""" Testing for Theil-Sen module (sklearn.linear_model.theil_sen) """ # Author: Florian Wilhelm # License: BSD 3 clause import os import re import sys from contextlib import contextmanager import numpy as np import pytest from numpy.testing import assert_array_equal, assert_array_less from numpy.testing import assert_array_almost_equal from scipy.linalg import norm from scipy.optimize import fmin_bfgs from sklearn.exceptions import ConvergenceWarning from sklearn.linear_model import LinearRegression, TheilSenRegressor from sklearn.linear_model._theil_sen import _spatial_median, _breakdown_point from sklearn.linear_model._theil_sen import _modified_weiszfeld_step from sklearn.utils._testing import assert_almost_equal @contextmanager def no_stdout_stderr(): old_stdout = sys.stdout old_stderr = sys.stderr with open(os.devnull, "w") as devnull: sys.stdout = devnull sys.stderr = devnull yield devnull.flush() sys.stdout = old_stdout sys.stderr = old_stderr def gen_toy_problem_1d(intercept=True): random_state = np.random.RandomState(0) # Linear model y = 3*x + N(2, 0.1**2) w = 3.0 if intercept: c = 2.0 n_samples = 50 else: c = 0.1 n_samples = 100 x = random_state.normal(size=n_samples) noise = 0.1 * random_state.normal(size=n_samples) y = w * x + c + noise # Add some outliers if intercept: x[42], y[42] = (-2, 4) x[43], y[43] = (-2.5, 8) x[33], y[33] = (2.5, 1) x[49], y[49] = (2.1, 2) else: x[42], y[42] = (-2, 4) x[43], y[43] = (-2.5, 8) x[53], y[53] = (2.5, 1) x[60], y[60] = (2.1, 2) x[72], y[72] = (1.8, -7) return x[:, np.newaxis], y, w, c def gen_toy_problem_2d(): random_state = np.random.RandomState(0) n_samples = 100 # Linear model y = 5*x_1 + 10*x_2 + N(1, 0.1**2) X = random_state.normal(size=(n_samples, 2)) w = np.array([5.0, 10.0]) c = 1.0 noise = 0.1 * random_state.normal(size=n_samples) y = np.dot(X, w) + c + noise # Add some outliers n_outliers = n_samples // 10 ix = random_state.randint(0, n_samples, size=n_outliers) y[ix] = 50 * random_state.normal(size=n_outliers) return X, y, w, c def gen_toy_problem_4d(): random_state = np.random.RandomState(0) n_samples = 10000 # Linear model y = 5*x_1 + 10*x_2 + 42*x_3 + 7*x_4 + N(1, 0.1**2) X = random_state.normal(size=(n_samples, 4)) w = np.array([5.0, 10.0, 42.0, 7.0]) c = 1.0 noise = 0.1 * random_state.normal(size=n_samples) y = np.dot(X, w) + c + noise # Add some outliers n_outliers = n_samples // 10 ix = random_state.randint(0, n_samples, size=n_outliers) y[ix] = 50 * random_state.normal(size=n_outliers) return X, y, w, c def test_modweiszfeld_step_1d(): X = np.array([1.0, 2.0, 3.0]).reshape(3, 1) # Check startvalue is element of X and solution median = 2.0 new_y = _modified_weiszfeld_step(X, median) assert_array_almost_equal(new_y, median) # Check startvalue is not the solution y = 2.5 new_y = _modified_weiszfeld_step(X, y) assert_array_less(median, new_y) assert_array_less(new_y, y) # Check startvalue is not the solution but element of X y = 3.0 new_y = _modified_weiszfeld_step(X, y) assert_array_less(median, new_y) assert_array_less(new_y, y) # Check that a single vector is identity X = np.array([1.0, 2.0, 3.0]).reshape(1, 3) y = X[0] new_y = _modified_weiszfeld_step(X, y) assert_array_equal(y, new_y) def test_modweiszfeld_step_2d(): X = np.array([0.0, 0.0, 1.0, 1.0, 0.0, 1.0]).reshape(3, 2) y = np.array([0.5, 0.5]) # Check first two iterations new_y = _modified_weiszfeld_step(X, y) assert_array_almost_equal(new_y, np.array([1 / 3, 2 / 3])) new_y = _modified_weiszfeld_step(X, new_y) assert_array_almost_equal(new_y, np.array([0.2792408, 0.7207592])) # Check fix point y = np.array([0.21132505, 0.78867497]) new_y = _modified_weiszfeld_step(X, y) assert_array_almost_equal(new_y, y) def test_spatial_median_1d(): X = np.array([1.0, 2.0, 3.0]).reshape(3, 1) true_median = 2.0 _, median = _spatial_median(X) assert_array_almost_equal(median, true_median) # Test larger problem and for exact solution in 1d case random_state = np.random.RandomState(0) X = random_state.randint(100, size=(1000, 1)) true_median = np.median(X.ravel()) _, median = _spatial_median(X) assert_array_equal(median, true_median) def test_spatial_median_2d(): X = np.array([0.0, 0.0, 1.0, 1.0, 0.0, 1.0]).reshape(3, 2) _, median = _spatial_median(X, max_iter=100, tol=1.0e-6) def cost_func(y): dists = np.array([norm(x - y) for x in X]) return np.sum(dists) # Check if median is solution of the Fermat-Weber location problem fermat_weber = fmin_bfgs(cost_func, median, disp=False) assert_array_almost_equal(median, fermat_weber) # Check when maximum iteration is exceeded a warning is emitted warning_message = "Maximum number of iterations 30 reached in spatial median." with pytest.warns(ConvergenceWarning, match=warning_message): _spatial_median(X, max_iter=30, tol=0.0) def test_theil_sen_1d(): X, y, w, c = gen_toy_problem_1d() # Check that Least Squares fails lstq = LinearRegression().fit(X, y) assert np.abs(lstq.coef_ - w) > 0.9 # Check that Theil-Sen works theil_sen = TheilSenRegressor(random_state=0).fit(X, y) assert_array_almost_equal(theil_sen.coef_, w, 1) assert_array_almost_equal(theil_sen.intercept_, c, 1) def test_theil_sen_1d_no_intercept(): X, y, w, c = gen_toy_problem_1d(intercept=False) # Check that Least Squares fails lstq = LinearRegression(fit_intercept=False).fit(X, y) assert np.abs(lstq.coef_ - w - c) > 0.5 # Check that Theil-Sen works theil_sen = TheilSenRegressor(fit_intercept=False, random_state=0).fit(X, y) assert_array_almost_equal(theil_sen.coef_, w + c, 1) assert_almost_equal(theil_sen.intercept_, 0.0) # non-regression test for #18104 theil_sen.score(X, y) def test_theil_sen_2d(): X, y, w, c = gen_toy_problem_2d() # Check that Least Squares fails lstq = LinearRegression().fit(X, y) assert norm(lstq.coef_ - w) > 1.0 # Check that Theil-Sen works theil_sen = TheilSenRegressor(max_subpopulation=1e3, random_state=0).fit(X, y) assert_array_almost_equal(theil_sen.coef_, w, 1) assert_array_almost_equal(theil_sen.intercept_, c, 1) def test_calc_breakdown_point(): bp = _breakdown_point(1e10, 2) assert np.abs(bp - 1 + 1 / (np.sqrt(2))) < 1.0e-6 @pytest.mark.parametrize( "param, ExceptionCls, match", [ ( {"n_subsamples": 1}, ValueError, re.escape("Invalid parameter since n_features+1 > n_subsamples (2 > 1)"), ), ( {"n_subsamples": 101}, ValueError, re.escape("Invalid parameter since n_subsamples > n_samples (101 > 50)"), ), ], ) def test_checksubparams_invalid_input(param, ExceptionCls, match): X, y, w, c = gen_toy_problem_1d() theil_sen = TheilSenRegressor(**param, random_state=0) with pytest.raises(ExceptionCls, match=match): theil_sen.fit(X, y) def test_checksubparams_n_subsamples_if_less_samples_than_features(): random_state = np.random.RandomState(0) n_samples, n_features = 10, 20 X = random_state.normal(size=(n_samples, n_features)) y = random_state.normal(size=n_samples) theil_sen = TheilSenRegressor(n_subsamples=9, random_state=0) with pytest.raises(ValueError): theil_sen.fit(X, y) def test_subpopulation(): X, y, w, c = gen_toy_problem_4d() theil_sen = TheilSenRegressor(max_subpopulation=250, random_state=0).fit(X, y) assert_array_almost_equal(theil_sen.coef_, w, 1) assert_array_almost_equal(theil_sen.intercept_, c, 1) def test_subsamples(): X, y, w, c = gen_toy_problem_4d() theil_sen = TheilSenRegressor(n_subsamples=X.shape[0], random_state=0).fit(X, y) lstq = LinearRegression().fit(X, y) # Check for exact the same results as Least Squares assert_array_almost_equal(theil_sen.coef_, lstq.coef_, 9) def test_verbosity(): X, y, w, c = gen_toy_problem_1d() # Check that Theil-Sen can be verbose with no_stdout_stderr(): TheilSenRegressor(verbose=True, random_state=0).fit(X, y) TheilSenRegressor(verbose=True, max_subpopulation=10, random_state=0).fit(X, y) def test_theil_sen_parallel(): X, y, w, c = gen_toy_problem_2d() # Check that Least Squares fails lstq = LinearRegression().fit(X, y) assert norm(lstq.coef_ - w) > 1.0 # Check that Theil-Sen works theil_sen = TheilSenRegressor(n_jobs=2, random_state=0, max_subpopulation=2e3).fit( X, y ) assert_array_almost_equal(theil_sen.coef_, w, 1) assert_array_almost_equal(theil_sen.intercept_, c, 1) def test_less_samples_than_features(): random_state = np.random.RandomState(0) n_samples, n_features = 10, 20 X = random_state.normal(size=(n_samples, n_features)) y = random_state.normal(size=n_samples) # Check that Theil-Sen falls back to Least Squares if fit_intercept=False theil_sen = TheilSenRegressor(fit_intercept=False, random_state=0).fit(X, y) lstq = LinearRegression(fit_intercept=False).fit(X, y) assert_array_almost_equal(theil_sen.coef_, lstq.coef_, 12) # Check fit_intercept=True case. This will not be equal to the Least # Squares solution since the intercept is calculated differently. theil_sen = TheilSenRegressor(fit_intercept=True, random_state=0).fit(X, y) y_pred = theil_sen.predict(X) assert_array_almost_equal(y_pred, y, 12)