# Source code for ax.modelbridge.cross_validation

```
#!/usr/bin/env python3
# Copyright (c) Meta Platforms, Inc. and affiliates.
#
# This source code is licensed under the MIT license found in the
# LICENSE file in the root directory of this source tree.
from abc import ABC, abstractmethod
from collections import defaultdict
from enum import Enum
from functools import partial
from logging import Logger
from numbers import Number
from typing import (
Any,
Callable,
cast,
Dict,
Iterable,
List,
Mapping,
NamedTuple,
Optional,
Set,
Tuple,
)
import numpy as np
from ax.core.observation import Observation, ObservationData
from ax.core.optimization_config import OptimizationConfig
from ax.modelbridge.base import ModelBridge
from ax.utils.common.logger import get_logger
from ax.utils.stats.model_fit_stats import (
_correlation_coefficient,
_fisher_exact_test_p,
_log_likelihood,
_mape,
_mean_prediction_ci,
_rank_correlation,
_total_raw_effect,
compute_model_fit_metrics,
ModelFitMetricProtocol,
)
logger: Logger = get_logger(__name__)
CVDiagnostics = Dict[str, Dict[str, float]]
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"
LOG_LIKELIHOOD = "Log likelihood"
[docs]class CVResult(NamedTuple):
"""Container for cross validation results."""
observed: Observation
predicted: ObservationData
[docs]class AssessModelFitResult(NamedTuple):
"""Container for model fit assessment results"""
good_fit_metrics_to_fisher_score: Dict[str, float]
bad_fit_metrics_to_fisher_score: Dict[str, float]
[docs]def cross_validate(
model: ModelBridge,
folds: int = -1,
# pyre-fixme[24]: Generic type `Callable` expects 2 type parameters.
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_selector: 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 n == 0:
raise ValueError(
f"{model.__class__.__name__} has no training data. Either it has been "
"incorrectly initialized or should not be cross validated."
)
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]) -> CVDiagnostics:
"""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 multiple change from the smallest observed
mean to the largest observed mean, i.e. `(max - min) / min`.
- '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]))
y_obs = _arrayify_dict_values(y_obs)
y_pred = _arrayify_dict_values(y_pred)
se_pred = _arrayify_dict_values(se_pred)
# We need to cast here since pyre infers specific types T < ModelFitMetricProtocol
# for the dict values, which is type variant upon initialization, leading
# diagnostic_fns to not be recognized as a Mapping[str, ModelFitMetricProtocol],
# see the last tip in the Pyre docs on [9] Incompatible Variable Type:
# https://staticdocs.internalfb.com/pyre/docs/errors/#9-incompatible-variable-type
diagnostic_fns = cast(
Mapping[str, ModelFitMetricProtocol],
{
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,
LOG_LIKELIHOOD: _log_likelihood,
},
)
diagnostics = compute_model_fit_metrics(
y_obs=y_obs, y_pred=y_pred, se_pred=se_pred, fit_metrics_dict=diagnostic_fns
)
return diagnostics
def _arrayify_dict_values(d: Dict[str, List[float]]) -> Dict[str, np.ndarray]:
"""Helper to convert dictionary values to numpy arrays."""
return {k: np.array(v) for k, v in d.items()}
[docs]def assess_model_fit(
diagnostics: CVDiagnostics,
significance_level: float = 0.1,
) -> AssessModelFitResult:
"""Assess model fit for given diagnostics results.
