def test_weights_to_lmbdas_equals_log_version():
N = 30
sum_old_weights = 1
new_weights = np.ones(N - 1)
lmbdas = weights_to_lmbdas(sum_old_weights, new_weights)
log_sum_old_weights = np.log(sum_old_weights)
log_new_weights = np.log(new_weights)
lmbdas2 = log_weights_to_lmbdas(log_sum_old_weights, log_new_weights)
assert_allclose(lmbdas, lmbdas2)
def test_weights_to_lmbdas_equals_log_version():
N = 30
sum_old_weights = 1
new_weights = np.ones(N - 1)
lmbdas = weights_to_lmbdas(sum_old_weights, new_weights)
log_sum_old_weights = np.log(sum_old_weights)
log_new_weights = np.log(new_weights)
lmbdas2 = log_weights_to_lmbdas(log_sum_old_weights, log_new_weights)
assert_allclose(lmbdas, lmbdas2)
def update_b_L_C_weighted(X, b, L_C, log_sum_weights, log_weights, omega, u):
m = 1 if np.isscalar(u) else len(u)
N = X.shape[0]
D = X.shape[1]
# transform weights into (1-\lmbda)*old_mean+ \lmbda*new_term style updates
lmbdas = log_weights_to_lmbdas(log_sum_weights, log_weights)
# first and (negative) second derivatives of rff feature map
projection = np.dot(X, omega) + u
Phi = np.cos(projection) * np.sqrt(2. / m)
Phi2 = np.sin(projection) * np.sqrt(2. / m)
# not needed any longer
del projection
# work on upper triangular cholesky internally
L_R = L_C.T
b_new_term = np.zeros(m)
for i in range(N):
# downscale L_C once for every datum
L_R *= np.sqrt(1 - lmbdas[i])
b_new_term[:] = 0
for d in range(D):
b_new_term += Phi[i] * (omega[d, :]**2)
# L_C is updated D times for every datum, each with fixed lmbda
C_new_term = Phi2[i] * omega[d, :] * np.sqrt(lmbdas[i])
cholupdate(L_R, C_new_term)
# b is updated once per datum
b = (1 - lmbdas[i]) * b + lmbdas[i] * b_new_term
# transform back to lower triangular version
L_C = L_R.T
return b, L_C
def update_b_L_C_weighted(X, b, L_C, log_sum_weights, log_weights, omega, u):
m = 1 if np.isscalar(u) else len(u)
N = X.shape[0]
D = X.shape[1]
# transform weights into (1-\lmbda)*old_mean+ \lmbda*new_term style updates
lmbdas = log_weights_to_lmbdas(log_sum_weights, log_weights)
# first and (negative) second derivatives of rff feature map
projection = np.dot(X, omega) + u
Phi = np.cos(projection) * np.sqrt(2. / m)
Phi2 = np.sin(projection) * np.sqrt(2. / m)
# not needed any longer
del projection
# work on upper triangular cholesky internally
L_R = L_C.T
b_new_term = np.zeros(m)
for i in range(N):
# downscale L_C once for every datum
L_R *= np.sqrt(1 - lmbdas[i])
b_new_term[:] = 0
for d in range(D):
b_new_term += Phi[i] * (omega[d, :] ** 2)
# L_C is updated D times for every datum, each with fixed lmbda
C_new_term = Phi2[i] * omega[d, :] * np.sqrt(lmbdas[i])
cholupdate(L_R, C_new_term)
# b is updated once per datum
b = (1 - lmbdas[i]) * b + lmbdas[i] * b_new_term
# transform back to lower triangular version
L_C = L_R.T
return b, L_C
