def plotDatas(RegObs, plotcov=False, plotNormal=False, num=1):
fig = plt.figure(num, figsize=set_size(twoColumns=True))
ax = fig.add_subplot(121)
RegObs.plot(ax, plotcov=plotcov, plotNormal=plotNormal)
#ax.set_xlim(-5,5)
#ax.set_ylim(-5,5)
ax.set_aspect('equal')
ax.set_title('inputs X with separator (blue) and covariances (red)')
ax = fig.add_subplot(122)
RegObs.plotOutputs(ax)
ax.set_title(r'ouputs means $sigma(x_i^Ttheta)$')
def XP_2D(sigma0, mu0, N, s, c, seed, name, num, nbLevels=0):
d = 2
################### GENERATE DATA #######################
RegObs = LogisticRegObservations(s,
N,
d,
c,
seed,
scale=1,
rotate=True,
normalize=True)
y, X = RegObs.datas
################### RUN KALMAN #######################
theta0 = mu0 * np.ones([d, 1]) / math.sqrt(d)
Cov0 = np.identity(d) * sigma0**2
# True posterior
posterior = PosteriorLogReg(theta0, Cov0).fit(X, y.reshape(N, ))
# Kalman algorithms
ekf = EKFLogReg(theta0, Cov0).fit(X, y.reshape(N, ))
qkf = QKFLogReg(theta0, Cov0).fit(X, y.reshape(N, ))
rvga = RVGALogReg(theta0, Cov0).fit(X, y.reshape(N, ))
rvgae = RVGALogRegExplicite(theta0, Cov0).fit(X, y.reshape(N, ))
lap = LaplaceLogisticRegression(theta0, Cov0).fit(X, y.reshape(N, ))
# Plot figure 1: Datas + KL
fig = plt.figure(num, figsize=set_size(twoColumns=True))
ax = fig.add_subplot(121)
ax.set_title('Distributions of inputs')
RegObs.plot(ax, plotcov=False, plotNormal=False)
#ax.set_xticks(fontsize=8)
#ax.set_yticks(fontsize=8)
ax.set_xlabel(
r'$\sigma_0=${0}, $||\mu_0||={1:.1f}$ , N={2}, d={3}, s={4:.1f}, c={5}'
.format(sigma0, mu0, N, d, s, c))
ax = fig.add_subplot(122)
ax.set_title('KL divergence', loc='left')
plotKL(ax, rvga, rvgae, ekf, qkf, lap, posterior, seed)
ax.set_ylabel('KL error')
#ax.set_xticks(fontsize=8)
#ax.set_yticks(fontsize=8)
fig.legend(loc="upper right", ncol=2)
#plt.savefig('./outputs/KL_mu0{}_sigma0{}_N{}_d{}_s{}_c{}'.format(int(mu0),int(sigma0),int(N),int(d),int(s),int(c)))
plt.savefig('./outputs/KL_2d_' + name)
# Plot figure 2: Covariances
num = num + 1
plotCov(rvga, rvgae, ekf, qkf, lap, posterior, num, nbLevels)
#plt.savefig('./outputs/Covariances_mu0{}_sigma0{}_N{}_d{}_s{}_c{}'.format(int(mu0),int(sigma0),int(N),int(d),int(s),int(c)))
plt.savefig('./outputs/Cov_2d_' + name)
def plotCov(rvga, rvgae, ekf, qkf, lap, posterior, num=1, nbLevels=0):
print('Plot covariances ... ')
fig = plt.figure(num, figsize=set_size(twoColumns=True))
ax = fig.add_subplot(141)
rvga.plotEllipsoid(ax, nbLevels=nbLevels, labelize=True)
lap.plotEllipsoid(ax, labelize=True)
if not posterior is None:
posterior.plot(ax, showMleMap=False)
ax.set_title('RVGA (implicit)')
#ax.xaxis.set_major_locator(plt.MaxNLocator(4))
#ax.yaxis.set_major_locator(plt.MaxNLocator(5))
ax = fig.add_subplot(142)
rvgae.plotEllipsoid(ax, nbLevels=nbLevels, labelize=False)
lap.plotEllipsoid(ax, labelize=False)
if not posterior is None:
posterior.plot(ax, showMleMap=False)
ax.set_title('RVGA (explicit)')
