#!/usr/bin/env python3
# Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
from collections import defaultdict
from typing import Callable, Dict, Iterable, List, NamedTuple, Optional, Set, Tuple
import numpy as np
from ax.core.observation import Observation, ObservationData
from ax.modelbridge.base import ModelBridge
from scipy.stats import fisher_exact, pearsonr, spearmanr
[docs]class CVResult(NamedTuple):
"""Container for cross validation results."""
observed: Observation
predicted: ObservationData
[docs]def cross_validate(
model: ModelBridge, folds: int = -1, test_selector: Optional[Callable] = None
) -> List[CVResult]:
"""Cross validation for model predictions.
Splits the model's training data into train/test folds and makes
out-of-sample predictions on the test folds.
Train/test splits are made based on arm names, so that repeated
observations of a arm will always be in the train or test set
together.
The test set can be limited to a specific set of observations by passing in
a test_selector callable. This function should take in an Observation
and return a boolean indiciating if it should be used in the test set or
not. For example, we can limit the test set to arms with trial 0 with
test_selector = lambda obs: obs.features.trial_index == 0
If not provided, all observations will be available for the test set.
Args:
model: Fitted model (ModelBridge) to cross validate.
folds: Number of folds. Use -1 for leave-one-out, otherwise will be
k-fold.
test_select: Function for selecting observations for the test set.
Returns:
A CVResult for each observation in the training data.
"""
# Get in-design training points
training_data = [
obs
for i, obs in enumerate(model.get_training_data())
if model.training_in_design[i]
]
arm_names = {obs.arm_name for obs in training_data}
n = len(arm_names)
if folds > n:
raise ValueError(f"Training data only has {n} arms, which is less than folds")
elif folds < 2 and folds != -1:
raise ValueError("Folds must be -1 for LOO, or > 1.")
elif folds == -1:
folds = n
arm_names_rnd = np.array(list(arm_names))
np.random.shuffle(arm_names_rnd)
result = []
for train_names, test_names in _gen_train_test_split(
folds=folds, arm_names=arm_names_rnd
):
# Construct train/test data
cv_training_data = []
cv_test_data = []
cv_test_points = []
for obs in training_data:
if obs.arm_name in train_names:
cv_training_data.append(obs)
elif obs.arm_name in test_names and (
test_selector is None or test_selector(obs)
):
cv_test_points.append(obs.features)
cv_test_data.append(obs)
if len(cv_test_points) == 0:
continue
# Make the prediction
cv_test_predictions = model.cross_validate(
cv_training_data=cv_training_data, cv_test_points=cv_test_points
)
# Form CVResult objects
for i, obs in enumerate(cv_test_data):
result.append(CVResult(observed=obs, predicted=cv_test_predictions[i]))
return result
[docs]def cross_validate_by_trial(model: ModelBridge, trial: int = -1) -> List[CVResult]:
"""Cross validation for model predictions on a particular trial.
Uses all of the data up until the specified trial to predict each of the
arms that was launched in that trial. Defaults to the last trial.
Args:
model: Fitted model (ModelBridge) to cross validate.
trial: Trial for which predictions are evaluated.
Returns:
A CVResult for each observation in the training data.
"""
# Get in-design training points
training_data = [
obs
for i, obs in enumerate(model.get_training_data())
if model.training_in_design[i]
]
all_trials = {
int(d.features.trial_index)
for d in training_data
if d.features.trial_index is not None
}
if len(all_trials) < 2:
raise ValueError(f"Training data has fewer than 2 trials ({all_trials})")
if trial < 0:
trial = max(all_trials)
elif trial not in all_trials:
raise ValueError(f"Trial {trial} not found in training data")
# Construct train/test data
cv_training_data = []
cv_test_data = []
cv_test_points = []
for obs in training_data:
if obs.features.trial_index is None:
continue
elif obs.features.trial_index < trial:
cv_training_data.append(obs)
elif obs.features.trial_index == trial:
cv_test_points.append(obs.features)
cv_test_data.append(obs)
# Make the prediction
cv_test_predictions = model.cross_validate(
cv_training_data=cv_training_data, cv_test_points=cv_test_points
)
# Form CVResult objects
result = [
CVResult(observed=obs, predicted=cv_test_predictions[i])
for i, obs in enumerate(cv_test_data)
]
return result
[docs]def compute_diagnostics(result: List[CVResult]) -> Dict[str, Dict[str, float]]:
"""Computes diagnostics for given cross validation results.
It provides a dictionary with values for the following diagnostics, for
each metric:
- 'Mean prediction CI': the average width of the CIs at each of the CV
predictions, relative to the observed mean.
