def fit(self, x_train, y_train):
self.num_bv = min(len(x_train), self.max_bv)
self._x_bv = np.empty((self.max_bv + 1, x_train.shape[1]))
self._y_bv = np.empty((self.max_bv + 1, y_train.shape[1]))
self.deleted_bv = GrowingArray(
(x_train.shape[1],), expected_rows=2 * self.max_bv)
self._C.fill(0.0)
self._alpha.fill(0.0)
self._K_inv.fill(0.0)
if len(x_train) > self.max_bv:
more_x = x_train[self.max_bv:, :]
more_y = y_train[self.max_bv:, :]
x_train = x_train[:self.max_bv, :]
y_train = y_train[:self.max_bv, :]
else:
more_x = more_y = None
self.x_bv[:] = x_train
self.y_bv[:] = y_train
L_inv = inv(cholesky(
self.kernel(x_train, x_train, y_train, y_train) +
np.eye(len(x_train)) * self.noise_var))
self.K_inv[:, :] = np.dot(L_inv.T, L_inv)
self.alpha[:] = np.squeeze(np.dot(self.K_inv, y_train))
self.C[:, :] = -self.K_inv
self.updates += 1
if more_x is not None:
self.add_observations(more_x, more_y)
class BatchPredictionUpdater(object):
def __init__(self, predictor, plume_recorder, max_train_size=3000):
self.predictor = predictor
self.plume_recorder = plume_recorder
self.max_train_size = max_train_size
self.last_update = None
self.noisy_positions = None
self.on_hold = False
def step(self, noisy_states):
if self.last_update is None:
self.last_update = np.array(len(noisy_states) * [0])
if self.noisy_positions is None:
self.noisy_positions = GrowingArray(
(len(noisy_states), 3),
expected_rows=self.plume_recorder.expected_steps)
self.noisy_positions.append([s.position for s in noisy_states])
can_do_first_training = self.plume_recorder.num_recorded > 1
do_update = not self.predictor.trained and can_do_first_training and \
not self.on_hold
if do_update:
self.update_prediction()
def target_reached(self):
if self.predictor.trained and not self.on_hold:
self.update_prediction()
def update_prediction(self, uavs=None):
is_limit_reached = self.predictor.y_train is not None and \
len(self.predictor.y_train.data) > self.max_train_size
if is_limit_reached:
raise TrainDataSizeLimitReachedError()
if uavs is None:
uavs = range(len(self.plume_recorder.plume_measurements))
for uav in uavs:
self.predictor.add_observations(
self.noisy_positions.data[self.last_update[uav]:, uav, :],
self.get_uncommited_measurements(uav)[:, None])
self.dismiss_measurements(uavs)
def get_uncommited_measurements(self, uav):
return self.plume_recorder.plume_measurements[
uav, self.last_update[uav]:]
def dismiss_measurements(self, uav):
self.last_update[uav] = len(self.noisy_positions.data)
def step(self, noisy_states):
if self.last_update is None:
self.last_update = np.array(len(noisy_states) * [0])
if self.noisy_positions is None:
self.noisy_positions = GrowingArray(
(len(noisy_states), 3),
expected_rows=self.plume_recorder.expected_steps)
self.noisy_positions.append([s.position for s in noisy_states])
can_do_first_training = self.plume_recorder.num_recorded > 1
do_update = not self.predictor.trained and can_do_first_training and \
not self.on_hold
if do_update:
self.update_prediction()
