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ICML_Figures_and_Tables.py
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"""
Figures for Spectral Subsampling MCMC for Stationary Time series data.
Figures of interest:
1. Effects of grouping for all four examples.
Option: 'GroupingEffectOnVariance'
1. For all four examples, Relative Computing Time (relative to MCMC) for Taylor and Coreset (coreset only on large dataset, does not make sense to do coreset for small groupsize).
Option: 'GroupingEffectOnVariance'
2. KDE for Subsampling MCMC, Taylor and Coreset and when possible (for ARMA) the MCMC on the true likelihood. This is a four by 2 (or 3) figure where each row corresponds to one example, and the columns are parameters.
3. As 2. but for all parameters. One figure for each example. These will go to the Supplement.
NOTE 1: To replicate the figures, the main code must be done to produce output for each of the models (see settings in the submission). This file then reads in that output to produce the figures.
NOTE 2: Obviously, the file paths in this program need to be changed.
"""
from __future__ import division
import autograd.scipy.special as sc_autograd
import matplotlib as mpl
import matplotlib.pyplot as plt
import matplotlib.colors as colors
import seaborn as sns
import sys
import os
import copy
import pandas as pd
import statsmodels.api as sm
import rpy2.robjects as robjects
import pickle
import numpy as np
import scipy.stats as sps
import scipy.special as sc
import random
alias = "GARCH-man"
which_plots = ['GroupingEffectOnVariance', 'RCT_plots',
'KDEs_all', 'KDEs_selected', 'Spectral_plots']
plotSaveDir = '/home/%s/Dropbox/Research/Papers/Started 2019/Temporal Subsampling code/FigsICMLPaper/' % alias
if not os.path.exists(plotSaveDir):
os.makedirs(plotSaveDir)
set_font_size = 22 # 20 #10
set_tick_size = 22
set_title_size = 18 # 35 #50
sns.set(style="ticks")
plt.ticklabel_format(style='sci', axis='x', scilimits=(0, 0))
mpl.rcParams['xtick.labelsize'] = 14
mpl.rcParams['ytick.labelsize'] = 14
mpl.rcParams['axes.titlesize'] = 18
plt.rc('axes', labelsize=12)
plt.rc('legend', fontsize=22)
mpl.rcParams['ps.useafm'] = True
mpl.rcParams['pdf.use14corefonts'] = True
mpl.rcParams['text.usetex'] = True
# For computing IF factors using R:
r = robjects.r
r.library('coda')
EffectiveSize = r['effectiveSize'] # Get function of interest
# from d to unconstrained
# z = np.arctanh(d) # 'log'-scales
# from unconstrained to d (-0.5, 0.5)
# d = 0.5*np.tanh(z) # 'exp'-scale
def p_gram(x): # Construct Periodogram
id = int(np.floor((len(x)-1)/2))
return np.square(np.abs(x[0:(id+1)]))/(2 * np.pi * len(x))
def f_ARTFIMA(id, phi, theta, var, d, lambda_, var2, n):
# General spectral density that includes all the ones in the paper as special cases.
# Note: var2 only exist if there is an ARTFIMA process on an SV model. Otherwise it is zero. This is for the Stochastic volatility ARTFIMA - see paper for details
omega = (2*np.pi*id/n)
FI_term = np.abs(1 - np.exp(-(lambda_ + 1j*omega))
)**(-2*d) # Fractional Integration Term
if phi.any():
log_arg_phi = np.outer(-1j*omega, np.arange(1, len(phi)+1))
vv1 = 1/(1 - np.sum(phi * np.exp(log_arg_phi), 1))
else:
vv1 = 1
if theta.any():
log_arg_theta = np.outer(-1j*omega, np.arange(1, len(theta)+1))
vv2 = (1 + np.sum(theta * np.exp(log_arg_theta), 1))
else:
vv2 = 1
f = FI_term * (var/(2*np.pi)) * (np.real(vv1)**2 + np.imag(vv1)**2) \
* (np.real(vv2)**2 + np.imag(vv2)**2) + (var2/(2*np.pi))
return f
def reparam(params, MA=False):
"""
Transforms params to induce stationarity/invertability.
Transformation if from partial-autocorrelations to standard parameterization.
"""
newparams = np.array(params, copy=True)
tmp = np.array(params, copy=True)
for j in range(1, len(params)):
if not MA:
tmp_new = tmp[:j] - \
np.array([(newparams[j]*newparams[j-k-1]) for k in range(j)])
else:
tmp_new = tmp[:j] + \
np.array([(newparams[j]*newparams[j-k-1]) for k in range(j)])
tmp = np.hstack([tmp_new, newparams[j:]])
newparams = np.hstack((tmp[:j], newparams[j:]))
return newparams
def nparray2rmatrix(x):
"""
Converts a nparray to an r matrix.
"""
try:
nr, nc = x.shape
except ValueError:
nr = x.shape[0]
nc = 1
xvec = robjects.FloatVector(x.transpose().reshape((x.size)))
xr = robjects.r.matrix(xvec, nrow=nr, ncol=nc)
return xr
############
# Figure: Relative variance to study the effect of grouping
############
if 'GroupingEffectOnVariance' in which_plots:
# 2 x 2 plot
nrow = 2
ncol = 2
titles = ['ARMA(2,3)', 'ARTFIMA(2,2)', 'ARFIMA(2,1)', 'ARTFIMA-SV(1,1)']
#file_names = ['sigma2_different_Gs_ARMA_ICML.pkl', 'sigma2_different_Gs_ARTFIMA_ICML.pkl', 'sigma2_different_Gs_ARFIMA_ICML.pkl', 'sigma2_different_Gs_ARTFIMA-SV_ICML.pkl']
file_names = ['sigma2_different_Gs_ARMA_ICML.pkl', 'sigma2_different_Gs_ARTFIMA_ICML.pkl',
'sigma2_different_Gs_ARFIMA_ICML.pkl', 'sigma2_different_Gs_ARTFIMA-SV_ICML.pkl']
file_path = "/home/%s/Dropbox/Research/Papers/Started 2019/Temporal Subsampling code/Results/Runs/" % alias
fig, ax = plt.subplots(nrow, ncol)
ind = 0
for ii in range(nrow):
for jj in range(ncol):
ax[ii][jj].spines['top'].set_visible(False)
ax[ii][jj].spines['right'].set_visible(False)
ax[ii][jj].get_xaxis().tick_bottom()
ax[ii][jj].get_yaxis().tick_left()
file_name = file_path + file_names[ind]
f = open(file_name, "rb")
loadDict = pickle.load(f)
f.close()
sigma2_G_collect = loadDict['sigma2_Gs']
GList = loadDict['Gs']
mcmc_length = len(sigma2_G_collect[0])
burnIn = 1001
sigma2_LL_groupingG10 = sigma2_G_collect[0][burnIn:]
sigma2_LL_groupingG100 = sigma2_G_collect[1][burnIn:]
sigma2_LL_no_grouping = sigma2_G_collect[2][burnIn:]
iteration = range(burnIn - 1, mcmc_length - 1)
ax[ii][jj].set_ylabel(
r'$\sigma^2_{\widehat{\ell}_{\mathrm{diff}}}/\sigma^2_{\widehat{\ell}_{\mathrm{gr}}}$')
ax[ii][jj].set_xlabel('MCMC iteration')
ax[ii][jj].set_title(titles[ind], fontsize=set_title_size)
G10, = ax[ii][jj].plot(iteration, sigma2_LL_no_grouping/sigma2_LL_groupingG10,
color='blue', lw=0.5, alpha=1) # , label = r'$|G|=100$')
G100, = ax[ii][jj].plot(iteration, sigma2_LL_no_grouping/sigma2_LL_groupingG100,
color='green', lw=0.5, alpha=1) # , label = r'$|G|=10$')
G1000, = ax[ii][jj].plot(iteration, np.ones(len(
sigma2_LL_no_grouping)), color='red', lw=0.5, alpha=1) # , label = r'$|G|=1$', lw=0.5)
ax[ii][jj].set_xticks([1000, 5000, 10000])
pow_ = 0.3
if ind == 0:
#ax[ii][jj].set_ylim([0, 30])
ax[ii][jj].set_ylim([10**(-.5*pow_), 400])
ax[ii][jj].set_yticks([10**(-pow_), 1, 10])
elif ind == 1:
#ax[ii][jj].set_ylim([0, 20])
ax[ii][jj].set_ylim([10**(-.5*pow_), 20])
ax[ii][jj].set_yticks([10**(-pow_), 1, 5, 10, 15])
elif ind == 2:
#ax[ii][jj].set_ylim([0, 20])
ax[ii][jj].set_ylim([10**(-.5*pow_), 20])
ax[ii][jj].set_yticks([10**(-pow_), 1, 5, 10, 15])
elif ind == 3:
#ax[ii][jj].set_ylim([0, 30])
ax[ii][jj].set_ylim([10**(-.5*pow_), 30])
ax[ii][jj].set_yticks([10**(-pow_), 1, 5, 10, 15, 20])
if ind == 0:
ax[ii][jj].legend((G10, G100, G1000), (r'$|G|=100$', r'$|G|=10$', r'$|G|=1$'), prop={
'size': set_tick_size-12}, loc="upper right")
try:
plt.tight_layout()
except ValueError:
print("Plots are corrupted")
ax[ii][jj].set_yscale('log')
ind = ind + 1
fig.subplots_adjust(hspace=0.8, wspace=0.4)
plt.savefig(plotSaveDir + "GroupingEffectOnVariance.pdf")
########################################
# RCTs for all examples 2 x 2.
########################################
if 'RCT_plots' in which_plots:
####
# 2 x 2 plot
nrow = 2
ncol = 2
set_tick_size = 13
file_path = "/home/%s/Dropbox/Research/Papers/Started 2019/Temporal Subsampling code/Results/Runs/" % alias
titles = ['ARMA(2,3)', 'ARTFIMA(2,2)', 'ARFIMA(2,1)', 'ARTFIMA-SV(1,1)']
file_names_MCMC = ['ARMA/MCMC_ARMA_dataVancouver_AR2_MA3_n22000_AR2_MA3_seed1_MCMCiter10000.pkl',
'ARTFIMA/MCMC_ARTFIMA_dataBromma_AR2_TFI_MA2_n225000_AR2_MA2_seed1_MCMCiter10000.pkl',
'ARFIMA/MCMC_ARFIMA_dataSimulated_AR2_FI_MA1_n2500000_AR2_MA1_seed1_MCMCiter10000.pkl',
'ARTFIMA_SV/MCMC_ARTFIMA_SV_dataBitcoin_AR1_TFI_MA1_SV_new_n500000_AR1_MA1_seed1_MCMCiter10000.pkl']
file_names_MCMC = [file_path + file_names_MCMC[item] for item in range(4)]
file_names_pseudo_MCMC_Taylor = ['ARMA/Taylor/2020-01-30/20:40/Pseudo_marginal_results.pkl',
'ARTFIMA/Taylor/2020-01-30/22:22/Pseudo_marginal_results.pkl',
'ARFIMA/Taylor/2020-02-01/12:13/Pseudo_marginal_results.pkl',
'ARTFIMA_SV/Taylor/2020-02-06/16:10/Pseudo_marginal_results.pkl']
file_names_pseudo_MCMC_Taylor = [
file_path + file_names_pseudo_MCMC_Taylor[item] for item in range(4)]
file_names_pseudo_MCMC_Coreset = [None,
'ARTFIMA/coreset/2020-01-31/00:29/Pseudo_marginal_results.pkl',
'ARFIMA/coreset/2020-02-01/06:35/Pseudo_marginal_results.pkl',
'ARTFIMA_SV/coreset/2020-02-06/17:31/Pseudo_marginal_results.pkl']
file_names_pseudo_MCMC_Coreset = [
None] + [file_path + file_names_pseudo_MCMC_Coreset[item] for item in range(1, 4)]
fig, ax = plt.subplots(nrow, ncol)
ind = 0
for ii in range(nrow):
for jj in range(ncol):
# Specific for each model
if ind == 0:
# ARMA(2,3)
n = 22000
G = 1000
m = 20
groupSize = n/G
mcmc_length = 10000
M = 200
q = 2
p = 3
elif ind == 1:
# ARTFIMA(2,2)
n = 225000
G = 1000
m = 10
groupSize = n/G
mcmc_length = 10000
M = 200
q = 2
p = 2
elif ind == 2:
# ARFIMA(2,1)
n = 2500000
G = 1000
m = 10
groupSize = n/G
mcmc_length = 10000
M = 200
q = 2
p = 1
elif ind == 3:
# ARTFIMA-SV(1,1)
n = 500000
G = 1000
m = 10
groupSize = n/G
mcmc_length = 10000
M = 200
q = 1
p = 1
ax[ii][jj].spines['top'].set_visible(False)
ax[ii][jj].spines['right'].set_visible(False)
ax[ii][jj].get_xaxis().tick_bottom()
ax[ii][jj].get_yaxis().tick_left()
dict_MCMC = pickle.load(open(file_names_MCMC[ind], 'rb'))
dict_pseudo_MCMC_Taylor = pickle.load(
open(file_names_pseudo_MCMC_Taylor[ind], 'rb'))
if file_names_pseudo_MCMC_Coreset[ind] is not None:
dict_pseudo_MCMC_Coreset = pickle.load(
open(file_names_pseudo_MCMC_Coreset[ind], 'rb'))
burnIn = 1000
samples_MCMC = dict_MCMC['samples'][burnIn + 1:, :]
samples_pseudo_MCMC_Taylor = dict_pseudo_MCMC_Taylor['samples'][burnIn + 1:, :]
if file_names_pseudo_MCMC_Coreset[ind] is not None:
samples_pseudo_MCMC_Coreset = dict_pseudo_MCMC_Coreset['samples'][burnIn + 1:, :]
