Mutual information for feature selection in ML Python - Practice Problems & Coding Challenges

Challenge - 5 Problems

🧠 Conceptual

intermediate

Understanding Mutual Information in Feature Selection

Which statement best describes the role of mutual information in feature selection?

A It quantifies the amount of shared information between a feature and the target variable, capturing any kind of dependency.

B It measures the linear correlation between features and the target variable.

C It ranks features based on their variance across the dataset.

D It removes features that have missing values in the dataset.

💡 Hint

Think about how mutual information captures relationships beyond just linear ones.

Mutual information measures how much knowing the value of one variable reduces uncertainty about another, capturing all types of dependencies, not just linear correlations.

❓ Predict Output

intermediate

Output of Mutual Information Calculation

What is the output of the following Python code that calculates mutual information between features and a binary target?

ML Python

from sklearn.feature_selection import mutual_info_classif
import numpy as np

X = np.array([[1, 2, 3], [1, 3, 3], [0, 2, 1], [0, 3, 1]])
y = np.array([0, 1, 0, 1])

mi = mutual_info_classif(X, y, discrete_features=[True, True, True], random_state=0)
print([round(v, 2) for v in mi])

A [0.0, 0.0, 0.0]

B [0.19, 0.0, 0.0]

C [0.0, 0.19, 0.0]

D [0.19, 0.19, 0.0]

💡 Hint

Mutual information is non-negative and measures dependency; check which feature varies with the target.

The second feature varies with the target, so it has positive mutual information; the others do not.

❓ Model Choice

advanced

Choosing Features Based on Mutual Information

You have 10 features and their mutual information scores with the target. Which approach best selects features to improve model performance?

A Select the top 3 features with the highest mutual information scores only.

B Select features with mutual information scores above zero, regardless of redundancy between features.

C Select features randomly to avoid bias from mutual information scores.

D Select features with high mutual information scores and low mutual information among themselves to reduce redundancy.

💡 Hint

Consider both relevance to target and redundancy among features.

Choosing features that are both relevant and not redundant helps improve model performance by providing diverse information.

❓ Hyperparameter

advanced

Hyperparameter Impact on Mutual Information Estimation

When using mutual_info_classif from scikit-learn, which hyperparameter affects the smoothness of the mutual information estimate for continuous features?

A <code>n_neighbors</code>

B <code>random_state</code>

C <code>discrete_features</code>

D <code>copy</code>

💡 Hint

Think about parameters controlling neighborhood size in nearest neighbor estimation.

The n_neighbors parameter controls the number of neighbors used in the k-nearest neighbors method for estimating mutual information, affecting smoothness.

🔧 Debug

expert

Debugging Mutual Information Calculation Error

What error will the following code raise when calculating mutual information, and why?

from sklearn.feature_selection import mutual_info_classif
import numpy as np

X = np.array([[1.5, 2.3], [3.1, 4.7], [5.2, 6.8]])
y = np.array([0, 1, 0])

mi = mutual_info_classif(X, y, discrete_features=True)
print(mi)

A RuntimeWarning due to division by zero in mutual information calculation.

B TypeError because <code>discrete_features</code> must be a boolean or array-like, not a single boolean when X has continuous features.

C No error; the code runs and outputs mutual information scores.

D ValueError because the number of samples in X and y do not match.

💡 Hint

Check the type and shape of discrete_features parameter relative to input data.

Setting discrete_features=True treats all features as discrete, but with continuous data this causes a TypeError; it should be a boolean array or False for continuous features.

Practice

1. What does mutual information measure in feature selection?

easy

A. The amount of shared information between a feature and the target variable

B. The correlation coefficient between two features

C. The difference between feature means

D. The number of missing values in a feature

Solution

1. Step 1: Understand mutual information concept

   Mutual information measures how much knowing one variable reduces uncertainty about another.

2. Step 2: Apply to feature selection context

   In feature selection, it measures how much information a feature shares with the target variable.

