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.
x_test = np.array(test.index)
y_test = np.array(test.reindex(train.columns, axis=1))
logprob = model.logpdf(torch.tensor(x_test),
torch.tensor(normaliser.normalise(y_test)))
logdet = normaliser.normalise_logdet(y_test)
pplp = logprob + logdet
wbml.out.kv("PPLP", pplp / B.length(y_test))
# Plot the result.
plt.figure(figsize=(12, 2))
wbml.plot.tex()
for i, name in enumerate(test.columns):
p = list(train.columns).index(name) # Index of output.
plt.subplot(1, 3, i + 1)
plt.plot(x, means[:, p], style="pred")
plt.fill_between(x, lowers[:, p], uppers[:, p], style="pred")
plt.scatter(x, y[:, p], style="train")
plt.scatter(test[name].index, test[name], style="test")
plt.xlabel("Time (year)")
plt.ylabel(name)
wbml.plot.tweak(legend=False)
def objective(vs):
return -construct_model(vs).logpdf(torch.tensor(x_train),
torch.tensor(y_train_norm))
# Perform optimisation.
minimise_l_bfgs_b(objective, vs, trace=True, iters=1000)
# Print variables.
vs.print()
# Predict.
model = construct_model(vs)
model = model.condition(torch.tensor(x_train), torch.tensor(y_train_norm))
means, lowers, uppers = B.to_numpy(model.predict(x_test))
# Compute RMSE.
wbml.out.kv("RMSE",
B.mean((normaliser.unnormalise(means) - y_test)**2)**0.5)
# Compute LML.
lml = -objective(vs) + normaliser.normalise_logdet(y_train)
wbml.out.kv("LML", lml / B.length(y_train))
# Compute PPLP.
logprob = model.logpdf(torch.tensor(x_test),
torch.tensor(normaliser.normalise(y_test)))
logdet = normaliser.normalise_logdet(y_test)
pplp = logprob + logdet
wbml.out.kv("PPLP", pplp / B.length(y_test))