How to Compute Entropy using SciPy?

How to compute element-wise entropy of an input tensor in PyTorch

What is Data Acquisition in Machine Learning?

Entropy is a fundamental concept in measuring the uncertainty or randomness in a dataset. Entropy plays a very significant role in machine learning models such as decision trees, helping to decide how best to partition input at each node. Even for those who are not very knowledgeable in the underlying mathematics, the Scipy library for Python, provides features that make computing entropy simple.

In this post, we will understand how to compute entropy using Popular python’s library scipy.

How to Compute Entropy using SciPy?

What is Entropy?
Why Compute Entropy?
Calculating Entropy with SciPy
Entropy Calculation for Binary Classification using Scipy
Entropy Calculation for Multi-Class Classification using Scipy
Conclusion
How to Compute Entropy using SciPy?- FAQs

What is Entropy?

Entropy, introduced by Claude Shannon is a measure of the amount of uncertainty or randomness in a probability distribution. It is computed by taking the logarithm of each outcome’s probability and adding up all of its negative sums. Entropy is a measure of a dataset’s impurity or uncertainty in machine learning, and it is crucial for decision tree-based algorithms.

The formula for entropy H(S) of a set S with multiple classes is:

[Tex]H(X) = -\sum_{x \in X} p(x) \log p(x)[/Tex], indicating the sum is taken over all values of x in X , and p(x) is the probability of each value x in X.

Why Compute Entropy?

Machine learning requires the computation of entropy for a number of reasons.

Decision Tree Induction: In decision tree techniques, entropy is utilized to identify the most advantageous feature for data splitting.
Feature Selection: The most informative feature in a dataset can be chosen using entropy.
Data analysis: Entropy sheds light on a dataset’s complexity and organizational structure.

Calculating Entropy with SciPy

SciPy, provides an effecient way for calculating entropy using the “entropy" function from “scipy.stats module“. This function calculates the Shannon entropy of a given probability distribution.

Setting Up your Environment

Before importing, and proceeding further, first we need to install the scipy package.

!pip install scipy

Computing Entropy using scipy.stats.entropy

In the example, we define a probability distribution p and compute the entropy using the entropy function with scipy stats entropy. The base parameter is set to 2, which means the entropy is calculated in bits. Distribution of data among all the classes is maximized when entropy is highest and when all feature samples belong to the same class, the entropy is lowest. An entropy of zero is obtained for a totally homogeneous dataset (when all instances belong to the same class). Generally, Entropy values range from 0 to 1, where:

0: represents a perfectly pure dataset (no uncertainty)
1: represents a perfectly random dataset (maximum uncertainty)

Python

from scipy.stats import entropy
p = [0.4, 0.3, 0.3] # probability distribution
ent = entropy(p, base=2)
print("Entropy:", ent)

Output:

Entropy: 1.570950594454669

In the example above, the entropy value for 1.57, indicates a level of high uncertainty and random dataset.

Entropy Calculation for Binary Classification using SciPy

In the code, we define the target variable y by converting multi-classification into a binary classification tasks for simplicity.

Here, we will use iris dataset and classify Setosa (class 0) vs. Non-Setosa (class 1) species.
Using np.bincount, we compute the frequency of each unique value in the target variable, which essentially gives us the counts of class 0 and class 1.
Finally, we pass these counts to the entropy function along with the base of 2 to compute the entropy of the target variable.

Python

from sklearn import datasets
from scipy.stats import entropy
import numpy as np

iris = datasets.load_iris()
X = iris.data

# For simplicity, we'll classify the Iris species into two classes: Setosa (class 0) and Non-Setosa (class 1)
y = (iris.target != 0).astype(int)  # Setosa (class 0) vs Non-Setosa (class 1)
y_entropy = entropy(np.bincount(y), base=2) # Compute the entropy of the target variable (y)
print("Entropy of Iris dataset (binary classification):", y_entropy)

Output:

Entropy of Iris dataset (binary classification): 0.9182958340544894

Entropy Calculation for Multi-Class Classification using SciPy

In the example, we will calculate the entropy value of the target variable in the Wine dataset, providing insights into the uncertainty or randomness associated with the multiclass classification problem.

Python

from sklearn import datasets
from scipy.stats import entropy
import numpy as np

wine = datasets.load_wine()
X = wine.data
y = wine.target
y_entropy = entropy(np.bincount(y), base=2)
print("Entropy of Wine dataset (multiclass classification):", y_entropy)

Output:

Entropy of Wine dataset (multiclass classification): 1.5668222768551812

Conclusion

To sum up, we understood the concept of entropy and its significance in measuring uncertainty within datasets and demonstrated how to compute entropy using the scipy.stats.entropy function, making use of the efficient features provided by the SciPy library in Python. Through examples, we calculated entropy for both binary and multi-class classification problems using real-world datasets like Iris and Wine.

For more refer to:

How to Compute Entropy using SciPy?- FAQs

What does entropy means within machine learning context?

Disorder and uncertainty are captured by a parameter entropy in a dataset. This is a way of classifying impurity in machine learning, they give a bunch of examples that correspond to a subset.

In information theory, how can entropy be incorporated into the decision trees?

In decision tree, entropy is employed to decide on which attribute to split data beijingen the node. The purpose of the call is to limit the amount of entropy, a state of uncertainty, and highlight the impurity in the new subsets that splits from the bigger set.

Which is the connection of entropy and information gain?

Information gain is a measure used in determining which segregating attribute to use in a decision tree. It involves the difference in the entropy between the distribution before and after the target variable is split. Traits which lead to the best information increase are selected for the splitting.

What are a couple of examples where entropy is used in machine learning?

Entropy is among the most widespread algorithms that are used for machine learning purposes in decision trees, random forests, and gradient boosting. And besides that it provides the classification of features, anomaly discovery, and other tasks of quantifying the errors and information gain.

Can the phenomenon of entropy be used in predicting future values?

Although entropy is mostly employed for classification, it’s conditional entropy and mutual information analogues can be utilized for purposes other than the classifications, e. g. regressions, to measure the connection between variables.

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