enh: initial implementation of a cross-validated hyperparameter selec…

…tion

src/eddymotion/model/gpr.py

@@ -28,27 +28,33 @@
 from typing import Callable, Mapping, Sequence
 
 import numpy as np
+from ConfigSpace import Configuration
 from scipy import optimize
 from scipy.optimize._minimize import Bounds
+from sklearn.base import clone
 from sklearn.gaussian_process import GaussianProcessRegressor
 from sklearn.gaussian_process.kernels import (
     Hyperparameter,
     Kernel,
 )
 from sklearn.metrics.pairwise import cosine_similarity
+from sklearn.model_selection import RepeatedKFold, cross_val_score
 from sklearn.utils._param_validation import Interval, StrOptions
 
 BOUNDS_A: tuple[float, float] = (0.1, 2.35)
 """The limits for the parameter *a* (angular distance in rad)."""
 BOUNDS_LAMBDA: tuple[float, float] = (1e-3, 1000)
 """The limits for the parameter λ (signal scaling factor)."""
+BOUNDS_ALPHA: tuple[float, float] = (1e-3, 500)
+"""The limits for the parameter σ² (noise adjustment, alpha in Scikit-learn's GP regressor)."""
 THETA_EPSILON: float = 1e-5
 """Minimum nonzero angle."""
 LBFGS_CONFIGURABLE_OPTIONS = {"disp", "maxiter", "ftol", "gtol"}
 """The set of extended options that can be set on the default BFGS."""
 CONFIGURABLE_OPTIONS: Mapping[str, set] = {
     "Nelder-Mead": {"disp", "maxiter", "adaptive", "fatol"},
     "CG": {"disp", "maxiter", "gtol"},
+    "cross-validation": {"scoring", "n_folds", "n_evaluations"},
 }
 """
 A mapping from optimizer names to the option set they allow.
@@ -161,6 +167,9 @@ class EddyMotionGPR(GaussianProcessRegressor):
         "normalize_y": ["boolean"],
         "n_targets": [Interval(Integral, 1, None, closed="left"), None],
         "random_state": ["random_state"],
+        "n_folds": [Interval(Integral, 3, None, closed="left")],
+        "n_evaluations": [Interval(Integral, 3, None, closed="left")],
+        "n_trials": [Interval(Integral, 3, None, closed="left")],
     }
 
     def __init__(
@@ -182,6 +191,10 @@ def __init__(
         gtol: float | None = None,
         adaptive: bool | int | None = None,
         fatol: float | None = None,
+        scoring: str = "neg_root_mean_squared_error",
+        n_folds: int | None = 10,
+        n_evaluations: int | None = 40,
+        n_trials: int | None = 200,
     ):
         super().__init__(
             kernel,
@@ -202,6 +215,10 @@ def __init__(
         self.gtol = gtol
         self.adaptive = adaptive
         self.fatol = fatol
+        self.scoring = scoring
+        self.n_folds = n_folds
+        self.n_evaluations = n_evaluations
+        self.n_trials = n_trials
 
     def _constrained_optimization(
         self,
@@ -210,6 +227,40 @@ def _constrained_optimization(
         bounds: Sequence[tuple[float, float]] | Bounds,
     ) -> tuple[float, float]:
         options = {}
+
+        if self.optimizer == "cross-validation":
+            from ConfigSpace import ConfigurationSpace, Float
+            from smac import HyperparameterOptimizationFacade, Scenario
+
+            cs = ConfigurationSpace()
+            beta_a = Float(
+                "kernel__beta_a",
+                tuple(self.kernel.a_bounds),
+                default=self.kernel_.beta_a,
+                log=True,
+            )
+            beta_l = Float(
+                "kernel__beta_l",
+                tuple(self.kernel.l_bounds),
+                default=self.kernel_.beta_l,
+                log=True,
+            )
+            cs.add([beta_a, beta_l])
+
+            # Scenario object specifying the optimization environment
+            scenario = Scenario(cs, n_trials=self.n_trials)
+
+            # Use SMAC to find the best configuration/hyperparameters
+            smac = HyperparameterOptimizationFacade(
+                scenario,
+                self.cross_validation,
+            )
+            incumbent = smac.optimize()
+            return (
+                np.log([incumbent["kernel__beta_a"], incumbent["kernel__beta_l"]]),
+                0,
+            )
+
         if self.optimizer == "fmin_l_bfgs_b":
             from sklearn.utils.optimize import _check_optimize_result
 
@@ -252,6 +303,27 @@ def _constrained_optimization(
 
         raise ValueError(f"Unknown optimizer {self.optimizer}.")
 
+    def cross_validation(
+        self,
+        config: Configuration,
+        seed: int | None = None,
+    ) -> float:
+        rkf = RepeatedKFold(
+            n_splits=self.n_folds,
+            n_repeats=max(self.n_evaluations // self.n_folds, 1),
+        )
+        gpr = clone(self)
+        gpr.set_params(**dict(config))
+        gpr.optimizer = None
+        scores = cross_val_score(
+            gpr,
+            self.X_train_,
+            self.y_train_,
+            scoring=self.scoring,
+            cv=rkf,
+        )
+        return np.mean(scores)
+
 
 class ExponentialKriging(Kernel):
     """A scikit-learn's kernel for DWI signals."""