From 71a821940669d991309491bb986213522f45db66 Mon Sep 17 00:00:00 2001 From: Laurent Sorber Date: Fri, 15 Mar 2024 17:47:19 +0000 Subject: [PATCH] feat: add Conformal Coherent Quantile Regression --- README.md | 117 ++- poetry.lock | 861 ++++++++++++++---- pyproject.toml | 13 +- src/conformal_tights/__init__.py | 6 + .../_coherent_linear_quantile_regressor.py | 248 +++++ .../_conformal_coherent_quantile_regressor.py | 338 +++++++ src/conformal_tights/_typing.py | 11 + tests/conftest.py | 34 + ...test_coherent_linear_quantile_regressor.py | 12 + tests/test_conformal_quantile_regressor.py | 49 + 10 files changed, 1512 insertions(+), 177 deletions(-) create mode 100644 src/conformal_tights/_coherent_linear_quantile_regressor.py create mode 100644 src/conformal_tights/_conformal_coherent_quantile_regressor.py create mode 100644 src/conformal_tights/_typing.py create mode 100644 tests/conftest.py create mode 100644 tests/test_coherent_linear_quantile_regressor.py create mode 100644 tests/test_conformal_quantile_regressor.py diff --git a/README.md b/README.md index 8f67a82..a271fed 100644 --- a/README.md +++ b/README.md @@ -2,11 +2,124 @@ # 👖 Conformal Tights -A scikit-learn [meta-estimator](https://scikit-learn.org/stable/glossary.html#term-meta-estimator) for computing tight [conformal predictions](https://en.wikipedia.org/wiki/Conformal_prediction). +A [scikit-learn meta-estimator](https://scikit-learn.org/stable/glossary.html#term-meta-estimator) that adds [conformal prediction](https://en.wikipedia.org/wiki/Conformal_prediction) of coherent [quantiles](https://en.wikipedia.org/wiki/Quantile) and [intervals](https://en.wikipedia.org/wiki/Prediction_interval) to any [scikit-learn regressor](https://scikit-learn.org/stable/glossary.html#term-regressor). Features: + +1. 🍬 *Meta-estimator*: add prediction of quantiles and intervals to any scikit-learn regressor +2. 🌡️ *Conformally calibrated:* accurate quantiles and intervals with reliable [coverage](https://en.wikipedia.org/wiki/Coverage_probability) +3. 🚦 *Coherent quantiles:* quantiles increase monotonically instead of [crossing](https://github.com/dmlc/xgboost/issues/9848) [each other](https://github.com/microsoft/LightGBM/issues/3447) +4. 👖 *Tight quantiles:* selects the lowest [dispersion](https://en.wikipedia.org/wiki/Statistical_dispersion) that provides the desired coverage +5. 🎁 *Data efficient:* requires only a small number of calibration examples to fit +6. 🐼 *Pandas support:* optionally predict on DataFrames and receive DataFrame output ## Using -To add and install this package as a dependency of your project, run `poetry add conformal-tights`. +### Installing + +First, install this package with: + +```sh +pip install conformal-tights +``` + +### Predicting quantiles + +Conformal Tights exposes a meta-estimator called `ConformalCoherentQuantileRegressor` that you can use to wrap any scikit-learn regressor, after which you can use `predict_quantiles` predict conformally calibrated quantiles. Example usage: + +```python +from conformal_tights import ConformalCoherentQuantileRegressor +from sklearn.datasets import fetch_openml +from sklearn.model_selection import train_test_split +from xgboost import XGBRegressor + +# Fetch dataset and split in train and test +X, y = fetch_openml("ames_housing", version=1, return_X_y=True, as_frame=True, parser="auto") +X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.15, random_state=42) + +# Create a regressor, wrap it, and fit on the train set +my_regressor = XGBRegressor(objective="reg:absoluteerror") +conformal_predictor = ConformalCoherentQuantileRegressor(estimator=my_regressor) +conformal_predictor.fit(X_train, y_train) + +# Predict with the wrapped regressor +ŷ_test = conformal_predictor.predict(X_test) + +# Predict quantiles with the conformal wrapper +ŷ_test_quantiles = conformal_predictor.predict_quantiles(X_test, quantiles=(0.025, 0.05, 0.1, 0.9, 0.95, 0.975)) +``` + +When the input data is a pandas DataFrame, the output is also a pandas DataFrame. For example, printing the head of `ŷ_test_quantiles` yields: + +| house_id | 0.025 | 0.05 | 0.1 | 0.9 | 0.95 | 0.975 | +|-----------:|--------:|-------:|-------:|-------:|-------:|--------:| +| 1357 | 121557 | 130272 | 139913 | 189399 | 211177 | 237309 | +| 2367 | 86005 | 92617 | 98591 | 130236 | 145686 | 164766 | +| 2822 | 116523 | 121711 | 134993 | 175583 | 194964 | 216891 | +| 2126 | 105712 | 113784 | 122145 | 164330 | 183352 | 206224 | +| 1544 | 85920 | 92311 | 99130 | 133228 | 148895 | 167969 | + +Let's visualize the predicted quantiles on the test set: + + + +
