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ndt_client3_gig01_dthr_vwcd.py
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# -*- coding: utf-8 -*-
"""
Voting Windows Changepoint Detection example
@author: Cleiton Moya de Almeida
"""
import numpy as np
from scipy.stats import betabinom
import matplotlib.pyplot as plt
import time
plt.rcParams.update({'font.size': 8, 'axes.titlesize': 8})
# Load the timeseries
file = 'dca6326b9c99_gig01_d_throughput.txt'
X = np.loadtxt(f'../Dataset/ndt/{file}', usecols=1, delimiter=',')
verbose = False
# Hyperparameters
w = 20 # window size
w0 = 20 # window used to estimate the post-change parameters
alpha = 1 # Beta-binomial hyperp - prior dist. window
beta = 1 # Beta-binomial hyperp - prior dist. window
p_thr = 0.8 # threshold probability to an window decide for a changepoint
pa_thr = 0.9 # threshold probabilty to decide for a changepoint
vote_n_thr = 0.5 # min. number of votes to decide for a changepoint
y0 = 0.5 # logistic prior hyperparameter
yw = 0.9 # logistic prior hyperparameter
aggreg = 'mean'
# Auxiliary functions
# Compute the window posterior probability given the log-likelihood and prior
# using the log-sum-exp trick
def pos_fun(ll, prior, tau):
c = np.nanmax(ll)
lse = c + np.log(np.nansum(prior*np.exp(ll - c)))
p = ll[tau] + np.log(prior[tau]) - lse
return np.exp(p)
# Aggregate a list of votes - compute the posterior probability
def votes_pos(vote_list, prior_v):
vote_list = np.array(vote_list)
prod1 = vote_list.prod()*prior_v
prod2 = (1-vote_list).prod()*(1-prior_v)
p = prod1/(prod1+prod2)
return p
# Prior probabily for votes aggregation
def logistic_prior(x, w, y0, yw):
a = np.log((1-y0)/y0)
b = np.log((1-yw)/yw)
k = (a-b)/w
x0 = a/k
y = 1./(1+np.exp(-k*(x-x0)))
return y
# Compute the log-likelihood value for the normal distribution
# Obs.: the scipy built-in function logpdf does not use numpy and so is inneficient
def loglik(x,loc,scale):
n = len(x)
c = 1/np.sqrt(2*np.pi)
y = n*np.log(c/scale) -(1/(2*scale**2))*((x-loc)**2).sum()
return y
# Auxiliary variables
N = len(X)
vote_n_thr = np.floor(w*vote_n_thr)
# Prior probatilty for a changepoint in a window - Beta-Binomial
i_ = np.arange(0,w-3)
prior_w = betabinom(n=w-4,a=alpha,b=beta).pmf(i_)
# prior for votes aggregation
x_votes = np.arange(1,w+1)
prior_v = logistic_prior(x_votes, w, y0, yw)
votes = {i:[] for i in range(N)} # dictionary of votes
votes_agg = {} # aggregated voteylims
lcp = 0 # last changepoint
CP = [] # changepoint list
M0 = [] # list of post-change mean
S0 = [] # list of post-change standard deviation
N_votes_tot = np.zeros(N)
N_votes_ele = np.zeros(N)
startTime = time.time()
for n in range(N):
if n>=w-1:
# estimate the paramaters (w0 window)
if n == lcp+w0:
# estimate the post-change mean and variace
m_w0 = X[n-w0+1:n+1].mean()
s_w0 = X[n-w0+1:n+1].std(ddof=1)
M0.append(m_w0)
S0.append(s_w0)
# current window
Xw = X[n-w+1:n+1]
LLR_h = []
for nu in range(1,w-3+1):
# MLE and log-likelihood for H1
x1 = Xw[:nu+1] #Xw até nu
m1 = x1.mean()
s1 = x1.std(ddof=1)
if np.round(s1,3) == 0:
s1 = 0.001
logL1 = loglik(x1, loc=m1, scale=s1)
# MLE and log-likelihood for H2
x2 = Xw[nu+1:]
m2 = x2.mean()
s2 = x2.std(ddof=1)
if np.round(s2,3) == 0:
s2 = 0.001
logL2 = loglik(x2, loc=m2, scale=s2)
# log-likelihood ratio
llr = logL1+logL2
LLR_h.append(llr)
# Compute the posterior probability
LLR_h = np.array(LLR_h)
pos = [pos_fun(LLR_h, prior_w, nu) for nu in range(w-3)]
pos = [np.nan] + pos + [np.nan]*2
pos = np.array(pos)
