def kernel_eval(self, input):

return self.theta_0**2*pairwise_kernels(input, self.X, metric=self.kernel) @ self.z

def f0(self):

f_0 = self.theta_0**2 * \

np.sum([self.z[i]*np.prod([self.prod_d(i, d)

for d in range(self.dim)]) for i in range(self.size)])

return f_0

def prod_ijt(self, i, j, t):

return np.sqrt(np.pi/2)/(2*self.c[t]) \

* np.exp(-0.5*self.c[t]**2*(self.X[i, t] - self.X[j, t])**2) \

* (erf(self.c[t]/np.sqrt(2)*(self.X[i, t] + self.X[j, t]))

- erf(self.c[t]/np.sqrt(2)*(self.X[i, t] + self.X[j, t]-2)))

def prod_ij(self, i, j):

return self.z[i] * self.z[j] * np.prod([self.prod_ijt(i, j, t) for t in range(self.dim)])

def total_variance(self):

s = 0

for i in range(self.X.shape[0]):

for j in range(self.X.shape[0]):

s += self.prod_ij(i, j)

sigma2 = self.theta_0**4 * s - self.f0()**2

return sigma2

def prod_d(self, i, d):

return np.sqrt(np.pi)/(2*self.c[d])*(erf(self.c[d]*(1-self.X[i, d])) + erf(self.c[d] * self.X[i, d]))

def P_i(self, i, t):

return np.prod([self.prod_d(i, d) for d in range(self.dim) if d != t])

def main_effect(self, t):

f0 = self.f0()

s1 = 0

for i in range(self.X.shape[0]):

for j in range(self.X.shape[0]):

s1 += self.z[i]*self.z[j] * \

self.P_i(i, t)*self.P_i(j, t)*self.prod_ijt(i, j, t)

s1 *= self.theta_0**4

s2 = 0

for i in range(self.X.shape[0]):

s2 += self.z[i] * self.prod_d(i, t) * self.P_i(i, t)

s2 *= -2*self.theta_0**2*f0

return s1 + s2 + f0**2

def f_t(self, x, t):

s = 0

for i in range(self.X.shape[0]):

s += self.z[i]*np.exp(-self.c[t]**2 *

(x - self.X[i, t])**2)*self.P_i(i, t)

return self.theta_0**2 * s-self.f0()

def __init__(self, X, y, theta_0, theta_1):

self.X = X

self.size, self.dim = self.X.shape

y = y

ε = 1e-2

self.theta_0 = theta_0

self.theta_1 = theta_1

self.c = np.sqrt(theta_1**2 + ε)

length_scale = 1.0/(np.sqrt(2)*self.c)

self.kernel = RBF(length_scale=length_scale)

K = theta_0**2*pairwise_kernels(X, metric=self.kernel)