+Expand to see the code that generated the graph above + +```python +import matplotlib.pyplot as plt +import matplotlib.ticker as ticker +%config InlineBackend.figure_format = "retina" +plt.rcParams["font.size"] = 8 +idx = (-ŷ_test.sample(50, random_state=42)).sort_values().index +y_ticks = list(range(1, len(idx) + 1)) +plt.figure(figsize=(4, 5)) +for j in range(3): + end = ŷ_test_quantiles.shape[1] - 1 - j + coverage = round(100 * (ŷ_test_quantiles.columns[end] - ŷ_test_quantiles.columns[j])) + plt.barh( + y_ticks, + ŷ_test_quantiles.loc[idx].iloc[:, end] - ŷ_test_quantiles.loc[idx].iloc[:, j], + left=ŷ_test_quantiles.loc[idx].iloc[:, j], + label=f"{coverage}% Prediction interval", + color=["#b3d9ff", "#86bfff", "#4da6ff"][j], + ) +plt.plot(y_test.loc[idx], y_ticks, "s", markersize=3, markerfacecolor="none", markeredgecolor="#e74c3c", label="Actual value") +plt.plot(ŷ_test.loc[idx], y_ticks, "s", color="blue", markersize=0.6, label="Predicted value") +plt.xlabel("House price") +plt.ylabel("Test house index") +plt.yticks(y_ticks, y_ticks) +plt.tick_params(axis="y", labelsize=6) +plt.grid(axis="x", color="lightsteelblue", linestyle=":", linewidth=0.5) +plt.gca().xaxis.set_major_formatter(ticker.StrMethodFormatter("${x:,.0f}")) +plt.gca().spines["top"].set_visible(False) +plt.gca().spines["right"].set_visible(False) +plt.legend() +plt.tight_layout() +plt.show() +``` +
+ +### Predicting intervals + +In addition to quantile prediction, you can use `predict_interval` to predict conformally calibrated prediction intervals. Compared to quantiles, these focus on reliable coverage over quantile accuracy. Example usage: + +```python +# Predict an interval for each example with the conformal wrapper +ŷ_test_interval = conformal_predictor.predict_interval(X_test, coverage=0.95) + +# Measure the coverage of the prediction intervals on the test set +coverage = ((ŷ_test_interval.iloc[:, 0] <= y_test) & (y_test <= ŷ_test_interval.iloc[:, 1])).mean() +print(coverage) # 96.6% +``` + +When the input data is a pandas DataFrame, the output is also a pandas DataFrame. 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https://python-poetry.org/docs/dependency-specification/ python = ">=3.10,<4.0" -lightgbm = ">=4.0.0" -scikit-learn = ">=1.1.0" +scikit-learn = ">=1.0.0" +xgboost = ">=2.0.0" [tool.poetry.group.test.dependencies] # https://python-poetry.org/docs/master/managing-dependencies/ commitizen = ">=3.2.1" coverage = { extras = ["toml"], version = ">=7.2.5" } +lightgbm = ">=4.3.0" mypy = ">=1.2.0" +pandas = ">=2.2.1" poethepoet = ">=0.20.0" pre-commit = ">=3.3.1" pytest = ">=7.3.1" @@ -34,12 +36,13 @@ pytest-xdist = ">=3.2.1" ruff = ">=0.2.1" safety = ">=2.3.4,!=2.3.5" shellcheck-py = ">=0.9.0" -typeguard = ">=3.0.2" [tool.poetry.group.dev.dependencies] # https://python-poetry.org/docs/master/managing-dependencies/ cruft = ">=2.14.0" ipykernel = ">=6.29.2" +matplotlib = ">=3.8.3" pdoc = ">=13.1.1" +tabulate = ">=0.9.0" [tool.coverage.report] # https://coverage.readthedocs.io/en/latest/config.html#report fail_under = 50 @@ -69,7 +72,7 @@ show_error_context = true warn_unreachable = true [tool.pytest.ini_options] # https://docs.pytest.org/en/latest/reference/reference.html#ini-options-ref -addopts = "--color=yes --doctest-modules --exitfirst --failed-first --strict-config --strict-markers --typeguard-packages=conformal_tights --verbosity=2 --junitxml=reports/pytest.xml" +addopts = "--color=yes --doctest-modules --exitfirst --failed-first --strict-config --strict-markers --verbosity=2 --junitxml=reports/pytest.xml" filterwarnings = ["error", "ignore::DeprecationWarning"] testpaths = ["src", "tests"] xfail_strict = true @@ -83,7 +86,7 @@ target-version = "py310" [tool.ruff.lint] ignore-init-module-imports = true select = ["A", "ASYNC", "B", "BLE", "C4", "C90", "D", "DTZ", "E", "EM", "ERA", "F", "FBT", "FLY", "FURB", "G", "I", "ICN", "INP", "INT", "ISC", "LOG", "N", "NPY", "PERF", "PGH", "PIE", "PL", "PT", "PTH", "PYI", "Q", "RET", "RSE", "RUF", "S", "SIM", "SLF", "SLOT", "T10", "T20", "TCH", "TID", "TRY", "UP", "W", "YTT"] -ignore = ["D203", "D213", "E501", "RET504", "S101", "S307"] +ignore = ["D203", "D213", "E501", "N803", "N806", "RET504", "RUF002", "RUF003", "S101", "S307"] unfixable = ["ERA001", "F401", "F841", "T201", "T203"] [tool.ruff.lint.flake8-tidy-imports] diff --git