from copy import deepcopy
from typing import Any
import numpy as np
import tqdm
from numpy.typing import NDArray
from caliber.regression.conformal_regression.base import AbstractRegressionModel
[docs]
class JackknifePlusRegressionModel(AbstractRegressionModel):
"""
A conformalised bootstrap model based on leave-one-out (LOO).
Given inputs and targets, it trains an arbitrary model multiple times with LOO and stores the prediction error on the left-out input.
At prediction time, it provides a confidence interval around the mean predicted, with quantiles corrected via the errors stored at training time.
Given a coverage level `alpha`, a target variable `Y` and the predicted confidence interval `[Q1, Q2]`,
if the training and test sets are IID the algorithm ensures that `P(Y in [Q1, Q2]) >= alpha`.
"""
def __init__(
self,
model: Any,
coverage: float,
loo_size: int = 100,
seed: int = 0,
loo_prediction: bool = False,
) -> None:
"""
Args:
model (Any): An instantiated model class with `fit` and `predict` methods.
coverage (float): A coverage value between 0 and 1.
For example, `coverage=0.95` means that the target variable will be expected to lay within the confidence interval 95% of the times.
loo_size (int, optional): The number of leave-one-out (LOO) validations. Defaults to 100.
seed (int, optional): The random seed. Defaults to 0.
loo_prediction (bool, optional): Whether to predict the mean prediction using the leave-one-out models or rather a single model. Defaults to False.
"""
self._model = model
self._coverage = coverage
self._loo_size = loo_size
self._loo_prediction = loo_prediction
self._rng = np.random.default_rng(seed)
[docs]
def fit(
self, inputs: NDArray[np.float64], targets: NDArray[np.float64]
) -> NDArray[np.float64]:
indices = self._rng.choice(len(inputs), size=self._loo_size, replace=False)
self._models = []
self._loo_errors: NDArray[np.float64] = np.zeros((self._loo_size,))
for i, val_idx in enumerate(tqdm(indices, desc="Leave-One-Out")):
train_indices = [idx for idx in range(len(inputs)) if idx != val_idx]
train_inputs, train_targets = inputs[train_indices], targets[train_indices]
val_inputs, val_targets = inputs[None, val_idx], targets[None, val_idx]
model = deepcopy(self._model)
model.fit(train_inputs, train_targets)
val_preds = model.predict(val_inputs)
if val_preds.ndim == 2:
if val_preds.shape[1] != 1:
raise ValueError(
"This method is supported only for scalar targets."
)
val_preds = val_preds.squeeze(1)
self._loo_errors[i] = np.abs(val_targets - val_preds)[0]
self._models.append(model)
if not self._loo_prediction:
self._model.fit(inputs, targets)
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def predict(self, inputs: NDArray[np.float64]) -> NDArray[np.float64]:
if self._loo_prediction:
preds = np.zeros(len(inputs))
for model in self._models:
preds_i = model.predict(inputs)
if preds_i.ndim == 2:
if preds_i.shape[1] != 1:
raise ValueError(
"This method is supported only for scalar targets."
)
preds_i = preds_i.squeeze(1)
preds += preds_i
preds /= self._loo_size
return preds
return self._model.predict(inputs)
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def predict_quantiles(self, inputs: NDArray[np.float64]) -> NDArray[np.float64]:
loo_preds = np.zeros((self._loo_size, len(inputs)))
for i, model in enumerate(self._models):
preds = model.predict(inputs)
if preds.ndim == 2:
if preds.shape[1] != 1:
raise ValueError(
"This method is supported only for scalar targets."
)
preds = preds.squeeze(1)
loo_preds[i] = preds
left = loo_preds - self._loo_errors[:, None]
right = loo_preds + self._loo_errors[:, None]
qleft = np.quantile(left, q=1 - self._coverage, axis=0)
qright = np.quantile(right, q=self._coverage, axis=0)
return np.array(list(zip(qleft, qright)))