# Cast partial auto-correlation to ordinary parameterization.
samples_MCMC[:, :q] = np.vstack(
map(lambda x: reparam(x, MA=False), samples_MCMC[:, :q]))
samples_pseudo_MCMC_Taylor[:, :q] = np.vstack(
map(lambda x: reparam(x, MA=False), samples_pseudo_MCMC_Taylor[:, :q]))
if file_names_pseudo_MCMC_Coreset[ind] is not None:
samples_pseudo_MCMC_Coreset[:, :q] = np.vstack(
map(lambda x: reparam(x, MA=False), samples_pseudo_MCMC_Coreset[:, :q]))
samples_MCMC[:, q:(
q + p)] = np.vstack(map(lambda x: reparam(x, MA=True), samples_MCMC[:, q:(q + p)]))
samples_pseudo_MCMC_Taylor[:, q:(q + p)] = np.vstack(
map(lambda x: reparam(x, MA=True), samples_pseudo_MCMC_Taylor[:, q:(q + p)]))
if file_names_pseudo_MCMC_Coreset[ind] is not None:
samples_pseudo_MCMC_Coreset[:, q:(q + p)] = np.vstack(
map(lambda x: reparam(x, MA=True), samples_pseudo_MCMC_Coreset[:, q:(q + p)]))
# End Cast partial auto-correlation
# ['ARMA(2,3)', 'ARTFIMA(2,2)', 'ARFIMA(2,1)', 'ARTFIMA-SV(1,1)']
if ind == 0:
# ARMA
sigma2_ind_from_last = -1
d_ind_from_last = None
lambda_ind_from_last = None
var2_ind_from_last = None
elif ind == 1:
# ARTFIMA
sigma2_ind_from_last = -2
d_ind_from_last = -1
lambda_ind_from_last = -3
var2_ind_from_last = None
elif ind == 2:
# ARFIMA
sigma2_ind_from_last = -2
d_ind_from_last = -1
lambda_ind_from_last = None
var2_ind_from_last = None
elif ind == 3:
# ARTFIMA-SV
sigma2_ind_from_last = -2
d_ind_from_last = -1
lambda_ind_from_last = -3
var2_ind_from_last = -4
# d parameter
if d_ind_from_last is not None and ind == 2:
samples_MCMC[:, d_ind_from_last] = 0.5 * \
np.tanh(samples_MCMC[:, d_ind_from_last])
samples_pseudo_MCMC_Taylor[:, d_ind_from_last] = 0.5 * \
np.tanh(samples_pseudo_MCMC_Taylor[:, d_ind_from_last])
samples_pseudo_MCMC_Coreset[:, d_ind_from_last] = 0.5 * \
np.tanh(samples_pseudo_MCMC_Coreset[:, d_ind_from_last])
# NOTE: For ind = 1 and ind = 3 the parameterization is just d (unrestricted).
# variance param (all models have it)
samples_MCMC[:, sigma2_ind_from_last] = np.exp(
samples_MCMC[:, sigma2_ind_from_last])
samples_pseudo_MCMC_Taylor[:, sigma2_ind_from_last] = np.exp(
samples_pseudo_MCMC_Taylor[:, sigma2_ind_from_last])
if file_names_pseudo_MCMC_Coreset[ind] is not None:
samples_pseudo_MCMC_Coreset[:, sigma2_ind_from_last] = np.exp(
samples_pseudo_MCMC_Coreset[:, sigma2_ind_from_last])
# Lambda
if lambda_ind_from_last is not None:
samples_MCMC[:, lambda_ind_from_last] = np.exp(
samples_MCMC[:, lambda_ind_from_last])
samples_pseudo_MCMC_Taylor[:, lambda_ind_from_last] = np.exp(
samples_pseudo_MCMC_Taylor[:, lambda_ind_from_last])
samples_pseudo_MCMC_Coreset[:, lambda_ind_from_last] = np.exp(
samples_pseudo_MCMC_Coreset[:, lambda_ind_from_last])
# var2 parameter
if var2_ind_from_last is not None:
samples_MCMC[:, var2_ind_from_last] = np.exp(
samples_MCMC[:, var2_ind_from_last])
samples_pseudo_MCMC_Taylor[:, var2_ind_from_last] = np.exp(
samples_pseudo_MCMC_Taylor[:, var2_ind_from_last])
samples_pseudo_MCMC_Coreset[:, var2_ind_from_last] = np.exp(
samples_pseudo_MCMC_Coreset[:, var2_ind_from_last]) # Coreset included for this example
if file_names_pseudo_MCMC_Coreset[ind] is not None:
coreset_sizes = dict_pseudo_MCMC_Coreset['coreset_sizes']
pVar = samples_MCMC.shape[1]
# Cost:
cost_MCMC = mcmc_length*n
# all data once, then groupSize x number of samples groups
cost_pseudo_MCMC_Taylor = n + mcmc_length*m*groupSize
if file_names_pseudo_MCMC_Coreset[ind] is not None:
# Constructing coreset for every group, then evaluating the subsample plus evaluating the coreset. NOTE: One could argue that if we run in paralllel the construction of the coreset is M*n/G
cost_pseudo_MCMC_Coreset = M*n + mcmc_length * \
(m*groupSize + np.sum(coreset_sizes))
IF_MCMC = np.zeros(pVar)
IF_pseudo_MCMC_Taylor = np.zeros(pVar)
if file_names_pseudo_MCMC_Coreset[ind] is not None:
IF_pseudo_MCMC_Coreset = np.zeros(pVar)
CT_MCMC = np.zeros(pVar)