3. Final Answer:

   The amount of shared information between a feature and the target variable -> Option A

4. Quick Check:

   Mutual information = shared info [OK]

Hint: Mutual info = shared info between feature and target [OK]

Common Mistakes:

• Confusing mutual information with correlation
• Thinking it measures missing data
• Assuming it measures difference in means

2. Which Python function is used to compute mutual information for classification tasks?

easy

A. mutual_info_classif

B. mutual_info_regression

C. mutual_info_score

D. mutual_info_classifier

Solution

1. Step 1: Recall mutual information functions in sklearn

   For classification, sklearn provides mutual_info_classif.

2. Step 2: Differentiate from regression function

   mutual_info_regression is for regression, not classification.

3. Final Answer:

   mutual_info_classif -> Option A

4. Quick Check:

   Classification uses mutual_info_classif [OK]

Hint: Classification uses mutual_info_classif function [OK]

Common Mistakes:

• Using mutual_info_regression for classification
• Confusing function names
• Assuming mutual_info_score exists in sklearn

3. Given this code snippet, what is the output?

from sklearn.feature_selection import mutual_info_classif
import numpy as np
X = np.array([[1, 2], [2, 3], [3, 4], [4, 5]])
y = np.array([0, 1, 0, 1])
mi = mutual_info_classif(X, y, discrete_features=[True, True])
print(np.round(mi, 2))

medium

A. [0.0 0.0]

B. [0.69 0.0]

C. [0.0 0.69]

D. [0.69 0.69]

Solution

1. Step 1: Understand input data and parameters

   X has two discrete features, y is binary. Using mutual_info_classif with discrete_features=True for both.

2. Step 2: Calculate mutual information values

   Both features vary similarly with y, so both have similar mutual information around 0.69 (close to ln(2)).

3. Final Answer:

   [0.69 0.69] -> Option D

4. Quick Check:

   Both features share info with y ~0.69 [OK]

Hint: Discrete features with binary target give ~0.69 MI if informative [OK]

Common Mistakes:

• Assuming zero mutual information for all features
• Mixing up discrete_features parameter
• Rounding errors in output

4. Identify the error in this code snippet for mutual information feature selection:

from sklearn.feature_selection import mutual_info_classif
X = [[1, 2], [2, 3], [3, 4]]
y = [0, 1, 0]
mi = mutual_info_classif(X, y)
print(mi)

medium

A. y should be a 2D array, not 1D

B. X should be a numpy array, not a list of lists

C. mutual_info_classif requires discrete_features parameter

D. mutual_info_classif cannot handle integer data

Solution

1. Step 1: Check input data types

   mutual_info_classif expects numpy arrays or similar, not plain Python lists.

2. Step 2: Identify error cause

   Passing list of lists for X can cause unexpected behavior or errors; converting to numpy array fixes this.

3. Final Answer:

   X should be a numpy array, not a list of lists -> Option B

4. Quick Check:

   Use numpy arrays for X [OK]

Hint: Always convert input data to numpy arrays before sklearn functions [OK]

Common Mistakes:

• Thinking y must be 2D
• Assuming discrete_features is always required
• Believing mutual_info_classif rejects integer data

5. You have a dataset with 10 features. After computing mutual information scores, you find two features have the highest scores but are highly correlated with each other. What is the best approach to select features?

hard

A. Select both features because they have the highest mutual information

B. Select features randomly to avoid bias

C. Select only one of the two correlated features with the highest mutual information

D. Discard both features to avoid redundancy

Solution

1. Step 1: Understand mutual information and correlation

   High mutual information means features are informative, but high correlation means redundancy.

2. Step 2: Choose features to reduce redundancy

   To avoid redundant information, select only one of the correlated features with the highest mutual information.

3. Final Answer:

   Select only one of the two correlated features with the highest mutual information -> Option C

4. Quick Check:

   Pick one correlated feature with highest MI [OK]

Hint: Avoid redundant features by picking one with highest MI [OK]

Common Mistakes:

• Selecting both correlated features causing redundancy
• Discarding informative features unnecessarily
• Choosing features randomly without criteria