#ax.xaxis.set_major_locator(plt.MaxNLocator(4))
#ax.yaxis.set_major_locator(plt.MaxNLocator(5))
ax = fig.add_subplot(143)
ekf.plotEllipsoid(ax, nbLevels=nbLevels, labelize=False)
lap.plotEllipsoid(ax, labelize=False)
if not posterior is None:
posterior.plot(ax, showMleMap=False)
ax.set_title('EKF')
#ax.xaxis.set_major_locator(plt.MaxNLocator(4))
#ax.yaxis.set_major_locator(plt.MaxNLocator(5))
ax = fig.add_subplot(144)
qkf.plotEllipsoid(ax, nbLevels=nbLevels, labelize=False)
lap.plotEllipsoid(ax, labelize=False)
if not posterior is None:
posterior.plot(ax, showMleMap=False)
ax.set_title('QKF')
#ax.xaxis.set_major_locator(plt.MaxNLocator(4))
#ax.yaxis.set_major_locator(plt.MaxNLocator(5))
fig.legend(loc="lower center", ncol=4)
def plotPredictionMap(RegObs, rvga, rvgae, ekf, qkf, lap, num=3):
print('Compute prediction maps ... ')
fig = plt.figure(num, figsize=set_size(twoColumns=True))
ax = fig.add_subplot(151)
ax.set_title('RVGA')
rvga.plotPredictionMap(ax)
RegObs.plot(ax)
ax = fig.add_subplot(152)
ax.set_title('RVGA-exp')
rvgae.plotPredictionMap(ax)
RegObs.plot(ax)
ax = fig.add_subplot(153)
ax.set_title('EKF')
ekf.plotPredictionMap(ax)
RegObs.plot(ax)
ax = fig.add_subplot(154)
ax.set_title('QKF')
qkf.plotPredictionMap(ax)
RegObs.plot(ax)
ax = fig.add_subplot(155)
ax.set_title('Laplace')
lap.plotPredictionMap(ax)
RegObs.plot(ax)
ekf = EKFLogReg(theta0, Cov0).fit(X, y.reshape(N, ))
qkf = QKFLogReg(theta0, Cov0).fit(X, y.reshape(N, ))
rvga = RVGALogReg(theta0, Cov0).fit(X, y.reshape(N, ))
rvgae = RVGALogRegExplicite(theta0, Cov0).fit(X, y.reshape(N, ))
lap = LaplaceLogisticRegression(theta0, Cov0).fit(X, y.reshape(N, ))
plotDatas(RegObs, plotcov=True, plotNormal=True, num=1)
if d == 2:
plotCov(rvga, rvgae, ekf, qkf, lap, posterior, num=2, nbLevels=4)
else:
plotCov(rvga, rvgae, ekf, qkf, lap, None, num=2, nbLevels=4)
plt.suptitle('covariances over iterations')
plt.savefig('./outputs/Cov_outputs')
fig = plt.figure(3, figsize=set_size(twoColumns=False))
ax = fig.add_subplot(111)
plotKL(ax, rvga, rvgae, ekf, qkf, lap, posterior, seed)
ax.set_title('Evolution of the KL divergence with iterations')
plt.legend(loc='upper right')
fig.text(0.5,
0.04,
'number of iterations \n ({} pass x {} samples)'.format(1, N),
ha='center')
plotPredictionMap(RegObs, rvga, rvgae, ekf, qkf, lap, num=4)
plt.savefig('./outputs/Map_outputs')
plt.suptitle('outputs probabilities')
plt.show()
num = num + 2
XP_2D(10, 0, N, 10, 1, 1, 's10', num, nbLevels=4)
num = num + 2
# XP in High Dim
# TEST HD1 sensitivity to dimension with Sharp prior sigma0=1
if 'HD1' in Test:
sigma0 = 1
mu0 = 0
d_list = [30, 70, 100]
N = 500
s = 2
c = 0
seed = 10
fig = plt.figure(num, figsize=set_size(ratio=0.5))
num = num + 1
ax1 = fig.add_subplot(131)
XP_HighDim(np.array([ax1]),
sigma0,
mu0,
N,
d_list[0],
s,
c,
seed,
label=True)
ax1.set_title('d={}'.format(d_list[0]))
ax2 = fig.add_subplot(132)
XP_HighDim(np.array([ax2]),
sigma0,