CT_pseudo_MCMC_Taylor = np.zeros(pVar)
if file_names_pseudo_MCMC_Coreset[ind] is not None:
CT_pseudo_MCMC_Coreset = np.zeros(pVar)
for j in range(pVar):
# Compute effective samples
PosteriorDrawsBetaRFormat = nparray2rmatrix(samples_MCMC[:, j])
ESS_MCMC = np.array(EffectiveSize(PosteriorDrawsBetaRFormat))
PosteriorDrawsBetaRFormat = nparray2rmatrix(
samples_pseudo_MCMC_Taylor[:, j])
ESS_pseudo_MCMC_Taylor = np.array(
EffectiveSize(PosteriorDrawsBetaRFormat))
if file_names_pseudo_MCMC_Coreset[ind] is not None:
PosteriorDrawsBetaRFormat = nparray2rmatrix(
samples_pseudo_MCMC_Coreset[:, j])
ESS_pseudo_MCMC_Coreset = np.array(
EffectiveSize(PosteriorDrawsBetaRFormat))
IF_MCMC[j] = (len(samples_MCMC)/ESS_MCMC[0])
IF_pseudo_MCMC_Taylor[j] = (
len(samples_pseudo_MCMC_Taylor)/ESS_pseudo_MCMC_Taylor)
if file_names_pseudo_MCMC_Coreset[ind] is not None:
IF_pseudo_MCMC_Coreset[j] = (
len(samples_pseudo_MCMC_Coreset)/ESS_pseudo_MCMC_Coreset)
CT_MCMC = cost_MCMC*IF_MCMC
CT_pseudo_MCMC_Taylor = cost_pseudo_MCMC_Taylor*IF_pseudo_MCMC_Taylor
if file_names_pseudo_MCMC_Coreset[ind] is not None:
CT_pseudo_MCMC_Coreset = cost_pseudo_MCMC_Coreset*IF_pseudo_MCMC_Coreset
if file_names_pseudo_MCMC_Coreset[ind] is not None:
RCT_pseudo_MCMC_Coreset = CT_MCMC/CT_pseudo_MCMC_Coreset
RCT_pseudo_MCMC_Taylor = CT_MCMC/CT_pseudo_MCMC_Taylor
if ind == 0:
# Plot without coreset.
RCT_pseudo_MCMC_Taylor = CT_MCMC/CT_pseudo_MCMC_Taylor
ax[ii][jj].set_title(titles[ind], fontsize=set_title_size)
# Weights for CT
collist = ['#ffff33', '#377eb8', 'r']
collist = ['#4daf4a', '#377eb8', 'r'] # NOTE: Green, blue, red
h0 = RCT_pseudo_MCMC_Taylor
NN = len(h0)
ind_ = np.arange(NN) # the x locations for the groups
width = 0.15 # the width of the bars
rects = ax[ii][jj].bar(
2*ind_, h0, width, color=collist[1], edgecolor=collist[1])
# add some text for labels, title and axes ticks
ax[ii][jj].set_ylabel(
r'$\mathrm{RCT}$', fontsize=set_font_size)
ax[ii][jj].set_xlim([-1, 2*NN])
ax[ii][jj].set_ylim([0, 100])
ax[ii][jj].set_xticks(ind_*2)
#ax[ii][jj].legend((rects[0]), ('sisen'), prop={'size' : set_tick_size-4}, loc = "upper right")
ax[ii][jj].set_xticklabels(
(r'$\phi_{1}$', r'$\phi_{2}$', r'$\theta_{1}$', r'$\theta_{2}$', r'$\theta_{3}$', r'$\sigma^2$'))
ax[ii][jj].tick_params(
axis='both', which='major', labelsize=set_tick_size)
else:
ax[ii][jj].set_title(titles[ind], fontsize=set_title_size)
# Weights for CT
collist = ['#ffff33', '#377eb8', 'r']
collist = ['#4daf4a', '#377eb8', 'r'] # NOTE: Green, blue, red
h0 = RCT_pseudo_MCMC_Coreset
h1 = RCT_pseudo_MCMC_Taylor
NN = len(h0)
ind_ = np.arange(NN) # the x locations for the groups
width = 0.15 # the width of the bars
rects1 = ax[ii][jj].bar(
ind_, h0, width, color=collist[0], edgecolor=collist[0])
rects2 = ax[ii][jj].bar(
ind_+width, h1, width, color=collist[1], edgecolor=collist[1])
# add some text for labels, title and axes ticks
# NOTE: More parameters, need to change this
ax[ii][jj].set_ylabel(
r'$\mathrm{RCT}$', fontsize=set_font_size)
if ind == 1:
ax[ii][jj].legend((rects1[0], rects2[0]), (r'$\mathrm{Coreset}$', r'$\mathrm{Taylor}$'), prop={
'size': set_tick_size-4}, loc="upper right")
ax[ii][jj].set_ylim([0, 180])
ax[ii][jj].set_xlim([-1, NN + 1])
else:
ax[ii][jj].set_ylim([0, 130])
ax[ii][jj].set_xlim([-1, NN + 1])
ax[ii][jj].set_yticks([0, 25, 50, 75, 100])
ax[ii][jj].set_xticks(ind_+0.5*width)
# ['ARMA(2,3)', 'ARTFIMA(2,2)', 'ARFIMA(2,1)', 'ARTFIMA-SV(1,1)']
if ind == 1:
ax[ii][jj].set_xticklabels(
(r'$\phi_1$', r'$\phi_2$', r'$\theta_1$', r'$\theta_2$', r'$\lambda$', r'$\sigma^2$', r'$d$'))
elif ind == 2:
ax[ii][jj].set_xticklabels(
(r'$\phi_1$', r'$\phi_2$', r'$\theta_1$', r'$\sigma^2$', r'$d$'))
elif ind == 3:
ax[ii][jj].set_xticklabels(
(r'$\phi_1$', r'$\theta_1$', r'$\sigma_{\epsilon}^2$', r'$\lambda$', r'$\sigma^2$', r'$d$'))
ax[ii][jj].tick_params(
axis='both', which='major', labelsize=set_tick_size)
