n_cols=n_sig_cols+n_noise_cols
dictionary = {'x{}'.format(i):np.random.randn(n_data) for i in range(n_cols)}
X = pd.DataFrame(dictionary)
coeffs = np.random.randn(n_cols)
coeffs[0:n_noise_cols]=np.zeros(coeffs[0:n_noise_cols].shape)
y = pd.DataFrame(np.dot(X,coeffs)+np.random.randn(n_data)*noise)
X_train, X_test, y_train, y_test = time_series_split(X, y, test_size=0.2)
# Investigate the performance of the Lasso Regressor at 3 levels of alpha
alphas = [.05,.1,.3, 1, 50]
plt.figure(figsize=(len(alphas)*10, 10))
models = []
for i, alpha in enumerate(alphas):
model = BayesianLasso(sigma2=alpha)
models.append(model)
model.fit(X_train, y_train)
pred_train = model.predict(X_train)
pred_test = model.predict(X_test)
print np.array(model._map_betas), coeffs
plt.subplot(2, len(alphas), 1 + i)
plot_comparison(np.array(y_train), np.array(pred_train), 'Training Set for alpha={}'.format(alpha))
plt.subplot(2, len(alphas), len(alphas) + 1 + i)
plot_comparison(np.array(y_test), np.array(pred_test), 'Testing Set for alpha={}'.format(alpha))
plt.savefig('plots/bayesian_lasso_fit_comp_toy.png')
scaler = Pipeline([
('imputer', Imputer()),
('scaler', StandardScaler(with_mean=False))
])
X_scaled = scaler.fit_transform(X)
X_train, X_test, y_train, y_test = time_series_split(X_scaled, y, test_size=0.2)
# Investigate the performance of the Lasso Regressor at 3 levels of alpha
sigma2s = [.001,1,10000]
plt.figure(figsize=(len(sigma2s)*10, 10))
models = []
for i, sigma2 in enumerate(sigma2s):
model = BayesianLasso(sigma2=sigma2, use_mcmc=True)
models.append(model)
print "fitting model with sigma2={}".format(sigma2)
model.fit(X_scaled, y)
pred_train = model.predict(X_train)
pred_test = model.predict(X_test)
plt.subplot(2, len(sigma2s), 1 + i)
plot_comparison(y_train, pred_train, 'Training Set for sigma^2={}'.format(sigma2))
plt.subplot(2, len(sigma2s), len(sigma2s) + 1 + i)
plot_comparison(y_test, pred_test, 'Testing Set for sigma^2={}'.format(sigma2))
plt.savefig('plots/bayesian_lasso_fit_comp_2.png')
#Investigate the value of the Lasso's coeffecients at the same 3 levels of alpha
plt.figure(figsize=(len(sigma2s)*10, 10))