a/src/conformal_tights/__init__.py b/src/conformal_tights/__init__.py index 58b5f3c..fb137d4 100644 --- a/src/conformal_tights/__init__.py +++ b/src/conformal_tights/__init__.py @@ -1 +1,7 @@ """Conformal Tights package.""" + +from conformal_tights._conformal_coherent_quantile_regressor import ( + ConformalCoherentQuantileRegressor, +) + +__all__ = ["ConformalCoherentQuantileRegressor"] diff --git a/src/conformal_tights/_coherent_linear_quantile_regressor.py b/src/conformal_tights/_coherent_linear_quantile_regressor.py new file mode 100644 index 0000000..dc415a2 --- /dev/null +++ b/src/conformal_tights/_coherent_linear_quantile_regressor.py @@ -0,0 +1,248 @@ +"""Coherent Linear Quantile Regressor.""" + +from typing import TypeVar + +import numpy as np +import numpy.typing as npt +from scipy import sparse +from scipy.optimize import linprog +from scipy.sparse import csr_matrix +from sklearn.base import BaseEstimator, RegressorMixin +from sklearn.utils.validation import ( + check_array, + check_consistent_length, + check_is_fitted, + check_X_y, +) + +from conformal_tights._typing import FloatMatrix, FloatVector + +F = TypeVar("F", np.float32, np.float64) + + +def coherent_linear_quantile_regression( + X: FloatMatrix[F], + y: FloatVector[F], + *, + quantiles: FloatVector[F], + sample_weight: FloatVector[F] | None = None, + coherence_buffer: int = 3, +) -> FloatMatrix[F]: + """Solve a Coherent Linear Quantile Regression problem. + + Minimizes the quantile loss: + + ∑ᵢ,ⱼ { + qⱼ (yᵢ - ŷ⁽ʲ⁾ᵢ) : yᵢ ≥ ŷ⁽ʲ⁾ᵢ, + (1 - qⱼ)(ŷ⁽ʲ⁾ᵢ - yᵢ) : ŷ⁽ʲ⁾ᵢ > yᵢ + } + + with a linear model ŷ⁽ʲ⁾ := Xβ⁽ʲ⁾ for each quantile rank qⱼ of a given array of quantile ranks. + + We achieve so-called 'coherent' quantiles by enforcing monotonicity of the predicted quantiles + with the constraint Xβ⁽ʲ⁾ ≤ Xβ⁽ʲ⁺¹⁾ for each consecutive pair of quantile ranks in an extended + set of quantile ranks that comprises the requested quantile ranks and a number of auxiliary + quantile ranks in between. + + The optimization problem is formulated as a linear program by introducing the auxiliary residual + vectors Δ⁽ʲ⁾⁺, Δ⁽ʲ⁾⁻ ≥ 0 so that Xβ⁽ʲ⁾ - y = Δ⁽ʲ⁾⁺ - Δ⁽ʲ⁾⁻. The objective then becomes + ∑ᵢ,ⱼ qⱼΔ⁽ʲ⁾⁻ᵢ + (1 - qⱼ)Δ⁽ʲ⁾⁺ᵢ + αt⁽ʲ⁾ᵢ for t⁽ʲ⁾ := |β⁽ʲ⁾|. The L1 regularization parameter α is + automatically determined to minimize the impact on the solution β. + + Parameters + ---------- + X + The feature matrix. + y + The target values. + quantiles + The quantiles to estimate (between 0 and 1). + sample_weight + The optional sample weight to use for each sample. + coherence_buffer + The number of auxiliary quantiles to introduce. Smaller is faster, larger yields more + coherent quantiles. + + Returns + ------- + β + The estimated regression coefficients so that Xβ produces quantile predictions ŷ. + """ + # Learn the input dimensions. + num_samples, num_features = X.shape + # Add buffer quantile ranks in between the given quantile ranks so that we have an even stronger + # guarantee on the monotonicity of the predicted quantiles. + quantiles = np.interp( + x=np.linspace(0, len(quantiles) - 1, (len(quantiles) - 1) * (1 + coherence_buffer) + 1), + xp=np.arange(len(quantiles)), + fp=quantiles, + ).astype(quantiles.dtype) + num_quantiles = len(quantiles) + # Validate the input. + assert np.array_equal(quantiles, np.sort(quantiles)), "Quantile ranks must be sorted." + assert sample_weight is None or np.all(sample_weight >= 0), "Sample weights must be >= 0." + # Normalise the sample weights. + sample_weight = np.ones(num_samples, dtype=y.dtype) if sample_weight is None else sample_weight + sample_weight /= np.sum(sample_weight) + eps = np.finfo(y.dtype).eps + α = np.sqrt(eps) / (num_quantiles * num_features) + # Construct the objective function ∑ᵢ,ⱼ qⱼΔ⁽ʲ⁾⁻ᵢ + (1 - qⱼ)Δ⁽ʲ⁾⁺ᵢ + αt⁽ʲ⁾ᵢ for t⁽ʲ⁾ := |β⁽ʲ⁾|. + c = np.hstack( + [ + np.zeros(num_quantiles * num_features, dtype=y.dtype), # β⁽ʲ⁾ for each qⱼ + α * np.ones(num_quantiles * num_features, dtype=y.dtype), # t⁽ʲ⁾ for each qⱼ + np.kron((1 - quantiles) / num_quantiles, sample_weight), # Δ⁽ʲ⁾⁺ for each qⱼ + np.kron(quantiles / num_quantiles, sample_weight), # Δ⁽ʲ⁾⁻ for each qⱼ + ] + ) + # Construct the equalities Xβ⁽ʲ⁾ - y = Δ⁽ʲ⁾⁺ - Δ⁽ʲ⁾⁻ for each quantile rank qⱼ. + A_eq = sparse.hstack( + [ + # Xβ⁽ʲ⁾ for each qⱼ (block diagonal matrix) + sparse.kron(sparse.eye(num_quantiles, dtype=X.dtype), X), + # t⁽ʲ⁾ not used in this constraint + csr_matrix((num_quantiles * num_samples, num_quantiles * num_features), dtype=X.dtype), + # -Δ⁽ʲ⁾⁺ for each qⱼ (block diagonal matrix) + -sparse.eye(num_quantiles * num_samples, dtype=X.dtype), + # Δ⁽ʲ⁾⁻ for each qⱼ (block diagonal matrix) + sparse.eye(num_quantiles * num_samples, dtype=X.dtype), + ] + ) + b_eq = np.tile(y, num_quantiles) + # Construct the inequalities -t⁽ʲ⁾ <= β⁽ʲ⁾ <= t⁽ʲ⁾ for each quantile rank qⱼ so that + # t⁽ʲ⁾ := |β⁽ʲ⁾|. Also construct the monotonicity constraint Xβ⁽ʲ⁾ <= Xβ⁽ʲ⁺¹⁾ for each qⱼ, + # equivalent to Δ⁽ʲ⁾⁺ - Δ⁽ʲ⁾⁻ <= Δ⁽ʲ⁺¹⁾⁺ - Δ⁽ʲ⁺¹⁾⁻. + zeros_Δ = csr_matrix( + (num_quantiles * num_features, 2 * num_quantiles * num_samples), dtype=X.dtype + ) + zeros_βt = csr_matrix( + ((num_quantiles - 1) * num_samples, 2 * num_quantiles * num_features), dtype=X.dtype + ) + A_ub = sparse.vstack( + [ + sparse.hstack( + [ + sparse.eye(num_quantiles * num_features, dtype=X.dtype), # β⁽ʲ⁾ + -sparse.eye(num_quantiles * num_features, dtype=X.dtype), # -t⁽ʲ⁾ + zeros_Δ, # Δ⁽ʲ⁾⁺ and Δ⁽ʲ⁾⁺ not used for this constraint + ] + ), + sparse.hstack( + [ + -sparse.eye(num_quantiles * num_features, dtype=X.dtype), # -β⁽ʲ⁾ + -sparse.eye(num_quantiles * num_features, dtype=X.dtype), # -t⁽ʲ⁾ + zeros_Δ, # Δ⁽ʲ⁾⁺ and Δ⁽ʲ⁾⁺ not used for this constraint + ] + ), + sparse.hstack( + [ + zeros_βt, + sparse.kron( + sparse.diags( + diagonals=[1, -1], # Δ⁽ʲ⁾⁺ - Δ⁽ʲ⁺¹⁾⁺ + offsets=[0, 1], + shape=(num_quantiles - 1, num_quantiles), + dtype=X.dtype, + ), + sparse.eye(num_samples, dtype=X.dtype), + ), + sparse.kron( + sparse.diags( + diagonals=[-1, 1], # -Δ⁽ʲ⁾⁻ + Δ⁽ʲ⁺¹⁾⁻ + offsets=[0, 1], + shape=(num_quantiles - 1, num_quantiles), + dtype=X.dtype, + ), + sparse.eye(num_samples, dtype=X.dtype), + ), + ] + ), + ] + ) + b_ub = np.zeros(A_ub.shape[0], dtype=X.dtype) + # Construct the bounds. + bounds = ( + ([(None, None)] * num_quantiles * num_features) # β⁽ʲ⁾ for each qⱼ + + ([(0, None)] * num_quantiles * num_features) # t⁽ʲ⁾ for each qⱼ + + ([(0, None)] * num_quantiles * num_samples) # Δ⁽ʲ⁾⁺ for each qⱼ + + ([(0, None)] * num_quantiles * num_samples) # Δ⁽ʲ⁾⁻ for each qⱼ + ) + # Solve the Coherent Quantile Regression LP. + result = linprog(c=c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq, bounds=bounds, method="highs") + # Extract the solution. + β: FloatVector[F] = result.x[: num_quantiles * num_features].astype(y.dtype) + β = β.reshape(num_quantiles, num_features).T + β = β[:, 0 :: (coherence_buffer + 1)] # Drop the buffer quantile ranks we introduced earlier. + return β + + +class CoherentLinearQuantileRegressor(RegressorMixin, BaseEstimator): + """Coherent Linear Quantile Regressor. + + A linear model that regresses multiple quantiles coherently so that the predicted quantiles for + a given example increase monotonically. + """ + + def __init__( + self, + *, + quantiles: npt.ArrayLike = (0.025, 0.5, 0.975), + fit_intercept: bool = True, + coherence_buffer: int = 3, + ) -> None: + """Initialize the Coherent Quantile Regressor. + + Parameters + ---------- + quantiles + The target quantiles to fit and predict. + fit_intercept + Whether to fit an intercept term. + coherence_buffer + The number of auxiliary quantiles to introduce. Smaller is faster, larger yields more + coherent quantiles. + """ + self.quantiles = quantiles + self.fit_intercept = fit_intercept + self.coherence_buffer = coherence_buffer + + def fit( + self, X: FloatMatrix[F], y: FloatVector[F], *, sample_weight: FloatVector[F] | None = None + ) -> "CoherentLinearQuantileRegressor": + """Fit this predictor.""" + # Validate input. + X, y = check_X_y(X, y, y_numeric=True) + self.n_features_in_: int = X.shape[1] + self.y_dtype_: npt.DTypeLike = y.dtype # Used to cast predictions to the correct dtype. + if np.all(y.astype(int) == y): + self.y_dtype_ = np.intp # To satisfy sklearn's `check_regressors_int`. + y = y.astype(np.float64) # To support datetime64[ns] and timedelta64[ns]. + if sample_weight is not None: + check_consistent_length(y, sample_weight) + sample_weight = np.asarray(sample_weight).astype(np.float64) + # Add a constant column to X to allow for a bias in the regression. + if self.fit_intercept: + X = np.hstack([X, np.ones((X.shape[0], 1), dtype=X.dtype)]) + # Fit the coherent quantile regression model. + self.β_ = coherent_linear_quantile_regression( + X, + y, + quantiles=np.asarray(self.quantiles), + sample_weight=None if sample_weight is None else np.asarray(sample_weight), + coherence_buffer=self.coherence_buffer, + ) + return self + + def predict(self, X: FloatMatrix[F]) -> FloatMatrix[F]: + """Predict the output on a given dataset.""" + # Check input. + check_is_fitted(self) + X = check_array(X) + # Add a constant column to X to allow for a bias in the regression. + if self.fit_intercept: + X = np.hstack([X, np.ones((X.shape[0], 1), dtype=X.dtype)]) + # Predict the output. + ŷ: FloatMatrix[F] = X @ self.