ind = ind + 1
fig.subplots_adjust(hspace=0.5, wspace=0.4)
plt.savefig(plotSaveDir + "RCT_all_models.pdf")
if 'KDEs_selected' in which_plots:
bandwidthKDE = 0.5
####
# 4 x 3 plot
nrow = 4
ncol = 3
# Params to plot for each example. The full list
# ARMA(2,3) ind 0
# ARTFIMA(2,2) ind 1
# ARFIMA(2,1) ind 2
# ARTFIMA-SV(1,1) ind 3
param_names = [[r'$\phi_{1}$', r'$\phi_{2}$', r'$\theta_{1}$', r'$\theta_{2}$', r'$\theta_{3}$', r'$\sigma^2$'],
[r'$\phi_1$', r'$\phi_2$', r'$\theta_1$',
r'$\theta_2$', r'$\lambda$', r'$\sigma^2$', r'$d$'],
[r'$\phi_1$', r'$\phi_2$', r'$\theta_1$', r'$\sigma^2$', r'$d$'],
[r'$\phi_1$', r'$\theta_1$', r'$\sigma_{\epsilon}^2$', r'$\lambda$', r'$\sigma^2$', r'$d$']]
density_names = [[r'$\pi(\phi_{1})$', r'$\pi(\phi_{2})$', r'$\pi(\theta_{1})$', r'$\pi(\theta_{2})$', r'$\pi(\theta_{3})$', r'$\pi(\sigma^2)$'],
[r'$\pi(\phi_1)$', r'$\pi(\phi_2)$', r'$\pi(\theta_1)$',
r'$\pi(\theta_2)$', r'$\pi(\lambda)$', r'$\pi(\sigma^2)$', r'$\pi(d)$'],
[r'$\pi(\phi_1)$', r'$\pi(\phi_2)$', r'$\pi(\theta_1)$',
r'$\pi(\sigma^2)$', r'$\pi(d)$'],
[r'$\pi(\phi_1)$', r'$\pi(\theta_1)$', r'$\pi(\sigma_{\epsilon}^2)$', r'$\pi(\lambda)$', r'$\pi(\sigma^2)$', r'$\pi(d)$']]
paramsToPlot = [[1, 4, 5], [0, 4, 6], [0, 3, 4], [0, 2, 5]]
set_tick_size = 7
file_path = "/home/%s/Dropbox/Research/Papers/Started 2019/Temporal Subsampling code/Results/Runs/" % alias
titles = ['ARMA(2,3)', 'ARTFIMA(2,2)', 'ARFIMA(2,1)', 'ARTFIMA-SV(1,1)']
file_names_MCMC = ['ARMA/MCMC_ARMA_dataVancouver_AR2_MA3_n22000_AR2_MA3_seed1_MCMCiter10000.pkl',
'ARTFIMA/MCMC_ARTFIMA_dataBromma_AR2_TFI_MA2_n225000_AR2_MA2_seed1_MCMCiter10000.pkl',
'ARFIMA/MCMC_ARFIMA_dataSimulated_AR2_FI_MA1_n2500000_AR2_MA1_seed1_MCMCiter10000.pkl',
'ARTFIMA_SV/MCMC_ARTFIMA_SV_dataBitcoin_AR1_TFI_MA1_SV_new_n500000_AR1_MA1_seed1_MCMCiter10000.pkl']
file_names_MCMC = [file_path + file_names_MCMC[item] for item in range(4)]
file_names_pseudo_MCMC_Taylor = ['ARMA/Taylor/2020-01-30/20:40/Pseudo_marginal_results.pkl',
'ARTFIMA/Taylor/2020-01-30/22:22/Pseudo_marginal_results.pkl',
'ARFIMA/Taylor/2020-02-01/12:13/Pseudo_marginal_results.pkl',
'ARTFIMA_SV/Taylor/2020-02-06/16:10/Pseudo_marginal_results.pkl']
file_names_pseudo_MCMC_Taylor = [
file_path + file_names_pseudo_MCMC_Taylor[item] for item in range(4)]
file_names_pseudo_MCMC_Coreset = [None,
'ARTFIMA/coreset/2020-01-31/00:29/Pseudo_marginal_results.pkl',
'ARFIMA/coreset/2020-02-01/06:35/Pseudo_marginal_results.pkl',
'ARTFIMA_SV/coreset/2020-02-06/17:31/Pseudo_marginal_results.pkl']
file_names_pseudo_MCMC_Coreset = [
None] + [file_path + file_names_pseudo_MCMC_Coreset[item] for item in range(1, 4)]
fig, ax = plt.subplots(nrow, ncol)
for ind in range(nrow):
# things that are constant for each parameter within a model
# Specific for each model
if ind == 0:
# ARMA(2,3)
q = 2
p = 3
elif ind == 1:
# ARTFIMA(2,2)
q = 2
p = 2
elif ind == 2:
# ARFIMA(2,1)
q = 2
p = 1
elif ind == 3:
# ARTFIMA-SV(1,1)
q = 1
p = 1
dict_MCMC = pickle.load(open(file_names_MCMC[ind], 'rb'))
dict_pseudo_MCMC_Taylor = pickle.load(
open(file_names_pseudo_MCMC_Taylor[ind], 'rb'))
if ind == 0:
# Time domain likelihood:
dict_time_domain = pickle.load(open(
'/home/%s/Dropbox/Research/Papers/Started 2019/Temporal Subsampling code/Results/Runs/ARMA/MCMC_true_likelihood_ARMA_dataVancouver_AR2_MA3_n22000_AR2_MA3_seed1_MCMCiter10000.pkl' % alias, 'rb'))
if file_names_pseudo_MCMC_Coreset[ind] is not None:
dict_pseudo_MCMC_Coreset = pickle.load(
open(file_names_pseudo_MCMC_Coreset[ind], 'rb'))
burnIn = 1000
samples_MCMC = dict_MCMC['samples'][burnIn + 1:, :]
samples_pseudo_MCMC_Taylor = dict_pseudo_MCMC_Taylor['samples'][burnIn + 1:, :]
if ind == 0:
samples_time_domain_MCMC = dict_time_domain['samples'][burnIn + 1:, :]
if file_names_pseudo_MCMC_Coreset[ind] is not None:
samples_pseudo_MCMC_Coreset = dict_pseudo_MCMC_Coreset['samples'][burnIn + 1:, :]