- 'MAPE': mean absolute percentage error of the estimated mean relative
to the observed mean.
- 'Total raw effect': the percent change from the smallest observed
mean to the largest observed mean.
- 'Correlation coefficient': the Pearson correlation of the estimated
and observed means.
- 'Rank correlation': the Spearman correlation of the estimated
and observed means.
- 'Fisher exact test p': we test if the model is able to distinguish the
bottom half of the observations from the top half, using Fisher's
exact test and the observed/estimated means. A low p value indicates
that the model has some ability to identify good arms. A high p value
indicates that the model cannot identify arms better than chance, or
that the observations are too noisy to be able to tell.
Each of these is returned as a dictionary from metric name to value for
that metric.
Args:
result: Output of cross_validate
Returns:
A dictionary keyed by diagnostic name with results as described above.
"""
# Extract per-metric outcomes from CVResults.
y_obs = defaultdict(list)
y_pred = defaultdict(list)
se_pred = defaultdict(list)
for res in result:
for j, metric_name in enumerate(res.observed.data.metric_names):
y_obs[metric_name].append(res.observed.data.means[j])
# Find the matching prediction
k = res.predicted.metric_names.index(metric_name)
y_pred[metric_name].append(res.predicted.means[k])
se_pred[metric_name].append(np.sqrt(res.predicted.covariance[k, k]))
diagnostic_fns = {
"Mean prediction CI": _mean_prediction_ci,
"MAPE": _mape,
"Total raw effect": _total_raw_effect,
"Correlation coefficient": _correlation_coefficient,
"Rank correlation": _rank_correlation,
"Fisher exact test p": _fisher_exact_test_p,
}
diagnostics: Dict[str, Dict[str, float]] = defaultdict(dict)
# Get all per-metric diagnostics.
for metric_name in y_obs:
for name, fn in diagnostic_fns.items():
diagnostics[name][metric_name] = fn(
y_obs=np.array(y_obs[metric_name]),
y_pred=np.array(y_pred[metric_name]),
se_pred=np.array(se_pred[metric_name]),
)
return diagnostics
def _gen_train_test_split(
folds: int, arm_names: np.ndarray
) -> Iterable[Tuple[Set[str], Set[str]]]:
"""Return train/test splits of arm names.
Args:
folds: Number of folds to return
arm_names: Array of arm names
Returns:
Yields (train, test) tuple of arm names.
"""
n = len(arm_names)
test_size = n // folds # The size of all test sets but the last
final_size = test_size + (n - folds * test_size) # Grab the leftovers
for fold in range(folds):
# We will take the test set from the back of the array.
# Roll the list of arm names to get a fresh test set
arm_names = np.roll(arm_names, test_size)
n_test = test_size if fold < folds - 1 else final_size
yield set(arm_names[:-n_test]), set(arm_names[-n_test:])
def _mean_prediction_ci(
y_obs: np.ndarray, y_pred: np.ndarray, se_pred: np.ndarray
) -> float:
# Pyre does not allow float * np.ndarray.
return float(np.mean(1.96 * 2 * se_pred / np.abs(y_obs)))
def _mape(y_obs: np.ndarray, y_pred: np.ndarray, se_pred: np.ndarray) -> float:
return float(np.mean(np.abs((y_pred - y_obs) / y_obs)))
def _total_raw_effect(
y_obs: np.ndarray, y_pred: np.ndarray, se_pred: np.ndarray
) -> float:
return float((np.max(y_obs) - np.min(y_obs)) / np.min(y_obs))
def _correlation_coefficient(
y_obs: np.ndarray, y_pred: np.ndarray, se_pred: np.ndarray
) -> float:
with np.errstate(invalid="ignore"):
rho, _ = pearsonr(y_pred, y_obs)
return float(rho)
def _rank_correlation(
y_obs: np.ndarray, y_pred: np.ndarray, se_pred: np.ndarray
) -> float:
with np.errstate(invalid="ignore"):
rho, _ = spearmanr(y_pred, y_obs)
return float(rho)
def _fisher_exact_test_p(
y_obs: np.ndarray, y_pred: np.ndarray, se_pred: np.ndarray
) -> float:
n_half = len(y_obs) // 2
top_obs = y_obs.argsort(axis=0)[-n_half:]
top_est = y_pred.argsort(axis=0)[-n_half:]
# Construct contingency table
tp = len(set(top_est).intersection(top_obs))
fp = n_half - tp
fn = n_half - tp
tn = (len(y_obs) - n_half) - (n_half - tp)
table = np.array([[tp, fp], [fn, tn]])
# Compute the test statistic
_, p = fisher_exact(table, alternative="greater")
return float(p)
