noise = vs.pos(1e-2, name="noise")
latent_noises = vs.pos(1e-2 * B.ones(m), name="latent_noises")
h = Dense(vs.get(shape=(p, m), name="h"))
return ILMMPP(kernels, h, noise, latent_noises)
def objective(vs):
return -construct_model(vs).logpdf(torch.tensor(x),
torch.tensor(y_norm))
minimise_l_bfgs_b(objective, vs, trace=True, iters=1000)
# Predict.
model = construct_model(vs)
model = model.condition(torch.tensor(x), torch.tensor(y_norm))
means, lowers, uppers = B.to_numpy(model.predict(torch.tensor(x)))
# Undo normalisation
means, lowers, uppers = normaliser.unnormalise(means, lowers, uppers)
# For the purpose of comparison, standardise using the mean of the
# *training* data. This is not how the SMSE usually is defined!
pred = pd.DataFrame(means, index=train.index, columns=train.columns)
smse = ((pred - test)**2).mean(axis=0) / (
(train.mean(axis=0) - test)**2).mean(axis=0)
# Report average SMSE.
wbml.out.kv("SMSEs", smse.dropna())
wbml.out.kv("Average SMSE", smse.mean())
# Compute PPLP.
m = 10 # Number of latent processes
# Learn.
vs = Vars(torch.float64)
minimise_l_bfgs_b(lambda vs_: objective(vs_, m, x_data, y_data_norm, locs),
vs=vs,
trace=True,
iters=200)
wbml.out.kv('Learned spatial scales', vs['scales'])
# Predict.
lat_preds, obs_preds = predict(vs, m, x_data, y_data_norm, locs, x_pred)
# Convert to NumPy and undo normalisation.
obs_preds = [
tuple(x * data_mean[0, i] + data_scale[0, i] for x in B.to_numpy(tup))
for i, tup in enumerate(obs_preds)
]
# Plot first four latent processes.
plt.figure(figsize=(15, 5))
y_proj, _, S, _ = B.to_numpy(project(vs, m, y_data_norm, locs))
xs, _, _ = model(vs, m)
for i in range(4):
plt.subplot(2, 2, i + 1)
mean, lower, upper = lat_preds[i]
plt.title(f'Latent Process {i + 1} (${100 * S[i] / np.sum(S):.1f}\\%$) \n'
f'{xs[i].display(wbml.out.format)}')
plt.plot(x_data, y_proj[i], c='tab:blue')
plt.plot(x_pred, mean, c='tab:green')
plt.plot(x_pred, lower, c='tab:green', ls='--')
[sim.to_numpy()[:args.n].reshape(-1, 1) for sim in sims.values()],
axis=1)
corr_empirical = cov_to_corr(np.cov(all_obs.T))
# Compute predictions for latent processes.
model = construct_model(vs)
model = model.condition(x_data, y_data, x_ind=vs["x_ind"])
x_proj, y_proj, _, _ = model.project(x_data, y_data)
means, lowers, uppers = model.model.predict(x_proj)
# Save for processing.
wd.save(
B.to_numpy({
"n": args.n,
"m": m,
"p": p,
"m_r": m_r,
"m_s": m_s,
"x_proj": x_proj,
"y_proj": y_proj,
"means": means,
"lowers": lowers,
"uppers": uppers,
"learned_parameters": {name: vs[name]
for name in vs.names},
"corr_learned": corr_learned,
"corr_empirical": corr_empirical,
}),
f"results_mr{m_r}_ms{m_s}{suffix}.pickle",
)
u = vs.orth(shape=(p, m), name="u")
s_sqrt = vs.pos(shape=(m, ), name="s_sqrt")
h = Dense(u * s_sqrt[None, :])
return ILMMPP(kernels, h, noise, latent_noises)
def objective(vs):
return -construct_model(vs).logpdf(torch.tensor(x),
torch.tensor(y_norm))
minimise_l_bfgs_b(objective, vs, trace=True, iters=1000)
# Predict.
model = construct_model(vs)
model = model.condition(torch.tensor(x), torch.tensor(y_norm))
means, lowers, uppers = B.to_numpy(model.predict(x))
# Undo normalisation
means, lowers, uppers = normaliser.unnormalise(means, lowers, uppers)
# Report SMSE.
pred = pd.DataFrame(means, index=train.index, columns=train.columns)
smse = wbml.metric.smse(pred, test)
wbml.out.kv("SMSEs", smse.dropna())
wbml.out.kv("Average SMSEs", smse.mean())
# Compute PPLP.
for name, model in [
("OILMM", construct_model(vs)),
("ILMM", construct_model_ilmm_equivalent(vs)),
]: