def compute_reverse_KL(dnm, res):
samples = np.load('results/' + dnm + '_samples.npy')
samples = np.hstack((samples[:, 1:], samples[:, 0][:, np.newaxis]))
mup = samples.mean(axis=0)
Sigp = np.cov(samples, rowvar=False)
M = res['mus'].shape[0] - 1
kl = np.zeros(M + 1)
for m in range(M + 1):
mul = res['mus'][m, :]
Sigl = res['Sigs'][m, :, :]
kl[m] = gaussian.gaussian_KL(mul, np.linalg.inv(Sigl), mup, Sigp)
# kl = kl[2:][::plot_every]
return kl
#get laplace approximations for each weight setting, and KL divergence to full posterior laplace approx mup Sigp
#used for a quick/dirty performance comparison without expensive posterior sample comparisons (e.g. energy distance)
mus_laplace = np.zeros((M + 1, D))
Sigs_laplace = np.zeros((M + 1, D, D))
rkls_laplace = np.zeros(M + 1)
fkls_laplace = np.zeros(M + 1)
print(
'Computing coreset Laplace approximation + approximate KL(posterior || coreset laplace)'
)
for m in range(M + 1):
mul, LSigl, LSiglInv = get_laplace(w[m],
p[m],
Z.mean(axis=0)[:D],
diag=True)
mus_laplace[m, :] = mul
Sigs_laplace[m, :, :] = LSigl.dot(LSigl.T)
rkls_laplace[m] = gaussian.gaussian_KL(mul, Sigs_laplace[m, :, :], mup,
LSigpInv.T.dot(LSigpInv))
fkls_laplace[m] = gaussian.gaussian_KL(mup, Sigp, mul,
LSiglInv.T.dot(LSiglInv))
#save results
f = open('results/' + dnm + '_' + alg + '_results_' + ID + '.pk', 'wb')
if alg != 'DPBPSVI':
res = (cputs, w, p, mus_laplace, Sigs_laplace, rkls_laplace, fkls_laplace)
else:
res = (cputs, w, p, mus_laplace, Sigs_laplace, rkls_laplace, fkls_laplace,
dpbpsvi.get_privacy_params())
pk.dump(res, f)
f.close()
if alg != 'PRIOR':
coreset.build(1, m)
# record time and weights
cputs[m] = time.perf_counter() - t0
w, idcs = coreset.weights()
wts[m, idcs] = w
# get laplace approximations for each weight setting, and KL divergence to full posterior laplace approx mup Sigp
# used for a quick/dirty performance comparison without expensive posterior sample comparisons (e.g. energy distance)
mus_laplace = np.zeros((M + 1, D))
Sigs_laplace = np.zeros((M + 1, D, D))
kls_laplace = np.zeros(M + 1)
print(
'Computing coreset Laplace approximation + approximate KL(posterior || coreset laplace)'
)
for m in range(M + 1):
mul, Sigl = get_laplace(wts[m, :], Z, Z.mean(axis=0)[:D])
mus_laplace[m, :] = mul
Sigs_laplace[m, :, :] = Sigl
kls_laplace[m] = gaussian.gaussian_KL(mup, Sigp, mul, np.linalg.inv(Sigl))
# save results
np.savez('results/' + dnm + '_' + alg + '_results_' + str(ID) + '.npz',
cputs=cputs,
wts=wts,
Ms=np.arange(M + 1),
mus=mus_laplace,
Sigs=Sigs_laplace,
kls=kls_laplace)
for wts, pts, _ in res:
w.append(wts)
p.append(pts)
else:
for m in range(1, M + 1):
print('trial: ' + str(tr) + ' alg: ' + nm + ' ' + str(m) + '/' +
str(M))
alg.build(1)
#store weights/pts
wts, pts, _ = alg.get()
w.append(wts)
p.append(pts)
# computing kld and saving results
muw = np.zeros((M + 1, mu0.shape[0]))
Sigw = np.zeros((M + 1, mu0.shape[0], mu0.shape[0]))
rklw = np.zeros(M + 1)
fklw = np.zeros(M + 1)
for m in range(M + 1):
muw[m, :], LSigw, LSigwInv = gaussian.weighted_post(
mu0, Sig0inv, Siginv, p[m], w[m])
Sigw[m, :, :] = LSigw.dot(LSigw.T)
rklw[m] = gaussian.gaussian_KL(muw[m, :], Sigw[m, :, :], mup, SigpInv)
fklw[m] = gaussian.gaussian_KL(mup, Sigp, muw[m, :],
LSigwInv.T.dot(LSigwInv))
f = open(results_fldr + '/results_' + nm + '_' + str(tr) + '.pk', 'wb')
res = (x, mu0, Sig0, Sig, mup, Sigp, w, p, muw, Sigw, rklw, fklw)
pk.dump(res, f)
f.close()
##############################
##############################
# Normally at this point we'd run posterior inference on the coreset
# But for this (illustrative) example we will evaluate quality via Laplace posterior approx
print('Evaluating coreset quality...')
w = np.zeros(N)
w[idcs] = wts
# compute error using laplace approx
res = minimize(lambda mu: -log_joint(Z, mu, w),
Z.mean(axis=0),
jac=lambda mu: -grad_log_joint(Z, mu, w))
muw = res.x
# then find a quadratic expansion around the mode, and assume the distribution is Gaussian
covw = -np.linalg.inv(hess_log_joint_w(Z, muw, w))
print('Done!')
# compare posterior and coreset
np.set_printoptions(linewidth=10000)
print('Posterior requires ' + str(N) + ' data')
print('mu, cov = ' + str(mu) + '\n' + str(cov))
print('Coreset requires ' + str(idcs.shape[0]) + ' data')
print('muw, covw = ' + str(muw) + '\n' + str(covw))
print('KL(coreset || posterior) = ' +
str(gaussian.gaussian_KL(muw, covw, mu, np.linalg.inv(cov))))
wts = res['wts'][2:][::plot_every]
mu = res['mus'][2:][::plot_every]
Sig = res['Sigs'][2:][::plot_every]
cszs[tridx, :] = (wts > 0).sum(axis=1)
if is_forward_KL is not True:
samples = np.load('results/' + dnm + '_samples.npy')
samples = np.hstack(
(samples[:, 1:], samples[:, 0][:, np.newaxis]))
mup = samples.mean(axis=0)
Sigp = np.cov(samples, rowvar=False)
M = res['mus'].shape[0] - 1
kl = np.zeros(M + 1)
for m in range(M + 1):
mul = res['mus'][m, :]
Sigl = res['Sigs'][m, :, :]
kl[m] = gaussian.gaussian_KL(mul, np.linalg.inv(Sigl), mup,
Sigp)
kl = kl[2:][::plot_every]
else:
kl = res['kls'][2:][::plot_every]
kls[tridx, :] = kl[:len(Ms)] / kl0
if 'PRIOR' in fn:
kls[tridx, :] = np.median(kls[tridx, :])
cput50 = np.percentile(cputs, 50, axis=0)
cput25 = np.percentile(cputs, 35, axis=0)
cput75 = np.percentile(cputs, 65, axis=0)
csz50 = np.percentile(cszs, 50, axis=0)
csz25 = np.percentile(cszs, 35, axis=0)
csz75 = np.percentile(cszs, 65, axis=0)
