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 “Appendix - 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     45.703314
std       1.206643
min      43.239819
25%      44.971939
50%      45.771067
75%      46.777220
max      47.671119
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	46.811619	90.713153
1	46.814531	90.539353
2	44.226469	91.941912
3	43.690326	90.213912
4	47.661890	92.015862
5	45.198950	90.542490
6	43.861328	89.757566
7	44.979935	92.477244
8	44.773803	90.947952
9	44.996138	91.991373
10	47.290886	92.023571
11	46.450185	90.556965
12	45.686837	91.539567
13	45.274655	91.185225
14	46.873925	92.298971
15	44.480759	91.084639
16	45.925626	90.984471
17	46.674021	89.981744
18	44.969274	90.547140
19	47.095875	89.820219
20	43.239819	91.768721
21	45.828263	92.305556
22	45.379523	90.503017
23	46.673712	92.147974
24	45.870295	91.386320
25	45.903388	90.815660
26	44.230497	92.216574
27	46.851907	90.107460
28	45.713871	90.620318
29	47.671119	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")

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.