β_ + # Map back to the training target dtype. + ŷ = np.squeeze(ŷ.astype(self.y_dtype_), axis=1 if ŷ.shape[1] == 1 else ()) + return ŷ diff --git a/src/conformal_tights/_conformal_coherent_quantile_regressor.py b/src/conformal_tights/_conformal_coherent_quantile_regressor.py new file mode 100644 index 0000000..ce0bf58 --- /dev/null +++ b/src/conformal_tights/_conformal_coherent_quantile_regressor.py @@ -0,0 +1,338 @@ +"""Conformal Coherent Quantile Regressor meta-estimator.""" + +from typing import TYPE_CHECKING, Literal, TypeVar, overload + +import numpy as np +import numpy.typing as npt +from sklearn.base import BaseEstimator, MetaEstimatorMixin, RegressorMixin, clone +from sklearn.model_selection import train_test_split +from sklearn.utils.validation import ( + check_array, + check_consistent_length, + check_is_fitted, + check_X_y, +) +from xgboost import XGBRegressor + +from conformal_tights._coherent_linear_quantile_regressor import CoherentLinearQuantileRegressor +from conformal_tights._typing import FloatMatrix, FloatVector + +if TYPE_CHECKING: + import pandas as pd + +F = TypeVar("F", np.float32, np.float64) + + +class ConformalCoherentQuantileRegressor(MetaEstimatorMixin, RegressorMixin, BaseEstimator): + """Conformal Coherent Quantile Regressor meta-estimator. + + TODO: Explain approach + """ + + def __init__( # noqa: PLR0913 + self, + estimator: BaseEstimator | Literal["auto"] = "auto", + *, + nonconformity_estimator: XGBRegressor | Literal["auto"] = "auto", + nonconformity_quantiles: npt.ArrayLike | Literal["auto"] = "auto", + conformal_calibration_size: tuple[float, int] = (0.3, 1440), + random_state: int | np.random.RandomState | None = 42, + ) -> None: + """Initialize the Conformal Coherent Quantile Regressor. + + Parameters + ---------- + estimator + The regressor to wrap, used for point prediction. If "auto", uses an `XGBRegressor`. + nonconformity_estimator + A nonconformity estimator to use. If "auto", uses XGBoost's vector quantile regressor + for the given `nonconformity_quantiles`. + nonconformity_quantiles + The quantiles that the nonconformity estimator should predict when + `nonconformity_estimator` is "auto". If "auto", uses (1/8, 1/4, 1/2, 3/4, 7/8). + conformal_calibration_size + A tuple of the relative and absolute size of the conformal calibration set. The smallest + of the two is used. + random_state + The random state to use for reproducibility. + """ + self.estimator = estimator + self.nonconformity_estimator = nonconformity_estimator + self.nonconformity_quantiles = nonconformity_quantiles + self.conformal_calibration_size = conformal_calibration_size + self.random_state = random_state + + def fit( + self, + X: "FloatMatrix[F] | pd.DataFrame", + y: "FloatVector[F] | pd.Series", + *, + sample_weight: "FloatVector[F] | pd.Series | None" = None, + ) -> "ConformalCoherentQuantileRegressor": + """Fit this predictor.""" + # Validate input. + check_X_y(X, y, force_all_finite=False, ensure_min_samples=3, y_numeric=True) + # Learn dimensionality and dtypes. + if not hasattr(X, "dtypes"): + X = np.asarray(X) + y = np.ravel(np.asarray(y)) + self.n_features_in_: int = X.shape[1] + self.y_dtype_: npt.DTypeLike = y.dtype # Used to cast predictions to the correct dtype. + if np.all(y.astype(int) == y): + self.y_dtype_ = np.intp # To satisfy sklearn's `check_regressors_int`. + y = y.astype(np.float64) # To support datetime64[ns] and timedelta64[ns]. + if sample_weight is not None: + check_consistent_length(y, sample_weight) + sample_weight = np.ravel(np.asarray(sample_weight).astype(np.float64)) + # Use the smallest of the relative and absolute calibration sizes. + calib_size = min( + int(self.conformal_calibration_size[0] * X.shape[0]), self.conformal_calibration_size[1] + ) + # Split input into training and conformal calibration sets. + X_train, self.X_calib_, y_train, self.y_calib_, *sample_weights = train_test_split( + X, + y, + *([sample_weight] if sample_weight is not None else []), + test_size=calib_size, + random_state=self.random_state, + ) + sample_weight_train, sample_weight_calib = ( + sample_weights[:2] if sample_weight is not None else (None, None) + ) + # Split the