Choosing hyperparameters

After the exercise in the last chapter, you’re hopefully thinking “why am I spending my time trying different values of n_neighbors, can’t it do this automatically?” If so, you’re in luck!

It is a very common thing to need to try out a bunch of different values for your hyperparameters and so scikit-learn provides us with some tools to help out.

Let’s do a similar thing to the last chapter, but load a different file this time. One with four different classes and follow through the usual steps:

import pandas as pd

data = pd.read_csv("https://bristol-training.github.io/applied-data-analysis-in-python/data/blobs.csv")
X = data[["x1", "x2"]]
y = data["y"]

import seaborn as sns

sns.scatterplot(data=data, x="x1", y="x2", hue="y", palette="Dark2")

from sklearn.model_selection import train_test_split

train_X, test_X, train_y, test_y = train_test_split(X, y)

The tools that allows us to do the hyper-parameter searching is called GridSearchCV which will rerun the model training for every possible hyperparameter that we pass it.

The GridSearchCV constructor takes two things: 1. the model that we want to explore, 2. a dictionary containing the hyper-parameter values we want to test.

In this case, we are asking it to try every value of n_neighbors from 1 to 49 and it will use the training data to choose the best value.

from sklearn.model_selection import GridSearchCV
from sklearn.neighbors import KNeighborsClassifier

hyperparameters = {
    "n_neighbors" : range(1, 175),
}
model = GridSearchCV(KNeighborsClassifier(), hyperparameters)
model.fit(train_X, train_y)

GridSearchCV(estimator=KNeighborsClassifier(),
             param_grid={'n_neighbors': range(1, 175)})

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

The best way to visualise the data is to plot it. We can do this by grabbing the cv_results_ attribute of GridSearchCV and plotting the mean_test_score against the value of n_neighbors. GridSearchCV will run each experiment multiple times with different splits of training and validation data to provide some measure of uncertainty of the score:

cv_results = pd.DataFrame(model.cv_results_)
cv_results.plot.scatter("param_n_neighbors", "mean_test_score", yerr="std_test_score", figsize=(10,8))

One thing that GridSearchCV does, once it has scanned through all the parameters, is do a final fit using the whole training data set using the best hyperparameters from the search. This allows you to use the GridSearchCV object model as if it were a KNeighborsClassifier object.

from sklearn.inspection import DecisionBoundaryDisplay

DecisionBoundaryDisplay.from_estimator(model, X, cmap="Pastel2")
sns.scatterplot(data=X, x="x1", y="x2", hue=y, palette="Dark2")

or use it directly with predict:

new_X = pd.DataFrame({
    "x1": [0, -10, 5, -5],
    "x2": [10, 5, 0, -10],
})

model.predict(new_X)

array([0, 3, 1, 2])

or measure its performance against the test data set:

model.score(test_X, test_y)

0.928

Using something like GridSearchCV allows you to find the best hyperparameters for your models while keeping them working most generally.

Exercise

Grab the Iris data set from sklearn. This time we will simplify it down to only two features (sepal length and sepal width) to simplity the visualisation.

from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split

X, y = load_iris(as_frame=True, return_X_y=True)
X = X[["sepal length (cm)", "sepal width (cm)"]]  # Grab just two of the features

train_X, test_X, train_y, test_y = train_test_split(X, y, random_state=42)

Using GridSearchCV, find the best value of n_neighbors and print the score of that model when run over the test data set.

Answer

As usual, grab the data. The difference this time is that are only going to grab two of the features in order to make it a 2D problem which is easier to visualise.

from pandas import DataFrame
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split

X = DataFrame(load_iris().data, columns=load_iris().feature_names)
X = X[["sepal length (cm)", "sepal width (cm)"]]  # Grab just two of the features
y = load_iris().target

train_X, test_X, train_y, test_y = train_test_split(X, y, random_state=42)

We will look at values of n_neighbors from 0 to 59.

from sklearn.model_selection import GridSearchCV
from sklearn.neighbors import KNeighborsClassifier

hyperparameters = {
    "n_neighbors" : range(1, 40),
}
clf = GridSearchCV(KNeighborsClassifier(), hyperparameters).fit(train_X, train_y)

To easily look at the results, we put the output into a DataFrame, sort it by the test score (how well that value did against its validation set) and grab the top few rows.

cv_results = DataFrame(clf.cv_results_)
cv_results = cv_results.sort_values(["rank_test_score", "mean_test_score"])
cv_results.head()[["param_n_neighbors", "mean_test_score", "std_test_score", "rank_test_score"]]

	param_n_neighbors	mean_test_score	std_test_score	rank_test_score
30	31	0.795652	0.056227	1
28	29	0.795257	0.042471	2
17	18	0.786561	0.048231	3
27	28	0.786561	0.048231	3
29	30	0.786561	0.048231	3

It looks like the best one is n_neighbors=31 but let’s look on a plot to see how it varies:

cv_results.plot.scatter("param_n_neighbors", "mean_test_score", yerr="std_test_score")

<Axes: xlabel='param_n_neighbors', ylabel='mean_test_score'>

Indeed n_neighbors=31 is the best in the range but they all have large standard deviations. It’s worth plotting it like this so that you might want to pick a lower mean in order to get a tighter distribution.

from sklearn.inspection import DecisionBoundaryDisplay
import seaborn as sns

DecisionBoundaryDisplay.from_estimator(clf, X, cmap="Pastel2")
sns.scatterplot(data=X, x="sepal length (cm)", y="sepal width (cm)", hue=y, palette="Dark2")

<Axes: xlabel='sepal length (cm)', ylabel='sepal width (cm)'>

clf.score(test_X, test_y)

0.868421052631579