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computations_circular_precision_sensitivity.py
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computations_circular_precision_sensitivity.py
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#!/usr/bin/env python
# encoding: utf-8
"""
computations_circular_precision_sensitivity.py
Created by Loic Matthey on 2013-10-05
Copyright (c) 2013 Gatsby Unit. All rights reserved.
"""
import matplotlib.pyplot as plt
import numpy as np
import scipy.stats as spst
import dataio as DataIO
import utils
import em_circularmixture
# from statisticsmeasurer import *
# from randomfactorialnetwork import *
# from datagenerator import *
# from slicesampler import *
import progress
def check_precision_sensitivity_determ():
''' Let's construct a situation where we have one Von Mises component and one random component. See how the random component affects the basic precision estimator we use elsewhere.
'''
N = 1000
kappa_space = np.array([3., 10., 20.])
# kappa_space = np.array([3.])
nb_repeats = 20
ratio_to_kappa = False
savefigs = True
precision_nb_samples = 101
N_rnd_space = np.linspace(0, N/2, precision_nb_samples).astype(int)
precision_all = np.zeros((N_rnd_space.size, nb_repeats))
kappa_estimated_all = np.zeros((N_rnd_space.size, nb_repeats))
precision_squared_all = np.zeros((N_rnd_space.size, nb_repeats))
kappa_mixtmodel_all = np.zeros((N_rnd_space.size, nb_repeats))
mixtmodel_all = np.zeros((N_rnd_space.size, nb_repeats, 2))
dataio = DataIO.DataIO()
target_samples = np.zeros(N)
for kappa in kappa_space:
true_kappa = kappa*np.ones(N_rnd_space.size)
# First sample all as von mises
samples_all = spst.vonmises.rvs(kappa, size=(N_rnd_space.size, nb_repeats, N))
for repeat in progress.ProgressDisplay(xrange(nb_repeats)):
for i, N_rnd in enumerate(N_rnd_space):
samples = samples_all[i, repeat]
# Then set K of them to random [-np.pi, np.pi] values.
samples[np.random.randint(N, size=N_rnd)] = utils.sample_angle(N_rnd)
# Estimate precision from those samples.
precision_all[i, repeat] = utils.compute_precision_samples(samples, square_precision=False, remove_chance_level=False)
precision_squared_all[i, repeat] = utils.compute_precision_samples(samples, square_precision=True)
# convert circular std dev back to kappa
kappa_estimated_all[i, repeat] = utils.stddev_to_kappa(1./precision_all[i, repeat])
# Fit mixture model
params_fit = em_circularmixture.fit(samples, target_samples)
kappa_mixtmodel_all[i, repeat] = params_fit['kappa']
mixtmodel_all[i, repeat] = params_fit['mixt_target'], params_fit['mixt_random']
print "%d/%d N_rnd: %d, Kappa: %.3f, precision: %.3f, kappa_tilde: %.3f, precision^2: %.3f, kappa_mixtmod: %.3f" % (repeat, nb_repeats, N_rnd, kappa, precision_all[i, repeat], kappa_estimated_all[i, repeat], precision_squared_all[i, repeat], kappa_mixtmodel_all[i, repeat])
if ratio_to_kappa:
precision_all /= kappa
precision_squared_all /= kappa
kappa_estimated_all /= kappa
true_kappa /= kappa
f, ax = plt.subplots()
ax.plot(N_rnd_space/float(N), true_kappa, 'k-', linewidth=3, label='Kappa_true')
utils.plot_mean_std_area(N_rnd_space/float(N), np.mean(precision_all, axis=-1), np.std(precision_all, axis=-1), ax_handle=ax, label='precision')
utils.plot_mean_std_area(N_rnd_space/float(N), np.mean(precision_squared_all, axis=-1), np.std(precision_squared_all, axis=-1), ax_handle=ax, label='precision^2')
utils.plot_mean_std_area(N_rnd_space/float(N), np.mean(kappa_estimated_all, axis=-1), np.std(kappa_estimated_all, axis=-1), ax_handle=ax, label='kappa_tilde')
utils.plot_mean_std_area(N_rnd_space/float(N), np.mean(kappa_mixtmodel_all, axis=-1), np.std(kappa_mixtmodel_all, axis=-1), ax_handle=ax, label='kappa mixt model')
ax.legend()
ax.set_title('Effect of random samples on precision. kappa: %.2f. ratiokappa %s' % (kappa, ratio_to_kappa))
ax.set_xlabel('Proportion random samples. N tot %d' % N)
ax.set_ylabel('Kappa/precision (not same units)')
f.canvas.draw()
if savefigs:
dataio.save_current_figure("precision_sensitivity_kappa%dN%d_{unique_id}.pdf" % (kappa, N))
# Do another plot, with kappa and mixt_target/mixt_random. Use left/right axis separately
f, ax = plt.subplots()
ax2 = ax.twinx()
# left axis, kappa
ax.plot(N_rnd_space/float(N), true_kappa, 'k-', linewidth=3, label='kappa true')
utils.plot_mean_std_area(N_rnd_space/float(N), np.mean(kappa_mixtmodel_all, axis=-1), np.std(kappa_mixtmodel_all, axis=-1), ax_handle=ax, label='kappa')
# Right axis, mixture probabilities
utils.plot_mean_std_area(N_rnd_space/float(N), np.mean(mixtmodel_all[..., 0], axis=-1), np.std(mixtmodel_all[..., 0], axis=-1), ax_handle=ax2, label='mixt target', color='r')
utils.plot_mean_std_area(N_rnd_space/float(N), np.mean(mixtmodel_all[..., 1], axis=-1), np.std(mixtmodel_all[..., 1], axis=-1), ax_handle=ax2, label='mixt random', color='g')
ax.set_title('Mixture model parameters evolution. kappa: %.2f, ratiokappa %s' % (kappa, ratio_to_kappa))
ax.set_xlabel('Proportion random samples. N tot %d' % N)
ax.set_ylabel('Kappa')
ax2.set_ylabel('Mixture proportions')
lines, labels = ax.get_legend_handles_labels()
lines2, labels2 = ax2.get_legend_handles_labels()
ax.legend(lines + lines2, labels + labels2)
if savefigs:
dataio.save_current_figure("precision_sensitivity_mixtmodel_kappa%dN%d_{unique_id}.pdf" % (kappa, N))
return locals()
if __name__ == '__main__':
all_vars = check_precision_sensitivity_determ()
for key, val in all_vars.items():
locals()[key] = val
plt.show()