# Cast partial auto-correlation to ordinary parameterization.
samples_MCMC[:, :q] = np.vstack(
map(lambda x: reparam(x, MA=False), samples_MCMC[:, :q]))
samples_pseudo_MCMC_Taylor[:, :q] = np.vstack(
map(lambda x: reparam(x, MA=False), samples_pseudo_MCMC_Taylor[:, :q]))
if ind == 0:
samples_time_domain_MCMC[:, :q] = np.vstack(
map(lambda x: reparam(x, MA=False), samples_time_domain_MCMC[:, :q]))
if file_names_pseudo_MCMC_Coreset[ind] is not None:
samples_pseudo_MCMC_Coreset[:, :q] = np.vstack(
map(lambda x: reparam(x, MA=False), samples_pseudo_MCMC_Coreset[:, :q]))
samples_MCMC[:, q:(
q + p)] = np.vstack(map(lambda x: reparam(x, MA=True), samples_MCMC[:, q:(q + p)]))
samples_pseudo_MCMC_Taylor[:, q:(q + p)] = np.vstack(
map(lambda x: reparam(x, MA=True), samples_pseudo_MCMC_Taylor[:, q:(q + p)]))
if ind == 0:
samples_time_domain_MCMC[:, q:(q + p)] = np.vstack(
map(lambda x: reparam(x, MA=True), samples_time_domain_MCMC[:, q:(q + p)]))
if file_names_pseudo_MCMC_Coreset[ind] is not None:
samples_pseudo_MCMC_Coreset[:, q:(q + p)] = np.vstack(
map(lambda x: reparam(x, MA=True), samples_pseudo_MCMC_Coreset[:, q:(q + p)]))
# End Cast partial auto-correlation
# ['ARMA(2,3)', 'ARTFIMA(2,2)', 'ARFIMA(2,1)', 'ARTFIMA-SV(1,1)']
if ind == 0:
# ARMA
sigma2_ind_from_last = -1
d_ind_from_last = None
lambda_ind_from_last = None
var2_ind_from_last = None
elif ind == 1:
# ARTFIMA
sigma2_ind_from_last = -2
d_ind_from_last = -1
lambda_ind_from_last = -3
var2_ind_from_last = None
elif ind == 2:
# ARFIMA
sigma2_ind_from_last = -2
d_ind_from_last = -1
lambda_ind_from_last = None
var2_ind_from_last = None
elif ind == 3:
# ARTFIMA-SV
sigma2_ind_from_last = -2
d_ind_from_last = -1
lambda_ind_from_last = -3
var2_ind_from_last = -4
# d parameter
if d_ind_from_last is not None and ind == 2:
samples_MCMC[:, d_ind_from_last] = 0.5 * \
np.tanh(samples_MCMC[:, d_ind_from_last])
samples_pseudo_MCMC_Taylor[:, d_ind_from_last] = 0.5 * \
np.tanh(samples_pseudo_MCMC_Taylor[:, d_ind_from_last])
samples_pseudo_MCMC_Coreset[:, d_ind_from_last] = 0.5 * \
np.tanh(samples_pseudo_MCMC_Coreset[:, d_ind_from_last])
# NOTE: For ind = 1 and ind = 3 the parameterization is just d (unrestricted).
# variance param (all models have it)
samples_MCMC[:, sigma2_ind_from_last] = np.exp(
samples_MCMC[:, sigma2_ind_from_last])
samples_pseudo_MCMC_Taylor[:, sigma2_ind_from_last] = np.exp(
samples_pseudo_MCMC_Taylor[:, sigma2_ind_from_last])
if ind == 0:
samples_time_domain_MCMC[:, sigma2_ind_from_last] = np.exp(
samples_time_domain_MCMC[:, sigma2_ind_from_last])
if file_names_pseudo_MCMC_Coreset[ind] is not None:
samples_pseudo_MCMC_Coreset[:, sigma2_ind_from_last] = np.exp(
samples_pseudo_MCMC_Coreset[:, sigma2_ind_from_last])
# Lambda
if lambda_ind_from_last is not None:
samples_MCMC[:, lambda_ind_from_last] = np.exp(
samples_MCMC[:, lambda_ind_from_last])
samples_pseudo_MCMC_Taylor[:, lambda_ind_from_last] = np.exp(
samples_pseudo_MCMC_Taylor[:, lambda_ind_from_last])
samples_pseudo_MCMC_Coreset[:, lambda_ind_from_last] = np.exp(
samples_pseudo_MCMC_Coreset[:, lambda_ind_from_last])
# var2 parameter
if var2_ind_from_last is not None:
samples_MCMC[:, var2_ind_from_last] = np.exp(
samples_MCMC[:, var2_ind_from_last])
samples_pseudo_MCMC_Taylor[:, var2_ind_from_last] = np.exp(
samples_pseudo_MCMC_Taylor[:, var2_ind_from_last])
samples_pseudo_MCMC_Coreset[:, var2_ind_from_last] = np.exp(
samples_pseudo_MCMC_Coreset[:, var2_ind_from_last]) # Coreset included for this example
if file_names_pseudo_MCMC_Coreset[ind] is not None:
coreset_sizes = dict_pseudo_MCMC_Coreset['coreset_sizes']
# end things that are constant...
for jj, param in enumerate(paramsToPlot[ind]):
ax[ind][jj].spines['top'].set_visible(False)
ax[ind][jj].spines['right'].set_visible(False)
ax[ind][jj].get_xaxis().tick_bottom()
ax[ind][jj].get_yaxis().tick_left()
