def plot_prediction_fixed_hparams(s, mus, alpha, beta):
# generating design matrix
Phi = gen_desmat_gaussian(X, params={'s': s, 'mus': mus})
Phi_test = gen_desmat_gaussian(Xcont, params={'s': s, 'mus': mus})
est = BayesianRidgeRegression(alpha=alpha, beta=beta)
est.fit(Phi, t, optimize_hyperparams=False)
pred_mean, pred_std = est.predict(Phi_test, return_std=True)
print(est.m)
plot_result(pred_mean, pred_std)
def crossval_test_nll(s_u):
nlls = []
for i in range(num_splits):
# make design matrices for training data for this fold
Phi_tr = gen_desmat_gaussian(X_tr_kf[i],
params={
's': s_w,
'mus': mus_w
})
Psi_tr = gen_desmat_gaussian(X_tr_kf[i],
params={
's': s_u,
'mus': mus_u
})
# train on this fold
print('minimizing s_u = %s, fold %s' % (s_u, i))
est.fit(Phi_tr,
Psi_tr,
t_tr_kf[i],
method='nelder-mead',
logging=False)
# make design matrices for test data for this fold
Phi_ts = gen_desmat_gaussian(X_ts_kf[i],
params={
's': s_w,
'mus': mus_w
})
Psi_ts = gen_desmat_gaussian(X_ts_kf[i],
params={
's': s_u,
'mus': mus_u
})
# Predict at test points
t_pred, loginvvar_pred = est.predict(Phi_ts, Psi_ts, noise_est=True)
# inverse variance beta at test points
beta_pred = np.exp(loginvvar_pred)
# neg log-likelihood of test data for this fold
nlls.append(neg_log_like(t_pred, t_ts_kf[i], beta_pred))
nll_av = np.mean(nlls)
print('nll_av = %s\n' % nll_av)
return nll_av
#%% setup Gaussian basis function params
# number of basis function for y(x), log inv var
M_w, M_u = 4, 4
# mus are centers of gbfs, s is spacing between gbfs
# 4 w gbfs, w/ edge gbfs at s_w/2 from boundary of data.
mus_w = np.array([-2.25, -0.75, 0.75, 2.25])
s_w = 1.5
# 4 u gbfs, w/ edge gbfs at s_u/2 from boundary of data.
mus_u = np.array([-2.25, -0.75, 0.75, 2.25])
s_u = 2.25
#%%
# generate y(x) gbf design matrix Phi from input data X
Phi = gen_desmat_gaussian(X, params={'s': s_w, 'mus': mus_w})
# generate log(beta) gbf design matrix Psi from input data X
Psi = gen_desmat_gaussian(X, params={'s': s_u, 'mus': mus_u})
#%% init estimator
est = BayesianHetRegression()
#%% use fit and predict methods
est.fit(Phi, Psi, t, method='sgd', logging=True)
u_weights, w_weights = est.u_fit, est.w_fit
t_gbfs = gen_desmat_gaussian(Xcont, params={'s': s_w, 'mus': mus_w})
loginvvar_gbfs = gen_desmat_gaussian(Xcont, params={'s': s_u, 'mus': mus_u})
t_gbfs_total, loginvvar_gbfs_total = est.predict(t_gbfs,
loginvvar_gbfs,
def make_Phi_Psi(X, s, mus):
Phi_mat = np.vstack((np.ones(len(X)), X)).T
Psi_mat = gen_desmat_gaussian(X, params={'s': s, 'mus': mus})
return Phi_mat, Psi_mat
def plot_prediction_fixed_hparams(s, mus, alpha, beta):
# generating design matrix
Phi = gen_desmat_gaussian(X, params={'s': s, 'mus': mus})
Phi_test = gen_desmat_gaussian(Xcont, params={'s': s, 'mus': mus})
est = BayesianRidgeRegression(alpha=alpha, beta=beta)
est.fit(Phi, t, optimize_hyperparams=False)
pred_mean, pred_std = est.predict(Phi_test, return_std=True)
print(est.m)
plot_result(pred_mean, pred_std)
plot_prediction_fixed_hparams(s, mus, alpha=1.0, beta=1.0)
#%%
Phi = gen_desmat_gaussian(X, params={'s': s, 'mus': mus})
Phi_test = gen_desmat_gaussian(Xcont, params={'s': s, 'mus': mus})
est = BayesianRidgeRegression(alpha=1.0, beta=1.0)
est.fit(Phi, t, optimize_hyperparams=False)
pred_mean, pred_std = est.predict(Phi_test, return_std=True)
w_means = est.m
#%%
# NEW
t_gbfs = gen_desmat_gaussian(Xcont, params={'s': s, 'mus': mus})
# weighted sum of gbfs. should equal predictive mean
t_gbfs_total = t_gbfs @ w_means
# plot the gbfs
def plot_result_with_gbf(pred_mean, pred_std):