.mu_g_t # Current estimate of g at X
pbar.update()
pbar.close()
# ----------------- PLOT -----------------
cs = [[x/256 for x in (205, 70, 49)], \
[x/256 for x in (105, 220, 158)], \
[x/256 for x in (102, 16, 242)], \
[x/256 for x in (7, 59, 58)]]
# Color scheme convert from [0,255] to [0,1]
cs = [[x/256 for x in (8, 65, 92)], \
[x/256 for x in (204, 41, 54)], \
[x/256 for x in (118, 148, 159)], \
[x/256 for x in (232, 197, 71)]]
plt.style.use('fast')
sns.set_style("whitegrid")
fig = plt.figure(figsize=(10,10), dpi=100)
gs = gridspec.GridSpec(2, 2, width_ratios=[1, 1], height_ratios=[1, 1])
ax = [None]*4
ax[0] = fig.add_subplot(gs[0, 0])
ax[1] = fig.add_subplot(gs[0, 1])
ax[2] = fig.add_subplot(gs[1, 0])
ax[3] = fig.add_subplot(gs[1, 1])
ax[0].plot(X_query, y_true, color=cs[1], label='True function')
ax[0].plot(X_query, mean_training[0], '--', color=cs[0], label='E[g(x)]')
ax[0].scatter(X_, y_, marker='o', s=20, color=cs[0], label='Basis Vectors')
ax[0].fill_between(X_query.reshape(-1),
mean_training[0].reshape(-1) - 2*np.sqrt(np.diag(cov_training[0])),
mean_training[0].reshape(-1) + 2*np.sqrt(np.diag(cov_training[0])), color=cs[3], alpha=0.1)
ax[0].set_xlim((min((min(X_t), min(X_query), min(X_))) , max((max(X_t), max(X_query), max(X_)))))
#plt.set_ylim((min((min(y_), min(y_t), min(y_true))) , max((max(y_), max(y_t), max(y_true)))))
ax[0].set_ylim((-2,2))
ax[0].set_xlabel('x')
ax[0].set_ylabel('y')
ax[0].legend()
ax[0].set_title('Prior with no training data')
ax[1].plot(X_query, y_true, color=cs[1], label='True function')
ax[1].scatter(X_, g_[-1], marker='o', s=20, color=cs[0], label='Basis Vectors')
ax[1].scatter(X_t, y_t, marker='+', color=cs[2], label='Training samples')
ax[1].plot(X_query, mean_training[-1], '--', color=cs[0], label='E[g(x)]')
ax[1].fill_between(X_query.reshape(-1),
mean_training[-1].reshape(-1) - 2*np.sqrt(np.diag(cov_training[-1])),
mean_training[-1].reshape(-1) + 2*np.sqrt(np.diag(cov_training[-1])), color=cs[3], alpha=0.1)
ax[1].set_xlim((min((min(X_t), min(X_query), min(X_))) , max((max(X_t), max(X_query), max(X_)))))
#plt.set_ylim((min((min(y_), min(y_t), min(y_true))) , max((max(y_), max(y_t), max(y_true)))))
ax[1].set_ylim((-2,2))
ax[1].set_xlabel('x')
ax[1].set_ylabel('y')
ax[1].legend()
ax[1].set_title('Posterior after training')
ax[2].plot(X_query, y_true - mean_training[0], color=cs[0])
ax[2].set_xlim((min((min(X_t), min(X_query), min(X_))) , max((max(X_t), max(X_query), max(X_)))))
#plt.set_ylim((min((min(y_), min(y_t), min(y_true))) , max((max(y_), max(y_t), max(y_true)))))
ax[2].set_ylim((-2,2))
ax[2].set_xlabel('x')
ax[2].set_ylabel('y')
ax[2].set_title('Difference (true - prior)')
ax[3].plot(X_query, y_true - mean_training[-1], color=cs[0])
ax[3].set_xlim((min((min(X_t), min(X_query), min(X_))) , max((max(X_t), max(X_query), max(X_)))))
#plt.set_ylim((min((min(y_), min(y_t), min(y_true))) , max((max(y_), max(y_t), max(y_true)))))
ax[3].set_ylim((-2,2))
ax[3].set_xlabel('x')
ax[3].set_ylabel('y')
ax[3].set_title('Difference (true - prior)')
plt.savefig('img/regression_comparisson.png')
plt.show()
# ----------------- ANIMATION -----------------
print('Rendering animation...')
def animate(i):
line_mean.set_data(X_query, mean_training[i])
scat_basis_vectors.set_offsets(np.array([X_.ravel(), g_[i].ravel()]).T)
scat_training_points.set_offsets(np.array([X_t[:i,:].ravel(), y_t[:i,:].ravel()]).T)
global fill_between
fill_between.remove()
fill_between = ax.fill_between(X_query.reshape(-1),
mean_training[i].reshape(-1) - 2*np.sqrt(np.diag(cov_training[i])),
mean_training[i].reshape(-1) + 2*np.sqrt(np.diag(cov_training[i])), color=cs[1], alpha=0.2)
pbar.update()
animation.writer = animation.writers['ffmpeg']
plt.ioff() # Turn off interactive mode to hide rendering animations
plt.style.use('fast')
sns.set_style("whitegrid")
#gs = gridspec.GridSpec(2, 2)
fig = plt.figure(figsize=(10,10), dpi=100)
ax = fig.add_subplot(111)
line_mean, = ax.plot([], [], '--', color=cs[0], label='E[g(x)]')
scat_training_points = ax.scatter([], [], marker='+', color=cs[1], label='Training samples')
scat_basis_vectors = ax.scatter([], [], marker='o', color=cs[2], label='Basis Vectors')
# Hack to be able to change the fill at each step
global fill_between
fill_between = ax.fill_between([],
[],
[], color=cs[3], alpha=0.2)
ax.plot(X_query, y_true, color='gray')
ax.set_xlim((min((min(X_t), min(X_query), min(X_))) , max((max(X_t), max(X_query), max(X_)))))
#ax.set_ylim((min((min(y_), min(y_t), min(y_true))) , max((max(y_), max(y_t), max(y_true)))))
ax.set_ylim((-2,2))
ax.set_xlabel('x')
ax.set_ylabel('y')
ax.set_title('Recursive Gaussian Process')
ax.legend()
pbar = tqdm(total=X_t.shape[0])
number_of_frames = len(mean_training)
ani = animation.FuncAnimation(fig, animate, frames=number_of_frames, interval=500)
ani.save('img/regression.gif', writer='imagemagick', fps=10, dpi=30)
ani.save('img/regression.mp4', writer='ffmpeg', fps=10, dpi=100)
pbar.close()
plt.show()
if __name__ == '__main__':
main()