# BEGIN PLOT three of the parameters.
theta_MCMC = samples_MCMC[:, param]
theta_pseudo_MCMC_Taylor = samples_pseudo_MCMC_Taylor[:, param]
if ind == 0:
theta_time_domain_MCMC = samples_time_domain_MCMC[:, param]
if file_names_pseudo_MCMC_Coreset[ind] is not None:
theta_pseudo_MCMC_Coreset = samples_pseudo_MCMC_Coreset[:, param]
min_x_MCMC = np.min(theta_MCMC)
max_x_MCMC = np.max(theta_MCMC)
min_x_pseudo_MCMC_Taylor = np.min(theta_pseudo_MCMC_Taylor)
max_x_pseudo_MCMC_Taylor = np.max(theta_pseudo_MCMC_Taylor)
if ind == 0:
min_x_time_domain_MCMC = np.min(theta_time_domain_MCMC)
max_x_time_domain_MCMC = np.max(theta_time_domain_MCMC)
if file_names_pseudo_MCMC_Coreset[ind] is not None:
min_x_pseudo_MCMC_Coreset = np.min(theta_pseudo_MCMC_Coreset)
max_x_pseudo_MCMC_Coreset = np.max(theta_pseudo_MCMC_Coreset)
# ['ARMA(2,3)', 'ARTFIMA(2,2)', 'ARFIMA(2,1)', 'ARTFIMA-SV(1,1)']
# Which KDEs to we plot for different examples?
if ind == 0:
# ARMA
min_x = np.min(
[min_x_MCMC, min_x_pseudo_MCMC_Taylor, min_x_time_domain_MCMC])
max_x = np.max(
[max_x_MCMC, max_x_pseudo_MCMC_Taylor, min_x_time_domain_MCMC])
elif ind == 1:
# ARTFIMA
min_x = np.min(
[min_x_MCMC, min_x_pseudo_MCMC_Taylor, min_x_pseudo_MCMC_Coreset])
max_x = np.max(
[max_x_MCMC, max_x_pseudo_MCMC_Taylor, max_x_pseudo_MCMC_Coreset])
elif ind == 2:
# ARFIMA
min_x = np.min(
[min_x_MCMC, min_x_pseudo_MCMC_Taylor, min_x_pseudo_MCMC_Coreset])
max_x = np.max(
[max_x_MCMC, max_x_pseudo_MCMC_Taylor, max_x_pseudo_MCMC_Coreset])
elif ind == 3:
# ARTFIMA-SV
min_x = np.min(
[min_x_MCMC, min_x_pseudo_MCMC_Taylor, min_x_pseudo_MCMC_Coreset])
max_x = np.max(
[max_x_MCMC, max_x_pseudo_MCMC_Taylor, max_x_pseudo_MCMC_Coreset])
x_grid = np.linspace(min_x, max_x, 500)
kde_MCMC = sps.gaussian_kde(theta_MCMC)
kde_pseudo_MCMC_Taylor = sps.gaussian_kde(theta_pseudo_MCMC_Taylor)
if ind == 0:
kde_time_domain_MCMC = sps.gaussian_kde(theta_time_domain_MCMC)
if file_names_pseudo_MCMC_Coreset[ind] is not None:
kde_pseudo_MCMC_Coreset = sps.gaussian_kde(
theta_pseudo_MCMC_Coreset)
if bandwidthKDE is not None:
kde_MCMC.set_bandwidth(bandwidthKDE)
kde_pseudo_MCMC_Taylor.set_bandwidth(bandwidthKDE)
if ind == 0:
kde_time_domain_MCMC.set_bandwidth(bandwidthKDE)
if file_names_pseudo_MCMC_Coreset[ind] is not None:
kde_pseudo_MCMC_Coreset.set_bandwidth(bandwidthKDE)
pdfvals_MCMC = kde_MCMC(x_grid)
pdfvals_pseudo_MCMC_Taylor = kde_pseudo_MCMC_Taylor(x_grid)
if ind == 0:
pdfvals_time_domain_MCMC = kde_time_domain_MCMC(x_grid)
if file_names_pseudo_MCMC_Coreset[ind] is not None:
pdfvals_pseudo_MCMC_Coreset = kde_pseudo_MCMC_Coreset(x_grid)
rects1 = ax[ind][jj].plot(
x_grid, pdfvals_MCMC, 'k', linewidth=2, label=r'$\mathrm{MCMC}$')
rects2 = ax[ind][jj].plot(x_grid, pdfvals_pseudo_MCMC_Taylor, 'magenta',
linewidth=2, linestyle='--', label=r'$\mathrm{Taylor}$')
if file_names_pseudo_MCMC_Coreset[ind] is not None:
rects3 = ax[ind][jj].plot(x_grid, pdfvals_pseudo_MCMC_Coreset,
'orange', linewidth=2, linestyle='--', label=r'$\mathrm{Coreset}$')
if ind == 0:
rects4 = ax[ind][jj].plot(x_grid, pdfvals_time_domain_MCMC, 'green',
linewidth=2, linestyle='--', label=r'$\mathrm{Coreset}$')
ax[ind][jj].set_yticks([])
ax[ind][jj].set_ylabel(density_names[ind][param], fontsize=10)
ax[ind][jj].set_title(param_names[ind][param], fontsize=12)
# Legend
if jj == 0:
if ind == 0:
ax[ind][jj].legend((rects1[0], rects2[0], rects4[0]), (
r'$\mathrm{MCMC}$', r'$\mathrm{Taylor}$', r'$\mathrm{Gauss-MCMC}$'), prop={'size': 6}, loc="upper right")
ax[ind][jj].set_xlim([min_x, max_x + 0.75])
else:
# for all other inds we include the coreset, but no time domain MCMC
ax[ind][jj].legend((rects1[0], rects2[0], rects3[0]), (
r'$\mathrm{MCMC}$', r'$\mathrm{Taylor}$', r'$\mathrm{Coreset}$'), prop={'size': 6}, loc="upper right")
if ind == 1:
ax[ind][jj].set_xlim([min_x, max_x + 0.02])
elif ind == 2:
ax[ind][jj].set_xlim([min_x, max_x + 0.007])
elif ind == 3:
ax[ind][jj].set_xlim([min_x, max_x + 0.25])
try:
plt.tight_layout()
except ValueError:
print("Plots are corrupted")
#fig.subplots_adjust(hspace = 0.5, wspace = 0.4)
plt.savefig(plotSaveDir + "KDE_all_models_selected_params.pdf")
