def test_scaling_match():
rnd = np.random.RandomState(42)
width = 16
n_tasks = 1
n_features = width**2
coefs = rnd.rand(width, width, n_tasks)
coefs_flat = coefs.reshape(n_features, -1)
M = utils.groundmetric2d(n_features, p=2, normed=False)
K = np.exp(-M)
scaling = K.dot(coefs_flat).flatten()
scaling_log = np.exp(
utils.logsumexp(np.log(coefs_flat)[None, :] - M, axis=1))
M = utils.groundmetric(width, p=2, normed=False)
K = np.exp(-M)
scaling_conv = utils.klconv1d_list(coefs, K).flatten()
scaling_conv_log = np.exp(utils.kls(np.log(coefs), -M))
assert_allclose(scaling, scaling_log.flatten())
assert_allclose(scaling, scaling_conv)
assert_allclose(scaling_conv_log.flatten(), scaling_conv)
def test_barycenter_match():
rnd = np.random.RandomState(42)
width = 16
n_tasks = 2
n_features = width**2
coefs_flat = rnd.rand(n_features, n_tasks)
coefs_flat[n_features // 2] = 0.
M = utils.groundmetric2d(n_features, p=2, normed=False)
m = np.median(M)
epsilon = 5. / n_features
gamma = 1.
maxiter = 50
K = -M / (m * epsilon)
options = dict(P=coefs_flat,
M=K,
epsilon=epsilon,
gamma=gamma,
maxiter=maxiter,
tol=0.)
f, log, ms, b, q = otfunctions.barycenterkl(**options)
fl, logl, msl, bl, ql = otfunctions.barycenterkl_log(**options)
M = utils.groundmetric(width, p=2, normed=False)
K = -M / (m * epsilon)
options["M"] = K
fc, logc, msc, bc, qc = otfunctions.barycenterkl_img(**options)
fcl, logcl, mscl, bcl, qcl = otfunctions.barycenterkl_img_log(**options)
assert_allclose(q, ql, rtol=1e-5, atol=1e-5)
assert_allclose(ms, msl, rtol=1e-5, atol=1e-5)
assert_allclose(b, np.exp(bl), rtol=1e-5, atol=1e-5)
assert_allclose(qc, qcl, rtol=1e-5, atol=1e-5)
assert_allclose(msc, mscl, rtol=1e-5, atol=1e-5)
assert_allclose(bc, np.exp(bcl), rtol=1e-5, atol=1e-5)
assert_allclose(q, qc.reshape(n_features), rtol=1e-5, atol=1e-5)
assert_allclose(ms, msc.reshape(-1, n_features), rtol=1e-5, atol=1e-5)
def test_mtw_convolution(positive, alpha, epsilon):
# Estimator params
seed = 42
width, n_tasks = 12, 2
nnz = 2
overlap = 0.
denoising = False
binary = False
corr = 0.9
# Gaussian Noise
snr = 4
# Deduce supplementary params
n_features = width**2
n_samples = n_features // 2
# ot params
epsilon = epsilon / n_features
stable = False
Mbig = utils.groundmetric2d(n_features, p=2, normed=False)
m = np.median(Mbig)
M = utils.groundmetric(width, p=2, normed=True)
M = utils.groundmetric(width, p=2, normed=False)
M /= m
# M = Mbig / m
# Generate Coefs
coefs = generate_dirac_images(width,
n_tasks,
nnz=nnz,
seed=seed,
overlap=overlap,
binary=binary,
positive=positive)
coefs_flat = coefs.reshape(-1, n_tasks)
# # Generate X, Y data
std = 1 / snr
X, Y = gaussian_design(n_samples,
coefs_flat,
corr=corr,
sigma=std,
denoising=denoising,
scaled=True,
seed=seed)
betamax = np.array([abs(x.T.dot(y)) for x, y in zip(X, Y)]).max()
beta_fr = 0.5
beta = beta_fr * betamax / n_samples
alpha = alpha / n_samples
callback_options = {
'callback': True,
'x_real': coefs_flat.reshape(-1, n_tasks),
'verbose': True,
'rate': 1,
'prc_only': False
}
gamma = utils.compute_gamma(0.8, M)
"""Fit mtw_model using convolutions to compute OT barycenters."""
mtw_model = MTW(M=M,
alpha=alpha,
beta=beta,
epsilon=epsilon,
gamma=gamma,
stable=stable,
tol_ot=1e-8,
tol=1e-5,
maxiter_ot=30,
maxiter=200,
**callback_options,
positive=positive)
# first fit
mtw_model.fit(X, Y)
assert mtw_model.log_['dloss'][-1] < 1e-4
M = Mbig / m
# mtw_model using standard sinkhorn
mtw_model2 = MTW(M=M,
alpha=alpha,
beta=beta,
epsilon=epsilon,
gamma=gamma,
stable=stable,
tol_ot=1e-8,
tol=1e-5,
maxiter_ot=30,
maxiter=200,
**callback_options,
positive=positive)
mtw_model2.fit(X, Y)
assert mtw_model2.log_['dloss'][-1] < 1e-4
assert_allclose(mtw_model.coefs_, mtw_model2.coefs_, atol=1e-5, rtol=1e-5)
# get positive / negative parts
coefs1, coefs2 = utils.get_unsigned(mtw_model.coefs_)
n_features = width ** 2
n_samples = n_features // 2
"""Generate Coefs and X, Y data..."""
coefs = generate_dirac_images(width, n_tasks, nnz=nnz, positive=positive,
seed=seed, overlap=overlap)
coefs_flat = coefs.reshape(-1, n_tasks)
std = 0.25
X, Y = gaussian_design(n_samples, coefs_flat, corr=0.95, sigma=std,
scaled=True, seed=seed)
###############################################################################
# set ot params
epsilon = 2.5 / n_features
M = utils.groundmetric2d(n_features, p=2, normed=True)
gamma = utils.compute_gamma(0.8, M)
###############################################################################
# set hyperparameters and fit MTW
betamax = np.array([x.T.dot(y) for x, y in zip(X, Y)]).max() / n_samples
alpha = 10. / n_samples
beta_fr = 0.35
beta = beta_fr * betamax
callback_options = {'callback': True,
'x_real': coefs.reshape(- 1, n_tasks),
'verbose': True, 'rate': 1}
print("Fitting MTW model...")