# Compute the MAP (vote)
p_vote_h = np.nanmax(pos)
nu_map_h = np.nanargmax(pos)
# Store the vote
j = n-w+1+nu_map_h # Adjusted index
votes[j].append(p_vote_h)
# Aggregate the votes for X[n-w+1]
votes_list = votes[n-w+1]
elegible_votes = [v for v in votes_list if v > p_thr]
num_votes_tot = len(votes_list) # number of total votes
num_votes_ele = len(elegible_votes) # number of elegible votes
N_votes_tot[n-w+1] = num_votes_tot
N_votes_ele[n-w+1] = num_votes_ele
# Decide for a changepoit
if num_votes_ele >= vote_n_thr:
if aggreg == 'posterior':
agg_vote = votes_pos(elegible_votes, prior_v[num_votes_ele-1])
elif aggreg == 'mean':
agg_vote = np.mean(elegible_votes)
votes_agg[n-w+1] = agg_vote
if agg_vote >= pa_thr:
if verbose: print(f'n={n}: Changepoint at n={n-w+1}, p={agg_vote:.2f}, num. votes={num_votes_ele}/{num_votes_tot}')
lcp = n-w+1 # last changepoint
CP.append(lcp)
endTime = time.time()
elapsedTime = endTime-startTime
if verbose: print(f'\nTotal: {len(CP)} changepoints')
if verbose: print(f'Elapsed time: {elapsedTime:.3f}s')
fig,ax=plt.subplots(figsize=(4.5,4), nrows=4, sharex=True, layout='constrained')
for ax_ in ax:
ax_.tick_params(axis='both', labelsize=6)
ax_.grid(linestyle=':')
ax[0].set_title('Voting window change-point detection')
ax[0].plot(X, linewidth=0.5)
if len(CP)>0:
for j,cp in enumerate(CP):
if j==0:
ax[0].axvline(cp, color='r', linewidth=0.5, label='change-point')
else:
ax[0].axvline(cp, color='r', linewidth=0.5)
ax[0].legend(loc='lower right')
ax[0].set_ylabel('Mbits/s', fontsize=6)
ax[0].set_yticks([400,500,600])
x1, x2, y1, y2 = 55, 75, 520, 550 # subregion of the original image
axins = ax[0].inset_axes([0.15, 0.1, 0.2, 0.4],
xlim=(x1, x2), ylim=(y1, y2), yticklabels=[])
axins.plot(range(55,76), X[55:76], linewidth=0.5, marker='o', markersize=1)
axins.axvline(66, linewidth=0.5, color='r', linestyle='--')
axins.set_yticks([530, 540])
axins.set_yticklabels([530, 550])
axins.yaxis.tick_right()
axins.grid(linestyle=':')
axins.tick_params(bottom=False)
axins.set_xticklabels('')
axins.tick_params(labelsize=6)
_ = ax[0].indicate_inset_zoom(axins, edgecolor="black")
ax[1].set_title('Total number of votes')
N_votes_tot_idx = np.where(N_votes_tot)[0]
N_votes_tot_nonzero = N_votes_tot[N_votes_tot_idx]
markerline, stemline, baseline = ax[1].stem(N_votes_tot_idx, N_votes_tot_nonzero)
plt.setp(markerline, markersize = 2)
plt.setp(baseline, linewidth=0)
plt.setp(stemline, linewidth=0.5)
ax[1].set_yticks([0,5,10,15,20])
ax[1].set_ylim([0,20])
ax[2].set_title('Number of votes above the threshold prob.')
N_votes_ele_idx = np.where(N_votes_ele)[0]
N_votes_ele_nonzero = N_votes_ele[N_votes_ele_idx]
markerline, stemline, baseline = ax[2].stem(N_votes_ele_idx, N_votes_ele_nonzero)
plt.setp(markerline, markersize = 2)
plt.setp(baseline, linewidth=0)
plt.setp(stemline, linewidth=0.5)
ax[2].axhline(vote_n_thr, color='red', linewidth=0.5, label='threshold')
ax[2].legend(loc='lower right')
ax[2].set_yticks([0,5,10,15,20])
ax[2].set_ylim([0,20])
ax[3].set_title('Votes aggregation (change-point probability)')
if len(CP)>0:
markerline, stemline, baseline = ax[3].stem(list(votes_agg), votes_agg.values())
plt.setp(markerline, markersize = 2)
plt.setp(baseline, linewidth=0)
plt.setp(stemline, linewidth=0.5)
ax[3].axhline(pa_thr, color='red', linewidth=0.5, label='threshold')
ax[3].legend(loc='lower right')
ax[3].set_yticks([0,0.25,0.5,0.75,1])
ax[3].set_ylim(bottom=0)
ax[3].set_xlabel('sample (t)', fontsize=6)
ax[3].set_xticks(np.arange(0,275,25))
ax[3].set_xlim([0,250])