if 'KDEs_all' in which_plots:
bandwidthKDE = 0.5
# Makes one figure for each of the examples, using ALL parameters
####
ncol = 1
# Params to plot for each example. The full list
# ARMA(2,3) ind 0
# ARTFIMA(2,2) ind 1
# ARFIMA(2,1) ind 2
# ARTFIMA-SV(1,1) ind 3
param_names = [[r'$\phi_{1}$', r'$\phi_{2}$', r'$\theta_{1}$', r'$\theta_{2}$', r'$\theta_{3}$', r'$\sigma^2$'],
[r'$\phi_1$', r'$\phi_2$', r'$\theta_1$',
r'$\theta_2$', r'$\lambda$', r'$\sigma^2$', r'$d$'],
[r'$\phi_1$', r'$\phi_2$', r'$\theta_1$', r'$\sigma^2$', r'$d$'],
[r'$\phi_1$', r'$\theta_1$', r'$\sigma_{\epsilon}^2$', r'$\lambda$', r'$\sigma^2$', r'$d$']]
density_names = [[r'$\pi(\phi_{1})$', r'$\pi(\phi_{2})$', r'$\pi(\theta_{1})$', r'$\pi(\theta_{2})$', r'$\pi(\theta_{3})$', r'$\pi(\sigma^2)$'],
[r'$\pi(\phi_1)$', r'$\pi(\phi_2)$', r'$\pi(\theta_1)$',
r'$\pi(\theta_2)$', r'$\pi(\lambda)$', r'$\pi(\sigma^2)$', r'$\pi(d)$'],
[r'$\pi(\phi_1)$', r'$\pi(\phi_2)$', r'$\pi(\theta_1)$',
r'$\pi(\sigma^2)$', r'$\pi(d)$'],
[r'$\pi(\phi_1)$', r'$\pi(\theta_1)$', r'$\pi(\sigma_{\epsilon}^2)$', r'$\pi(\lambda)$', r'$\pi(\sigma^2)$', r'$\pi(d)$']]
paramsToPlot = [[0, 1, 2, 3, 4, 5], [0, 1, 2, 3, 4, 5, 6],
[0, 1, 2, 3, 4], [0, 1, 2, 3, 4, 5]]
set_tick_size = 7
file_path = "/home/%s/Dropbox/Research/Papers/Started 2019/Temporal Subsampling code/Results/Runs/" % alias
titles = ['ARMA(2,3)', 'ARTFIMA(2,2)', 'ARFIMA(2,1)', 'ARTFIMA-SV(1,1)']
file_names_MCMC = ['ARMA/MCMC_ARMA_dataVancouver_AR2_MA3_n22000_AR2_MA3_seed1_MCMCiter10000.pkl',
'ARTFIMA/MCMC_ARTFIMA_dataBromma_AR2_TFI_MA2_n225000_AR2_MA2_seed1_MCMCiter10000.pkl',
'ARFIMA/MCMC_ARFIMA_dataSimulated_AR2_FI_MA1_n2500000_AR2_MA1_seed1_MCMCiter10000.pkl',
'ARTFIMA_SV/MCMC_ARTFIMA_SV_dataBitcoin_AR1_TFI_MA1_SV_new_n500000_AR1_MA1_seed1_MCMCiter10000.pkl']
file_names_MCMC = [file_path + file_names_MCMC[item] for item in range(4)]
file_names_pseudo_MCMC_Taylor = ['ARMA/Taylor/2020-01-30/20:40/Pseudo_marginal_results.pkl',
'ARTFIMA/Taylor/2020-01-30/22:22/Pseudo_marginal_results.pkl',
'ARFIMA/Taylor/2020-02-01/12:13/Pseudo_marginal_results.pkl',
'ARTFIMA_SV/Taylor/2020-02-06/16:10/Pseudo_marginal_results.pkl']
file_names_pseudo_MCMC_Taylor = [
file_path + file_names_pseudo_MCMC_Taylor[item] for item in range(4)]
file_names_pseudo_MCMC_Coreset = [None,
'ARTFIMA/coreset/2020-01-31/00:29/Pseudo_marginal_results.pkl',
'ARFIMA/coreset/2020-02-01/06:35/Pseudo_marginal_results.pkl',
'ARTFIMA_SV/coreset/2020-02-06/17:31/Pseudo_marginal_results.pkl']
file_names_pseudo_MCMC_Coreset = [
None] + [file_path + file_names_pseudo_MCMC_Coreset[item] for item in range(1, 4)]
for ind in range(4): # loop over examples
nrow = len(paramsToPlot[ind])
if ind == 0:
fig, ax = plt.subplots(2, 3)
elif ind == 1:
fig, ax = plt.subplots(3, 3)
ax[2, 1].axis('off')
ax[2, 2].axis('off')
elif ind == 2:
fig, ax = plt.subplots(2, 3)
ax[1, -1].axis('off')
elif ind == 3:
fig, ax = plt.subplots(2, 3)
# BEGIN PASTE
if ind == 0:
pass
elif ind == 1:
if jj == 2 and (ll == 1 or ll == 2):
ax[jj][ll].axis('off')
elif ind == 2:
if jj == 1 and ll == 2:
ax[jj][ll].axis('off')
elif ind == 3:
pass
# END PASTE
# things that are constant for each parameter within a model
# Specific for each model
if ind == 0:
# ARMA(2,3)
q = 2
p = 3
elif ind == 1:
# ARTFIMA(2,2)
q = 2
p = 2
elif ind == 2:
# ARFIMA(2,1)
q = 2
p = 1
elif ind == 3:
# ARTFIMA-SV(1,1)
q = 1
p = 1
dict_MCMC = pickle.load(open(file_names_MCMC[ind], 'rb'))
dict_pseudo_MCMC_Taylor = pickle.load(
open(file_names_pseudo_MCMC_Taylor[ind], 'rb'))
if ind == 0:
# Time domain likelihood:
dict_time_domain = pickle.load(open(
'/home/%s/Dropbox/Research/Papers/Started 2019/Temporal Subsampling code/Results/Runs/ARMA/MCMC_true_likelihood_ARMA_dataVancouver_AR2_MA3_n22000_AR2_MA3_seed1_MCMCiter10000.pkl' % alias, 'rb'))
if file_names_pseudo_MCMC_Coreset[ind] is not None:
dict_pseudo_MCMC_Coreset = pickle.load(
open(file_names_pseudo_MCMC_Coreset[ind], 'rb'))
burnIn = 1000
samples_MCMC = dict_MCMC['samples'][burnIn + 1:, :]
samples_pseudo_MCMC_Taylor = dict_pseudo_MCMC_Taylor['samples'][burnIn + 1:, :]