kss = self.cov(Xs[idx], diag=True) # self variance
Ks = self.cov(Xs[idx], X) # cross-covariances
ms = self.mean(Xs[idx])
al, sW, L, C = self.post.alpha, self.post.sW, self.post.L, self.post.C
fmu[idx] = ms + np.dot(Ks, al)
if L == None:
fs2[idx] = kss + np.sum(Ks * np.dot(Ks, L), axis=1)
else:
V = np.linalg.solve(L, sW * Ks.T)
fs2[idx] = kss - np.sum(V * V, axis=0)
if ys == 0: yi = 0
else: yi = ys[idx]
lp[idx], ymu[idx], ys2[idx] = self.lik.pred(yi, fmu[idx], fs2[idx])
na += nb
return fmu, fs2, ymu, ys2, lp
if __name__ == "__main__":
def f(x):
return x * np.sin(x)
X = np.atleast_2d([1., 3., 5., 6., 7., 8.]).T
y = f(X).ravel()
Xs = np.atleast_2d(np.linspace(0, 10, 2007)).T
from gp import GaussianProcess as gp
gp = gp(mean=1.0 * one())
post, nlZ, dnlZ = gp.inference(X, y, deriv=True)
fmu, fs2, ymu, ys2, lp = gp.predict(X, y, Xs)
ymu,ys2 = np.zeros(ns),np.zeros(ns)
lp = np.zeros(ns)
while na<ns:
idx = np.arange(na,min(na+nb,ns))
kss = self.cov(Xs[idx],diag=True) # self variance
Ks = self.cov(Xs[idx],X) # cross-covariances
ms = self.mean(Xs[idx])
al,sW,L,C = self.post.alpha,self.post.sW,self.post.L,self.post.C
fmu[idx] = ms + np.dot(Ks,al)
if L==None:
fs2[idx] = kss + np.sum(Ks*np.dot(Ks,L),axis=1)
else:
V = np.linalg.solve(L,sW*Ks.T)
fs2[idx] = kss - np.sum(V*V,axis=0)
if ys==0: yi = 0
else: yi = ys[idx]
lp[idx],ymu[idx],ys2[idx] = self.lik.pred(yi,fmu[idx],fs2[idx])
na += nb
return fmu,fs2,ymu,ys2,lp
if __name__ == "__main__":
def f(x): return x * np.sin(x)
X = np.atleast_2d([1., 3., 5., 6., 7., 8.]).T
y = f(X).ravel()
Xs = np.atleast_2d(np.linspace(0, 10, 2007)).T
from gp import GaussianProcess as gp
gp = gp(mean=1.0*one())
post,nlZ,dnlZ = gp.inference(X,y,deriv=True)
fmu,fs2,ymu,ys2,lp = gp.predict(X,y,Xs)
def show_1d(X,y,Xs,ym,ys):
plt.fill(np.concatenate([Xs, Xs[::-1]]),
np.concatenate([ym - 1.96*ys,(ym + 1.96*ys)[::-1]]),
alpha=0.25, fc='k', ec='k', label='95% confidence interval')
plt.plot(X,y,'b+',ms=10)
plt.plot(Xs,ym,'b',lw=2)
plt.grid()
plt.xlabel('input X')
plt.ylabel('output y')
def f(x): return x * np.sin(x)
X = np.atleast_2d([1., 3., 5., 6., 7., 8.]).T
y = f(X).ravel()
Xs = np.atleast_2d(np.linspace(0, 10, 2007)).T
from sklearn import gaussian_process
gp = gaussian_process.GaussianProcess(corr='cubic', theta0=1e-2, thetaL=1e-4, thetaU=1e-1, random_start=100)
gp.fit(X,y)
ymn,ys2 = gp.predict(Xs, eval_MSE=True); ysd = np.sqrt(ys2)
from gp import GaussianProcess as gp
gp = gp(X=X,y=y)
post = gp.inference(X,y)
fmu,fs2,ymu,ys2,lp = gp.predict(X,y,Xs)
f0 = plt.figure(0); plt.clf()
show_1d(X,y,Xs,ymn,ysd)
f1 = plt.figure(1); plt.clf()
show_1d(X,y,Xs,ymu,ys2)
def f(x):
return x * np.sin(x)
X = np.atleast_2d([1., 3., 5., 6., 7., 8.]).T
y = f(X).ravel()
Xs = np.atleast_2d(np.linspace(0, 10, 2007)).T
from sklearn import gaussian_process
gp = gaussian_process.GaussianProcess(corr='cubic',
theta0=1e-2,
thetaL=1e-4,
thetaU=1e-1,
random_start=100)
gp.fit(X, y)
ymn, ys2 = gp.predict(Xs, eval_MSE=True)
ysd = np.sqrt(ys2)
from gp import GaussianProcess as gp
gp = gp(X=X, y=y)
post = gp.inference(X, y)
fmu, fs2, ymu, ys2, lp = gp.predict(X, y, Xs)
f0 = plt.figure(0)
plt.clf()
show_1d(X, y, Xs, ymn, ysd)
f1 = plt.figure(1)
plt.clf()
show_1d(X, y, Xs, ymu, ys2)