conformal calibration set into two levels. + X_calib_l1, X_calib_l2, y_calib_l1, y_calib_l2, *sample_weights_calib = train_test_split( + self.X_calib_, + self.y_calib_, + *([sample_weight_calib] if sample_weight_calib is not None else []), + test_size=self.conformal_calibration_size[0], + random_state=self.random_state, + ) + self.sample_weight_calib_l1_, self.sample_weight_calib_l2_ = ( + sample_weights_calib[:2] if sample_weight is not None else (None, None) # type: ignore[has-type] + ) + # Fit the given estimator on the training data. + self.estimator_ = ( + clone(self.estimator) + if self.estimator != "auto" + else XGBRegressor(objective="reg:absoluteerror") + ) + if isinstance(self.estimator_, XGBRegressor): + self.estimator_.set_params(enable_categorical=True, random_state=self.random_state) + self.estimator_.fit(X_train, y_train, sample_weight=sample_weight_train) + # Fit a nonconformity estimator on the training data with XGBRegressor's vector quantile + # regression. We fit a minimal number of quantiles to reduce the computational cost, but + # also to reduce the risk of overfitting in the coherent quantile regressor that is applied + # on top of the nonconformity estimates. + self.nonconformity_quantiles_ = ( + (1 / 8, 1 / 4, 1 / 2, 3 / 4, 7 / 8) + if self.nonconformity_quantiles == "auto" + else self.nonconformity_quantiles + ) + self.nonconformity_estimator_ = ( + clone(self.nonconformity_estimator) + if self.nonconformity_estimator != "auto" + else XGBRegressor() + ) + if isinstance(self.nonconformity_estimator_, XGBRegressor): + self.nonconformity_estimator_.set_params( + objective="reg:quantileerror", + quantile_alpha=self.nonconformity_quantiles_, + enable_categorical=True, + random_state=self.random_state, + ) + self.nonconformity_estimator_.fit(X_train, y_train, sample_weight=sample_weight_train) + # Predict on the level 1 calibration set. + self.ŷ_calib_l1_ = self.estimator_.predict(X_calib_l1) + self.ŷ_calib_l1_nonconformity_ = self.nonconformity_estimator_.predict(X_calib_l1) + self.residuals_calib_l1_ = self.ŷ_calib_l1_ - y_calib_l1 + # Predict on the level 2 calibration set. + self.ŷ_calib_l2_ = self.estimator_.predict(X_calib_l2) + self.ŷ_calib_l2_nonconformity_ = self.nonconformity_estimator_.predict(X_calib_l2) + self.residuals_calib_l2_ = self.ŷ_calib_l2_ - y_calib_l2 + # Lazily fit level 1 conformal predictors as coherent linear quantile regression models that + # predict quantiles of the (relative) residuals given the nonconformity estimates, and + # level 2 conformal biases. + self.conformal_l1_: dict[str, dict[tuple[float, ...], CoherentLinearQuantileRegressor]] = { + "Δŷ": {}, + "Δŷ/ŷ": {}, + } + self.conformal_l2_: dict[str, dict[tuple[float, ...], FloatVector[F]]] = { + "Δŷ": {}, + "Δŷ/ŷ": {}, + } + return self + + def _lazily_fit_conformal_predictor( + self, target_type: str, quantiles: npt.ArrayLike + ) -> tuple[CoherentLinearQuantileRegressor, FloatVector[F]]: + """Lazily fit a conformal predictor for a given array of quantiles.""" + quantiles = np.asarray(quantiles) + quantiles_tuple = tuple(quantiles) + if quantiles_tuple in self.conformal_l1_[target_type]: + # Retrieve level 1 and level 2. + cqr_l1 = self.conformal_l1_[target_type][quantiles_tuple] + bias_l2 = self.conformal_l2_[target_type][quantiles_tuple] + else: + # Fit level 1: a coherent quantile regressor that predicts quantiles of the (relative) + # residuals. + eps = np.finfo(self.ŷ_calib_l1_.dtype).eps + abs_ŷ_calib_l1 = np.maximum(np.abs(self.ŷ_calib_l1_), eps) + X_cqr = self.ŷ_calib_l1_nonconformity_ + y_cqr = self.residuals_calib_l1_ / (abs_ŷ_calib_l1 if "/ŷ" in target_type else 1) + cqr_l1 = CoherentLinearQuantileRegressor(quantiles=quantiles) + cqr_l1.fit(X_cqr, y_cqr, sample_weight=self.sample_weight_calib_l1_) + self.conformal_l1_[target_type][quantiles_tuple] = cqr_l1 + # Fit level 2: a per-quantile conformal bias on top of the level 1 conformal quantile + # predictions of the (relative) residuals. + abs_ŷ_calib_l2 = np.maximum(np.abs(self.ŷ_calib_l2_), eps) + Δŷ_calib_l2_quantiles = cqr_l1.predict(self.ŷ_calib_l2_nonconformity_) + bias_l2 = np.empty(quantiles.shape, dtype=self.