sidx = np.where(sids == s + 1)[0]
y[sidx] += b0[s] + np.random.normal(0, np.sqrt(s2h[s]), len(sidx))
# add the site specific intercepts to the design matrix
for s in range(n_site):
site = np.zeros((N, 1))
site[idx[s]] = 1
Phi = np.concatenate((Phi, site), axis=1)
site_te = np.zeros((Xs.shape[0], 1))
site_te[idx_te[s]] = 1
Phis = np.concatenate((Phis, site_te), axis=1)
hyp0 = np.zeros(4)
Bh = BLR(hyp0, Phi, y, var_groups=sids)
Bh.loglik(hyp0, Phi, y)
Bh.dloglik(hyp0, Phi, y)
hyp = Bh.estimate(hyp0, Phi, y)
yhat, s2 = Bh.predict(hyp, Phi, y, Phis, var_groups_test=sids_te)
for s in range(n_site):
plt.scatter(X[idx[s]], y[idx[s]])
plt.plot(Xs[idx_te[s]], yhat[idx_te[s]], color=cols[s])
plt.fill_between(Xs[idx_te[s]],
yhat[idx_te[s]] - 1.96 * np.sqrt(s2[idx_te[s]]),
yhat[idx_te[s]] + 1.96 * np.sqrt(s2[idx_te[s]]),
alpha=0.2,
color=cols[s])
plt.show()
Omega = np.zeros((D, Nf))
for f in range(Nf):
Omega[:, f] = np.sqrt(ell2_est) * np.random.randn(Omega.shape[0])
XO = X.dot(Omega)
Phi = np.sqrt(sf2_est / Nf) * np.c_[np.cos(XO), np.sin(XO)]
XsO = Xs.dot(Omega)
Phis = np.sqrt(sf2_est / Nf) * np.c_[np.cos(XsO), np.sin(XsO)]
# add linear component
Phi = np.c_[Phi, X]
Phis = np.c_[Phis, Xs]
hyp_blr = np.asarray([np.log(1 / sn2_est), np.log(1)])
B = BLR(hyp_blr, Phi, y)
B.loglik(hyp_blr, Phi, y)
yhat_blr, s2_blr = B.predict(hyp_blr, Phi, y, Phis)
#plt.plot(Xs[:,0],yhat_blr,'y')
#plot_dist(Xs[:,0].ravel(), yhat_blr.ravel(),
# yhat_blr.ravel() - 2*np.sqrt(s2_blr).ravel(),
# yhat_blr.ravel() + 2*np.sqrt(s2_blr).ravel(),'y','y')
print('running RFA ...')
R = GPRRFA(hyp, X, y, n_feat=Nf)
# find good starting hyperparameters
lm = LinearRegression()
lm.fit(create_poly_basis(X, 3), y)
yhat = lm.predict(create_poly_basis(X, 3))
hyp0 = np.zeros(D + 2)
hyp0[0] = np.log(np.sqrt(np.var(y - yhat)))
Phi[:, colid] = np.vstack(X**d)
colid += 1
b = [0.5, -0.1, 0.005] # true regression coefficients
s2 = 0.05 # noise variance
y = Phi.dot(b) + np.random.normal(0, s2, N)
yid = range(0, N, 1)
hyp0 = np.zeros(2)
hyp0 = np.zeros(4)
B = BLR(hyp0, Phi[yid, :], y[yid])
#B = BLR()
#B.post(hyp0,Phi[yid,:],y[yid])
B.loglik(hyp0, Phi[yid, :], y[yid])
B.dloglik(hyp0, Phi[yid, :], y[yid])
hyp = B.estimate(hyp0, Phi[yid, :], y[yid])
yhat, s2 = B.predict(hyp, Phi[yid, :], y[yid], Phi)
plt.plot(X, y)
plt.plot(X, yhat)
plt.show()
## test GPR
#y = y-y.mean()
#hyp0 = np.zeros(3)
#G = GPR(hyp0, covSqExp, Phi[yid,:], y[yid])
#G.loglik(hyp0, covSqExp, Phi[yid,:], y[yid])
#G.dloglik(hyp0, covSqExp, Phi[yid,:], y[yid])