Comparing model performance with a simple baseline#

In this notebook, we present how to compare the generalization performance of a model to a minimal baseline. In regression, we can use the DummyRegressor class to predict the mean target value observed on the training set without using the input features.

We now demonstrate how to compute the score of a regression model and then compare it to such a baseline on the California housing dataset.

Note

If you want a deeper overview regarding this dataset, you can refer to the section named β€œAppendix - Datasets description” at the end of this MOOC.

from sklearn.datasets import fetch_california_housing

data, target = fetch_california_housing(return_X_y=True, as_frame=True)
target *= 100  # rescale the target in k$

Across all evaluations, we will use a ShuffleSplit cross-validation splitter with 20% of the data held on the validation side of the split.

from sklearn.model_selection import ShuffleSplit

cv = ShuffleSplit(n_splits=30, test_size=0.2, random_state=0)

We start by running the cross-validation for a simple decision tree regressor which is our model of interest. Besides, we will store the testing error in a pandas series to make it easier to plot the results.

import pandas as pd
from sklearn.tree import DecisionTreeRegressor
from sklearn.model_selection import cross_validate

regressor = DecisionTreeRegressor()
cv_results_tree_regressor = cross_validate(
    regressor, data, target, cv=cv, scoring="neg_mean_absolute_error", n_jobs=2
)

errors_tree_regressor = pd.Series(
    -cv_results_tree_regressor["test_score"], name="Decision tree regressor"
)
errors_tree_regressor.describe()
count    30.000000
mean     45.685058
std       1.158101
min      43.421236
25%      44.964586
50%      45.569131
75%      46.665891
max      47.867438
Name: Decision tree regressor, dtype: float64

Then, we evaluate our baseline. This baseline is called a dummy regressor. This dummy regressor will always predict the mean target computed on the training target variable. Therefore, the dummy regressor does not use any information from the input features stored in the dataframe named data.

from sklearn.dummy import DummyRegressor

dummy = DummyRegressor(strategy="mean")
result_dummy = cross_validate(
    dummy, data, target, cv=cv, scoring="neg_mean_absolute_error", n_jobs=2
)
errors_dummy_regressor = pd.Series(
    -result_dummy["test_score"], name="Dummy regressor"
)
errors_dummy_regressor.describe()
count    30.000000
mean     91.140009
std       0.821140
min      89.757566
25%      90.543652
50%      91.034555
75%      91.979007
max      92.477244
Name: Dummy regressor, dtype: float64

We now plot the cross-validation testing errors for the mean target baseline and the actual decision tree regressor.

all_errors = pd.concat(
    [errors_tree_regressor, errors_dummy_regressor],
    axis=1,
)
all_errors
Decision tree regressor Dummy regressor
0 47.065086 90.713153
1 46.981610 90.539353
2 44.530029 91.941912
3 43.855612 90.213912
4 47.867438 92.015862
5 45.187782 90.542490
6 43.893401 89.757566
7 44.337276 92.477244
8 45.052026 90.947952
9 44.975015 91.991373
10 46.820199 92.023571
11 46.115036 90.556965
12 45.521452 91.539567
13 45.082433 91.185225
14 47.188412 92.298971
15 44.778288 91.084639
16 46.197794 90.984471
17 46.398124 89.981744
18 44.961110 90.547140
19 46.750891 89.820219
20 43.421236 91.768721
21 45.913218 92.305556
22 45.555419 90.503017
23 46.785363 92.147974
24 46.262156 91.386320
25 45.582844 90.815660
26 44.248108 92.216574
27 46.410893 90.107460
28 45.424819 90.620318
29 47.388681 91.165331
import matplotlib.pyplot as plt
import numpy as np

bins = np.linspace(start=0, stop=100, num=80)
all_errors.plot.hist(bins=bins, edgecolor="black")
plt.legend(bbox_to_anchor=(1.05, 0.8), loc="upper left")
plt.xlabel("Mean absolute error (k$)")
_ = plt.title("Cross-validation testing errors")
../_images/cross_validation_baseline_11_0.png

We see that the generalization performance of our decision tree is far from being perfect: the price predictions are off by more than 45,000 US dollars on average. However it is much better than the mean price baseline. So this confirms that it is possible to predict the housing price much better by using a model that takes into account the values of the input features (housing location, size, neighborhood income…). Such a model makes more informed predictions and approximately divides the error rate by a factor of 2 compared to the baseline that ignores the input features.

Note that here we used the mean price as the baseline prediction. We could have used the median instead. See the online documentation of the sklearn.dummy.DummyRegressor class for other options. For this particular example, using the mean instead of the median does not make much of a difference but this could have been the case for dataset with extreme outliers.