It determines if a model fit is good or bad based on Fisher exact test p
Args:
diagnostics: Output of compute_diagnostics
Returns:
Two dictionaries, one for good metrics, one for bad metrics, each
mapping metric name to p-value
"""
good_fit_metrics_to_fisher_score: Dict[str, float] = {}
bad_fit_metrics_to_fisher_score: Dict[str, float] = {}
for metric, score in diagnostics[FISHER_EXACT_TEST_P].items():
if score > significance_level:
bad_fit_metrics_to_fisher_score[metric] = score
else:
good_fit_metrics_to_fisher_score[metric] = score
if len(bad_fit_metrics_to_fisher_score) > 0:
logger.warning(
"{} {} {} unable to be reliably fit.".format(
("Metrics" if len(bad_fit_metrics_to_fisher_score) > 1 else "Metric"),
(" , ".join(bad_fit_metrics_to_fisher_score.keys())),
("were" if len(bad_fit_metrics_to_fisher_score) > 1 else "was"),
)
)
return AssessModelFitResult(
good_fit_metrics_to_fisher_score=good_fit_metrics_to_fisher_score,
bad_fit_metrics_to_fisher_score=bad_fit_metrics_to_fisher_score,
)
[docs]def has_good_opt_config_model_fit(
optimization_config: OptimizationConfig,
assess_model_fit_result: AssessModelFitResult,
) -> bool:
"""Assess model fit for given diagnostics results across the optimization
config metrics
Bad fit criteria: Any objective metrics are poorly fit based on
the Fisher exact test p (see assess_model_fit())
TODO[]: Incl. outcome constraints in assessment
Args:
optimization_config: Objective/Outcome constraint metrics to assess
diagnostics: Output of compute_diagnostics
Returns:
Two dictionaries, one for good metrics, one for bad metrics, each
mapping metric name to p-value
"""
# Bad fit criteria: Any objective metrics are poorly fit
# TODO[]: Incl. outcome constraints in assessment
has_good_opt_config_fit = all(
(m.name in assess_model_fit_result.good_fit_metrics_to_fisher_score)
for m in optimization_config.objective.metrics
)
return has_good_opt_config_fit
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:])
[docs]class BestModelSelector(ABC):
[docs] @abstractmethod
def best_diagnostic(self, diagnostics: List[CVDiagnostics]) -> int:
"""
Return the index of the best diagnostic.
"""
pass
[docs]class CallableEnum(Enum):
# pyre-fixme[3]: Return annotation cannot be `Any`.
def __call__(self, *args: Optional[Any], **kwargs: Optional[Any]) -> Any:
return self.value(*args, **kwargs)
[docs]class MetricAggregation(CallableEnum):
MEAN: Callable[[Iterable[Number]], Number] = partial(np.mean)
[docs]class DiagnosticCriterion(CallableEnum):
MIN: Callable[[Iterable[Number]], Number] = partial(np.amin)
[docs]class SingleDiagnosticBestModelSelector(BestModelSelector):
"""Choose the best model using a single cross-validation diagnostic.
The input is a list of CVDiagnostics, each corresponding to one model.
The specified diagnostic is extracted from each of the CVDiagnostics,
its values (each of which corresponds to a separate metric) are
aggregated with the aggregation function, the best one is determined
with the criterion, and the index of the best diagnostic result is returned.
Example:
::
s = SingleDiagnosticBestModelSelector(
diagnostic = 'Fisher exact test p',
criterion = DiagnosticCriterion.MIN,
metric_aggregation = MetricAggregation.MEAN,
)
best_diagnostic_index = s.best_diagnostic(diagnostics)
Args:
diagnostic (str): The name of the diagnostic to use, which should be
a key in CVDiagnostic.
metric_aggregation (MetricAggregation): Callable
applied to the values of the diagnostic for a single model to
produce a single number.
criterion (DiagnosticCriterion): Callable used
to determine which of the (aggregated) diagnostics is the best.
Returns:
int: index of the selected best diagnostic.
"""
def __init__(
self,
diagnostic: str,
metric_aggregation: MetricAggregation,
criterion: DiagnosticCriterion,
) -> None:
self.diagnostic = diagnostic
self.metric_aggregation = metric_aggregation
self.criterion = criterion
[docs] def best_diagnostic(self, diagnostics: List[CVDiagnostics]) -> int:
aggregated_diagnostic_values = [
self.metric_aggregation(list(d[self.diagnostic].values()))
for d in diagnostics
]
best_diagnostic = self.criterion(aggregated_diagnostic_values)
return aggregated_diagnostic_values.index(best_diagnostic)
```