class DefaultPrior(BasePrior):
def __init__(self, n_dims: int, rng: np.random.RandomState = None):
"""
This class is a verbatim copy of the implementation of RoBO:
Klein, A. and Falkner, S. and Mansur, N. and Hutter, F.
RoBO: A Flexible and Robust Bayesian Optimization Framework in Python
In: NIPS 2017 Bayesian Optimization Workshop
"""
if rng is None:
self.rng = np.random.RandomState(np.random.randint(0, 10000))
else:
self.rng = rng
# The number of hyperparameters
self.n_dims = n_dims
# Prior for the Matern52 lengthscales
self.tophat = TophatPrior(-10, 2, rng=self.rng)
# Prior for the covariance amplitude
self.ln_prior = LognormalPrior(mean=0.0, sigma=1.0, rng=self.rng)
# Prior for the noise
self.horseshoe = HorseshoePrior(scale=0.1, rng=self.rng)
def lnprob(self, theta: np.ndarray):
lp = 0
# Covariance amplitude
lp += self.ln_prior.lnprob(theta[0])
# Lengthscales
lp += self.tophat.lnprob(theta[1:-1])
# Noise
lp += self.horseshoe.lnprob(theta[-1])
return lp
def sample_from_prior(self, n_samples: int):
p0 = np.zeros([n_samples, self.n_dims])
# Covariance amplitude
p0[:, 0] = self.ln_prior.sample_from_prior(n_samples)[:, 0]
# Lengthscales
ls_sample = np.array([
self.tophat.sample_from_prior(n_samples)[:, 0]
for _ in range(1, (self.n_dims - 1))
]).T
p0[:, 1:(self.n_dims - 1)] = ls_sample
# Noise
p0[:, -1] = self.horseshoe.sample_from_prior(n_samples)[:, 0]
return p0
def gradient(self, theta: np.ndarray):
# TODO: Implement real gradient here
return np.zeros([theta.shape[0]])
def test_gradient(self):
for sigma in (0.5, 1., 2.):
prior = LognormalPrior(mean=0, sigma=sigma, rng=np.random.RandomState(1))
# The function appears to be unstable above 15
for theta in range(0, 15):
# Gradient approximation becomes unstable when going closer to zero
theta += 1e-2
error = scipy.optimize.check_grad(
lambda x: prior.lnprob(x[0]),
lambda x: prior.gradient(x[0]),
np.array([theta]),
epsilon=1e-5,
)
self.assertAlmostEqual(error, 0, delta=5, msg=theta)