ŷ_calib_l1_.dtype) + for j, quantile in enumerate(quantiles): + bias_l2[j] = np.quantile( + -( + (self.residuals_calib_l2_ / (abs_ŷ_calib_l2 if "/ŷ" in target_type else 1)) + + Δŷ_calib_l2_quantiles[:, j] + ), + quantile, + ) + self.conformal_l2_[target_type][quantiles_tuple] = bias_l2 + return cqr_l1, bias_l2 # type: ignore[return-value] + + @overload + def predict_quantiles( + self, + X: FloatMatrix[F], + *, + quantiles: npt.ArrayLike, + priority: Literal["accuracy", "coverage"] = "accuracy", + ) -> FloatMatrix[F]: ... + + @overload + def predict_quantiles( + self, + X: "pd.DataFrame", + *, + quantiles: npt.ArrayLike, + priority: Literal["accuracy", "coverage"] = "accuracy", + ) -> "pd.DataFrame": ... + + def predict_quantiles( + self, + X: "FloatMatrix[F] | pd.DataFrame", + *, + quantiles: npt.ArrayLike, + priority: Literal["accuracy", "coverage"] = "accuracy", + ) -> "FloatMatrix[F] | pd.DataFrame": + """Predict conformally calibrated quantiles on a given dataset.""" + # Predict the absolute and relative quantiles. + quantiles = np.asarray(quantiles) + ŷ = np.asarray(self.estimator_.predict(X)) + X_cqr = self.nonconformity_estimator_.predict(X) + cqr_abs, bias_abs = self._lazily_fit_conformal_predictor("Δŷ", quantiles) + cqr_rel, bias_rel = self._lazily_fit_conformal_predictor("Δŷ/ŷ", quantiles) + if priority == "coverage": # Only allow quantile expansion when the priority is coverage. + center = np.median(quantiles) + bias_abs[center <= quantiles] = np.maximum(bias_abs[center <= quantiles], 0) + bias_abs[quantiles <= center] = np.minimum(bias_abs[quantiles <= center], 0) + bias_rel[center <= quantiles] = np.maximum(bias_rel[center <= quantiles], 0) + bias_rel[quantiles <= center] = np.minimum(bias_rel[quantiles <= center], 0) + Δŷ_quantiles = np.dstack( + [ + cqr_abs.predict(X_cqr) + bias_abs[np.newaxis, :], + np.abs(ŷ[:, np.newaxis]) * (cqr_rel.predict(X_cqr) + bias_rel[np.newaxis, :]), + ] + ) + # Choose between the the absolute and relative quantiles for each example in order to + # minimise the dispersion of the predicted quantiles. + dispersion = np.std(Δŷ_quantiles, axis=1) + Δŷ_quantiles = Δŷ_quantiles[ + np.arange(Δŷ_quantiles.shape[0]), :, np.argmin(dispersion, axis=-1) + ] + ŷ_quantiles: FloatMatrix[F] = (ŷ[:, np.newaxis] + Δŷ_quantiles).astype(self.y_dtype_) + # Convert ŷ_quantiles to a pandas DataFrame if X is a pandas DataFrame. + if hasattr(X, "dtypes") and hasattr(X, "index"): + try: + import pandas as pd + + ŷ_quantiles = pd.DataFrame(ŷ_quantiles, index=X.index, columns=quantiles) + except ImportError: + pass + return ŷ_quantiles + + @overload + def predict_interval(self, X: FloatMatrix[F], *, coverage: float = 0.95) -> FloatMatrix[F]: ... + + @overload + def predict_interval(self, X: "pd.DataFrame", *, coverage: float = 0.95) -> "pd.DataFrame": ... + + def predict_interval( + self, X: "FloatMatrix[F] | pd.DataFrame", *, coverage: float = 0.95 + ) -> "FloatMatrix[F] | pd.DataFrame": + """Predict conformally calibrated intervals on a given dataset.""" + # Convert the coverage probability to lower and upper quantiles. + lb = (1 - coverage) / 2 + ub = 1 - lb + # Compute the prediction interval with predict_quantiles. + ŷ_quantiles = self.predict_quantiles(X, quantiles=(lb, ub), priority="coverage") + return ŷ_quantiles + + @overload + def predict( + self, X: FloatMatrix[F], *, coverage: None = None, quantiles: None = None + ) -> FloatVector[F]: ... + + @overload + def predict( + self, X: FloatMatrix[F], *, coverage: float, quantiles: None = None + ) -> FloatMatrix[F]: ... + + @overload + def predict( + self, X: FloatMatrix[F], *, coverage: None = None, quantiles: npt.ArrayLike + ) -> FloatMatrix[F]: ... + + @overload + def predict( + self, X: "pd.DataFrame", *, coverage: None = None, quantiles: None = None + ) -> "pd.Series": ... + + @overload + def predict( + self, X: "pd.DataFrame", *, coverage: float, quantiles: None = None + ) -> "pd.DataFrame": ... + + @overload + def predict( + self, X: "pd.DataFrame", *, coverage: None = None, quantiles: npt.ArrayLike + ) -> "pd.DataFrame": ... + + def predict( + self, + X: "FloatMatrix[F] | pd.DataFrame", + *, + coverage: float | None = None, + quantiles: npt.ArrayLike | None = None, + ) -> "FloatVector[F] | pd.Series | FloatMatrix[F] | pd.DataFrame": + """Predict on a given dataset.""" + assert coverage is None or quantiles is None + check_is_fitted(self) + check_array(X, force_all_finite=False) + if coverage is not None: + ŷ_interval = self.predict_interval(X, coverage=coverage) + return ŷ_interval + if quantiles is not None: + ŷ_quantiles = self.predict_quantiles(X, quantiles=quantiles) + return ŷ_quantiles + ŷ = self.estimator_.predict(X).astype(self.y_dtype_) + if hasattr(X, "dtypes") and hasattr(X, "index"): + try: + import pandas as pd + + ŷ = pd.Series(ŷ, index=X.index) + except ImportError: + pass + return ŷ + + def _more_tags(self) -> dict[str, bool]: + """Return more tags for the estimator.""" + return {"allow_nan": True} diff --git a/src/conformal_tights/_typing.py b/src/conformal_tights/_typing.py new file mode 100644 index 0000000..efe6f4b --- /dev/null +++ b/src/conformal_tights/_typing.py @@ -0,0 +1,11 @@ +"""Conformal Tights types.""" + +from typing import TypeAlias, TypeVar + +import numpy as np +import numpy.typing as npt + +F = TypeVar("F", np.float32, np.float64) + +FloatVector: TypeAlias = npt.NDArray[F] +FloatMatrix: TypeAlias = npt.NDArray[F] diff --git a/tests/conftest.py b/tests/conftest.py new file mode 100644 index 0000000..5954bcd --- /dev/null +++ b/tests/conftest.py @@ -0,0 +1,34 @@ +"""Test fixtures.""" + +from typing import TypeAlias + +import pandas as pd +import pytest +import sklearn.datasets +from _pytest.fixtures import SubRequest +from sklearn.model_selection import train_test_split + +Dataset: TypeAlias = tuple[pd.DataFrame, pd.DataFrame, pd.Series, pd.Series] + + +@pytest.fixture( + params=[ + pytest.param( + 43926, + id="dataset:ames_housing", # Regression + ), + pytest.param( + 287, + id="dataset:wine_quality", # Regression + ), + ], +) +def dataset(request: SubRequest) -> Dataset: + """Train and test dataset fixture.""" + # Download the dataset. + X, y = sklearn.datasets.fetch_openml( + data_id=request.param, return_X_y=True, as_frame=True, parser="auto" + ) + # Split in train and test set. + X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.15, random_state=42) + return X_train, X_test, y_train, y_test diff --git a/tests/test_coherent_linear_quantile_regressor.py b/tests/test_coherent_linear_quantile_regressor.py new file mode 100644 index 0000000..ee5cb9b --- /dev/null +++ b/tests/test_coherent_linear_quantile_regressor.py @@ -0,0 +1,12 @@ +"""Test the Coherent Linear Quantile Regressor.""" + +import numpy as np +from sklearn.utils.estimator_checks import check_estimator + +from conformal_tights._coherent_linear_quantile_regressor import CoherentLinearQuantileRegressor + + +def test_sklearn_check_estimator() -> None: + """Check that the meta-estimator conforms to sklearn's standards.""" + model = CoherentLinearQuantileRegressor(quantiles=np.array([0.5])) + check_estimator(model) diff --git a/tests/test_conformal_quantile_regressor.py b/tests/test_conformal_quantile_regressor.py new file mode 100644 index 0000000..753dd1e --- /dev/null +++ b/tests/test_conformal_quantile_regressor.py @@ -0,0 +1,49 @@ +"""Test the Conformal Coherent Quantile Regressor.""" + +import numpy as np +import pytest +from _pytest.fixtures import SubRequest +from lightgbm import LGBMRegressor +from sklearn.base import BaseEstimator +from sklearn.utils.estimator_checks import check_estimator +from xgboost import XGBRegressor + +from conformal_tights import ConformalCoherentQuantileRegressor +from tests.conftest import Dataset + + +@pytest.fixture( + params=[ + pytest.param(XGBRegressor(objective="reg:absoluteerror"), id="model:XGBRegressor"), + pytest.param(LGBMRegressor(objective="regression_l1"), id="model:LGBMRegressor"), + ] +) +def regressor(request: SubRequest) -> BaseEstimator: + """Return a regressor.""" + return request.param + + +def test_conformal_quantile_regressor_coverage(dataset: Dataset, regressor: BaseEstimator) -> None: + """Test ConformalCoherentQuantileRegressor's coverage.""" + # Unpack the dataset. + X_train, X_test, y_train, y_test = dataset + # Train the models. + model = ConformalCoherentQuantileRegressor(estimator=regressor) + model.fit(X_train, y_train) + # Verify the coherence of the predicted quantiles. + ŷ_quantiles = model.predict(X_test, quantiles=np.linspace(0.1, 0.9, 3)) + for i in range(ŷ_quantiles.shape[1] - 1): + assert np.all(ŷ_quantiles.iloc[:, i] <= ŷ_quantiles.iloc[:, i + 1]) + # Verify the coverage of the predicted intervals. + for desired_coverage in (0.7, 0.8, 0.9): + ŷ_interval = model.predict(X_test, coverage=desired_coverage) + assert np.all(ŷ_interval.iloc[:, 0] <= ŷ_interval.iloc[:, 1]) + covered = (ŷ_interval.iloc[:, 0] <= y_test) & (y_test <= ŷ_interval.iloc[:, 1]) + actual_coverage = np.mean(covered) + assert actual_coverage >= 0.97 * desired_coverage + + +def test_sklearn_check_estimator() -> None: + """Check that the meta-estimator conforms to sklearn's standards.""" + model = ConformalCoherentQuantileRegressor(estimator=XGBRegressor()) + check_estimator(model)