#!/usr/bin/env python3
# Copyright (c) Facebook, Inc. and its affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
from typing import TYPE_CHECKING, Callable, List, Optional, Tuple
import numpy as np
from ax.core.observation import ObservationData, ObservationFeatures
from ax.core.optimization_config import OptimizationConfig
from ax.core.search_space import SearchSpace
from ax.core.types import TConfig
from ax.modelbridge.transforms.base import Transform
from ax.utils.common.logger import get_logger
from scipy.stats import norm
if TYPE_CHECKING:
# import as module to make sphinx-autodoc-typehints happy
from ax.modelbridge import base as base_modelbridge # noqa F401 # pragma: no cover
logger = get_logger(__name__)
[docs]class LogY(Transform):
"""Apply (natural) log-transform to Y.
This essentially means that we are model the observations as log-normally
distributed. If `config` specifies `match_ci_width=True`, use a matching
procedure based on the width of the CIs, otherwise (the default), use the
delta method,
Transform is applied only for the metrics specified in the transform config.
Transform is done in-place.
"""
def __init__(
self,
search_space: SearchSpace,
observation_features: List[ObservationFeatures],
observation_data: List[ObservationData],
config: Optional[TConfig] = None,
) -> None:
if config is None:
raise ValueError("LogY requires a config.")
# pyre-fixme[6]: Expected `Iterable[Variable[_T]]` for 1st param but got
# `Union[List[Variable[_T]],
# botorch.acquisition.acquisition.AcquisitionFunction, float, int, str]`.
metric_names = list(config.get("metrics", []))
if len(metric_names) == 0:
raise ValueError("Must specify at least one metric in the config.")
super().__init__(
search_space=search_space,
observation_features=observation_features,
observation_data=observation_data,
config=config,
)
self.metric_names = metric_names
if config.get("match_ci_width", False):
# perform moment-matching to compute variance that results in a CI
# of same width as the when transforming the moments
self._transform = lambda m, v: match_ci_width(m, v, np.log)
self._untransform = lambda m, v: match_ci_width(m, v, np.exp)
else:
self._transform = lognorm_to_norm
self._untransform = norm_to_lognorm
def _tf_obs_data(
self,
observation_data: List[ObservationData],
observation_features: List[ObservationFeatures],
transform: Callable[[np.ndarray, np.ndarray], Tuple[np.ndarray, np.ndarray]],
) -> List[ObservationData]:
for obsd in observation_data:
cov = obsd.covariance
idcs = [
i for i, m in enumerate(obsd.metric_names) if m in self.metric_names
]
if len(idcs) != len(obsd.metric_names):
# TODO: Support covariances for a subset of observations
diff = cov - np.diag(np.diag(cov))
if not np.all(np.isnan(diff) | (diff == 0)):
raise NotImplementedError(
"LogY transform for a subset of metrics not supported for "
" correlated observations"
)
for i, m in enumerate(obsd.metric_names):
if m in self.metric_names:
mu, cov = transform(
np.array(obsd.means[i], ndmin=1),
np.array(obsd.covariance[i, i], ndmin=1),
)
obsd.means[i] = mu
obsd.covariance[i, i] = cov
else:
mu, cov = transform(obsd.means, obsd.covariance)
obsd.means = mu
obsd.covariance = cov
return observation_data
[docs]def match_ci_width(
mean: np.ndarray,
variance: np.ndarray,
transform: Callable[[np.ndarray], np.ndarray],
level: float = 0.95,
) -> np.ndarray:
fac = norm.ppf(1 - (1 - level) / 2)
d = fac * np.sqrt(variance)
width_asym = transform(mean + d) - transform(mean - d)
new_mean = transform(mean)
new_variance = (width_asym / 2 / fac) ** 2
# pyre-fixme[7]: Expected `ndarray` but got `Tuple[ndarray, float]`.
return new_mean, new_variance
[docs]def lognorm_to_norm(
mu_ln: np.ndarray, Cov_ln: np.ndarray
) -> Tuple[np.ndarray, np.ndarray]:
"""Compute mean and covariance of a MVN from those of the associated log-MVN
If `Y` is log-normal with mean mu_ln and covariance Cov_ln, then
`X ~ N(mu_n, Cov_n)` with
Cov_n_{ij} = log(1 + Cov_ln_{ij} / (mu_ln_{i} * mu_n_{j}))
mu_n_{i} = log(mu_ln_{i}) - 0.5 * log(1 + Cov_ln_{ii} / mu_ln_{i}**2)
"""
Cov_n = np.log(1 + Cov_ln / np.outer(mu_ln, mu_ln))
mu_n = np.log(mu_ln) - 0.5 * np.diag(Cov_n)
return mu_n, Cov_n
[docs]def norm_to_lognorm(
mu_n: np.ndarray, Cov_n: np.ndarray
) -> Tuple[np.ndarray, np.ndarray]:
"""Compute mean and covariance of a log-MVN from its MVN sufficient statistics
If `X ~ N(mu_n, Cov_n)` and `Y = exp(X)`, then `Y` is log-normal with
mu_ln_{i} = exp(mu_n_{i}) + 0.5 * Cov_n_{ii}
Cov_ln_{ij} = exp(mu_n_{i} + mu_n_{j} + 0.5 * (Cov_n_{ii} + Cov_n_{jj})) *
(exp(Cov_n_{ij}) - 1)
"""
diag_n = np.diag(Cov_n)
b = mu_n + 0.5 * diag_n
mu_ln = np.exp(b)
Cov_ln = (np.exp(Cov_n) - 1) * np.exp(b.reshape(-1, 1) + b.reshape(1, -1))
return mu_ln, Cov_ln