def _create_data_array(self, initial_data):
growing_array = GrowingArray(
initial_data.shape[1:], expected_rows=self.expected_samples)
growing_array.extend(initial_data)
return growing_array
class SparseGP(object):
def __init__(self, kernel=None, tolerance=0, noise_var=1.0, max_bv=1000):
self.kernel = kernel
self.tolerance = tolerance
self.noise_var = noise_var
self.max_bv = max_bv
self.num_bv = 0
self._x_bv = None
self._y_bv = None
self._alpha = np.zeros(max_bv + 1)
self._C = np.zeros((max_bv + 1, max_bv + 1))
self._K_inv = np.zeros((max_bv + 1, max_bv + 1))
self.updates = 0
x_bv = property(lambda self: self._x_bv[:self.num_bv])
y_bv = property(lambda self: self._y_bv[:self.num_bv])
alpha = property(lambda self: self._alpha[:self.num_bv])
C = property(lambda self: self._C[:self.num_bv, :self.num_bv])
K_inv = property(lambda self: self._K_inv[:self.num_bv, :self.num_bv])
trained = property(lambda self: self.updates > 0)
def fit(self, x_train, y_train):
self.num_bv = min(len(x_train), self.max_bv)
self._x_bv = np.empty((self.max_bv + 1, x_train.shape[1]))
self._y_bv = np.empty((self.max_bv + 1, y_train.shape[1]))
self.deleted_bv = GrowingArray(
(x_train.shape[1],), expected_rows=2 * self.max_bv)
self._C.fill(0.0)
self._alpha.fill(0.0)
self._K_inv.fill(0.0)
if len(x_train) > self.max_bv:
more_x = x_train[self.max_bv:, :]
more_y = y_train[self.max_bv:, :]
x_train = x_train[:self.max_bv, :]
y_train = y_train[:self.max_bv, :]
else:
more_x = more_y = None
self.x_bv[:] = x_train
self.y_bv[:] = y_train
L_inv = inv(cholesky(
self.kernel(x_train, x_train, y_train, y_train) +
np.eye(len(x_train)) * self.noise_var))
self.K_inv[:, :] = np.dot(L_inv.T, L_inv)
self.alpha[:] = np.squeeze(np.dot(self.K_inv, y_train))
self.C[:, :] = -self.K_inv
self.updates += 1
if more_x is not None:
self.add_observations(more_x, more_y)
def add_observations(self, x_train, y_train):
if not self.trained:
self.fit(x_train, y_train)
else:
for x, y in zip(x_train, y_train):
self.add_single_observation(x, y)
self.updates += 1
def add_single_observation(self, x, y):
x = np.atleast_2d(x)
k = self.kernel(self.x_bv, x, self.y_bv.T, y)
k_star = np.squeeze(self.kernel(x, x, y, y))
gamma = np.squeeze(k_star - np.einsum('ij,jk,kl', k.T, self.K_inv, k))
e_hat = np.atleast_1d(np.squeeze(np.dot(self.K_inv, k)))
if self.num_bv > 0:
sigma_x_sq = np.squeeze(self.noise_var + np.einsum(
'ij,jk,kl->il', k.T, self.C, k) + k_star)
else:
sigma_x_sq = self.noise_var + k_star
q = (y - np.dot(self.alpha, k)) / sigma_x_sq
r = -1.0 / sigma_x_sq
if gamma < self.tolerance:
self._reduced_update(k, e_hat, q, r)
else:
self._extend_basis(x, y, k, q, r)
self._update_K(gamma, e_hat)
if self.num_bv > self.max_bv:
self._delete_bv()
def _extend_basis(self, x, y, k, q, r):
s = np.concatenate((np.atleast_1d(np.squeeze(np.dot(self.C, k))), [1]))
self.num_bv += 1
self.x_bv[-1] = x
self.y_bv[-1] = y
self._update_alpha_and_C(q, r, s)
def _reduced_update(self, k, e_hat, q, r):
s = np.squeeze(np.dot(self.C, k)) + e_hat
