def bayesian_search(xmat,
y,
theta,
p,
xinit,
acq_func,
bounds=None,
constraints=None):
"""
Search best point to sample by maximizing acquisition function
Args:
xmat (numpy.ndarray) : the data points so far, shape = (n, k)
y (numpy.ndarray) : y, shape=(n, 1)
theta (numpy.ndarray) : vector of theta params, one by dim, shape = (k, )
p (numpy.ndarray) : powers used to compute the distance, one by dim, shape = (k, )
xinit (numpy.ndarray) : initial value for acquisition maximization, shape = (k, )
acq_func : Instance of one of the classes in Acquisition_Functions.py file
bounds (tuple) : bounds for acquisition maximization in scipy
Returns:
numpy.ndarray. The new point to sample from given the data so far
"""
R = exp_kernel.kernel_mat(xmat, theta, p)
Rinv = cho_inv.cholesky_inv(R)
beta_hat = pred.beta_est(y, Rinv)
opti_result = am.opti_acq_func(xmat, y, Rinv, beta_hat, theta, p, xinit,
acq_func, bounds)
return opti_result
def prediction_function_krigging(xnew, y, xmat, theta_vec, p_vec):
R = exp_kernel.kernel_mat(xmat, theta_vec, p_vec)
Rinv = cho_inv.cholesky_inv(R)
beta_hat = pred.beta_est(y, Rinv)
rx = exp_kernel.kernel_rx(xmat, xnew, theta_vec, p_vec)
y_hat = pred.y_est(rx, y, Rinv, beta_hat)
return y_hat
def bayesian_opti_plot_1d(xmat,
y,
n_it,
theta,
p,
acq_func,
objective_func,
bounds=None):
for i in range(0, n_it):
print(i)
xinit = initial.xinit_inbounds(bounds)
if acq_func.name == "EI":
acq_func.set_fmin(np.min(y))
opti_result = bayesian_search(xmat, y, theta, p, xinit, acq_func,
bounds)
xnew = opti_result.x
R = exp_kernel.kernel_mat(xmat, theta, p)
Rinv = cho_inv.cholesky_inv(R)
beta_hat = pred.beta_est(y, Rinv)
axes = viz.bayes_opti_plot_1d(xmat,
y,
Rinv,
beta_hat,
theta,
p,
bounds[0],
grid_size=1000,
acq_func=acq_func,
objective_func=objective_func)
y_acq = -opti_result.fun
axes[1].vlines(xnew[0],
0,
y_acq,
linestyles='dashed',
colors='r',
linewidth=2)
plt.show()
xmat, y = evaluate_add(xmat, xnew, y, objective_func)
def bayesian_optimization(n, nb_it, p_vec, theta_vec, function2Bmin):
# Ce serait bien de faire une fonction pour une iteration puis
# de boucler en utilisant cette fonction "atomique" cf infra
"""
Function for bayesian optimization with fixed p and theta
Args:
n (integer) : number of initial sampling observations
nb_it (integer) : number of iteration of sampling
theta_vec (numpy.ndarray) : vector of theta params, one by dim, shape = (2, )
p_vec (numpy.ndarray) : powers used to compute the distance, one by dim, shape = (2, )
Returns:
float. Minimum evaluation of the fonction to be minimized
numpy.ndarray Point minimizing the function to be minimized
"""
xtest = 5 * np.random.rand(n, 2)
y = np.zeros((n, 1))
for i in range(0, n):
y[i, 0] = test_func.mystery_vec(xtest[i, :])
for it in range(0, nb_it):
R = exp_kernel.kernel_mat(xtest, theta_vec, p_vec)
Rinv = cho_inv.cholesky_inv(R)
beta = pred.beta_est(y, Rinv)
xinit = 5 * np.random.rand(1, 2)
optiEI = af.max_EI(xtest, y, Rinv, beta, theta_vec, p_vec, xinit,
function2Bmin)
xnew = optiEI["x"].reshape(1, 2)
ynew = np.array(function2Bmin(xnew.reshape(2, 1))).reshape(1, 1)
xtest = np.concatenate((xtest, xnew), axis=0)
y = np.concatenate((y, ynew))
print(it)
return min(y), y, xtest[np.argmin(y), ], xtest
def log_likelihood(xmat, y, params_vec):
"""
Log likelihood
Args :
xmat (numpy.ndarray) : shape = (n, k)
y (numpy.ndarray) : shape = (n, 1)
params_vec (numpy.ndarray) : shape = (2*k, )
Returns :
float. log likelihood
"""
theta_vec, p_vec = params_to_vec(params_vec)
R = exp_kernel.kernel_mat(xmat, theta_vec, p_vec)
n = R.shape[0]
Rinv = cho_inv.cholesky_inv(R)
detR = np.linalg.det(R)
hat_sigz_sqr = hat_sigmaz_sqr_mle(y, Rinv)
# print("Theta vec" + str(theta_vec))
# print("p_vec" + str(p_vec))
# print("sigma " + str(hat_sigz_sqr))
# print("Det " + str(detR))
return -0.5 * (n * math.log(hat_sigz_sqr) + math.log(detR))
if perform_mle:
opti = max_llk.max_log_likelihood(
xmat,
y,
params_init,
fixed_p=False,
mins_list=[0.01, 0.01, 0.1, 0.1],
maxs_list=[None, None, 1.99, 1.99])
print(opti)
theta_vec = opti.x[0:d]
p_vec = opti.x[d:]
# Plot of initial acquisition function in 2d
if plot_acq_2d and (d == 2):
# Computation of the necessaries quantities
R = exp_kernel.kernel_mat(xmat, theta_vec, p_vec)
Rinv = cho_inv.cholesky_inv(R)
beta = pred.beta_est(y, Rinv)
# Plot acq_func1
viz.plot_acq_func_2d(xmat,
y,
Rinv,
beta,
theta_vec,
p_vec,
bounds,
(100, 100),
acq_func1)
# Plot acq_func2
viz.plot_acq_func_2d(xmat,
y,