add cross_validation

pyproject.toml

@@ -50,9 +50,12 @@ profile = "black"
 multi_line_output = 3
 
 [tool.ruff]
-select = ["E", "F", "W", "D"]
-ignore = ["D212", "D203"]
-unfixable = ["ERA"]
+extend-select = ["E", "F", "W", "D"]
+lint.ignore = ["D212", "D203"]
+lint.unfixable = ["ERA"]
+
+[tool.ruff.lint.per-file-ignores]
+"test_*.py" = ["D"]
 
 [tool.mypy]
 strict = true

src/resample/jackknife.py

@@ -18,7 +18,7 @@
 from typing import Any, Callable, Collection, Generator, List
 
 import numpy as np
-from numpy.typing import ArrayLike
+from numpy.typing import ArrayLike, floating
 
 
 def resample(
@@ -319,3 +319,40 @@ def variance(
     thetas = jackknife(fn, sample, *args)
     n = len(sample)
     return (n - 1) * np.var(thetas, ddof=0, axis=0)
+
+
+def cross_validation(
+    predict: Callable[..., float], x: "ArrayLike", y: "ArrayLike", *args: "ArrayLike"
+) -> floating[Any]:
+    """
+    Calculate mean-squared error of model with leave-one-out-cross-validation.
+
+    Wikipedia:
+    https://en.wikipedia.org/wiki/Cross-validation_(statistics)
+
+    Parameters
+    ----------
+    predict : callable
+        Function with the signature (x_in, y_in, x_out, *args). It takes x_in, y_in,
+        which are arrays with the same length. x_out should be one element of the x
+        array. *args are further optional arguments for the function. The function
+        should return the prediction y(x_out).
+    x : array-like
+        Explanatory variable. Must be an array of shape (N, ...), where N is the number
+        of samples.
+    y : array-like
+        Observations. Must be an array of shape (N, ...).
+    *args:
+        Optional arguments which are passed unmodified to predict.
+
+    Returns
+    -------
+    float
+        Variance of the difference (y[i] - predict(..., x[i], *args)).
+
+    """
+    deltas = []
+    for i, (x_in, y_in) in enumerate(resample(x, y, copy=False)):
+        yip = predict(x_in, y_in, x[i], *args)
+        deltas.append((y[i] - yip))
+    return np.var(deltas)

tests/test_jackknife.py

@@ -1,8 +1,15 @@
 import numpy as np
 import pytest
 from numpy.testing import assert_almost_equal, assert_equal
-
-from resample.jackknife import bias, bias_corrected, jackknife, resample, variance
+from scipy.optimize import curve_fit
+from resample.jackknife import (
+    bias,
+    bias_corrected,
+    jackknife,
+    resample,
+    variance,
+    cross_validation,
+)
 
 
 def test_resample_1d():
@@ -120,3 +127,22 @@ def test_resample_deprecation():
     with pytest.warns(VisibleDeprecationWarning):
         with pytest.raises(ValueError):  # too many arguments
             resample(data, True, 1)
+
+
+@pytest.mark.filterwarnings("ignore:Covariance")
+def test_cross_validation():
+    x = [1, 2, 3]
+    y = [3, 4, 5]
+
+    def predict(xi, yi, xo, npar):
+        def model(x, *par):
+            return np.polyval(par, x)
+
+        popt = curve_fit(model, xi, yi, p0=np.zeros(npar))[0]
+        return model(xo, *popt)
+
+    v = cross_validation(predict, x, y, 2)
+    assert v == pytest.approx(0)
+
+    v2 = cross_validation(predict, x, y, 1)
+    assert v2 == pytest.approx(1.5)