self._update_alpha_and_C(q, r, s)
def _update_alpha_and_C(self, q, r, s):
self.alpha[:] += q * s
self.C[:] += r * np.outer(s, s)
def _update_K(self, gamma, e_hat):
e_extended = np.concatenate((e_hat, [-1]))
self.K_inv[:, :] += np.outer(e_extended, e_extended) / (
self.noise_var + gamma)
def _delete_bv(self):
score = np.abs(self.alpha) / np.diag(self.K_inv)
min_bv = np.argmin(score)
self.deleted_bv.append(self.x_bv[min_bv])
self._exclude_from_vec(self.x_bv, min_bv)
self._exclude_from_vec(self.y_bv, min_bv)
alpha_star = self._exclude_from_vec(self.alpha, min_bv)
Q_star, q_star = self._exclude_from_mat(self.K_inv, min_bv)
C_star, c_star = self._exclude_from_mat(self.C, min_bv)
self.num_bv -= 1
self.alpha[:] -= alpha_star / q_star * Q_star
QQ_T = np.outer(Q_star, Q_star)
QC_T = np.outer(Q_star, C_star)
self.C[:, :] += c_star / (q_star ** 2) * QQ_T - \
(QC_T + QC_T.T) / q_star
self.K_inv[:, :] -= QQ_T / q_star
def _exclude_from_vec(self, vec, idx, fill_value=0):
excluded = vec[idx]
vec[idx:-1] = vec[idx + 1:]
vec[-1] = fill_value
return excluded
def _exclude_from_mat(self, mat, idx, fill_value=0):
excluded_diag = mat[idx, idx]
excluded_vec = np.empty(len(mat) - 1)
excluded_vec[:idx] = mat[idx, :idx]
excluded_vec[idx:] = mat[idx, idx + 1:]
mat[idx:-1, :] = mat[idx + 1:, :]
mat[:, idx:-1] = mat[:, idx + 1:]
mat[-1, :] = fill_value
mat[:, -1] = fill_value
return excluded_vec, excluded_diag
def predict(self, x, eval_MSE=False, eval_derivatives=False):
if eval_derivatives:
k, k_derivative = self.kernel(
x, self.x_bv, eval_derivative=True)
else:
k = self.kernel(x, self.x_bv, np.zeros(len(x)), self.y_bv.T)
pred = np.dot(k, np.atleast_2d(self.alpha).T)
if eval_MSE is not False:
noise_part = self.noise_var
if eval_MSE == 'err':
density = gaussian_kde(self.x_bv.T)
count = len(self.x_bv) * np.apply_along_axis(
density.integrate_gaussian, 1, x,
np.eye(3) * self.kernel.lengthscale)
noise_part /= (1 + count)
mse = np.maximum(
noise_part,
noise_part + self.kernel.diag(
x, x, np.zeros(len(x)), np.zeros(len(x))) + np.einsum(
'ij,jk,ki->i', k, self.C, k.T))
if eval_derivatives:
pred_derivative = np.einsum(
'ijk,lj->ilk', k_derivative, np.atleast_2d(self.alpha))
if eval_MSE:
mse_derivative = 2 * np.einsum(
'ijk,jl,li->ik', k_derivative, self.C, k.T)
return pred, pred_derivative, mse, mse_derivative
else:
return pred, pred_derivative
elif eval_MSE:
return pred, mse
else:
return pred
def calc_neg_log_likelihood(self, eval_derivative=False):
L_inv = cholesky(-self.C)
svs = np.dot(self.y_bv.T, L_inv)
log_likelihood = -0.5 * np.dot(svs, svs.T) + \
np.sum(np.log(np.diag(L_inv))) - \
0.5 * self.num_bv * np.log(2 * np.pi)
if eval_derivative:
alpha = np.dot(svs, L_inv.T)
grad_weighting = np.dot(alpha.T, alpha) + self.C
kernel_derivative = np.array([
0.5 * np.sum(np.einsum(
'ij,ji->i', grad_weighting, param_deriv))
for param_deriv in self.kernel.param_derivatives(
self.x_bv, self.x_bv)])
return -np.squeeze(log_likelihood), -kernel_derivative
else:
return -np.squeeze(log_likelihood)