# Entropy And Information Gain In Decision Trees

## Introduction

Entropy and information gain are essential parameters in big data analytics, and it is possible to implement these metrics in tree-structured models to optimize the frameworks.

## Decision Tree Overview

The general concept of decision trees concerns information representation, classification, and regression in an illustrative format. There are different types of decision trees, including classification, probability estimation, and regression trees, albeit the underlying idea is similar in all cases (Provost and Fawcett, 2013). Moreover, continuous variable decision trees predict numerical outcomes based on the input in a continuous manner, as opposed to categorical variable decision trees (Kurama, 2020). According to Provost and Fawcett (2013), decision tree types differ depending on the leaf values – simple values for classification trees, numeric values for regression trees, and probabilities for probability estimation trees. Each model is relevant to business analytics and should be utilized based on the objective.

## The Role of Entropy and Information Gain in Decision Trees

The concepts of entropy and information gain play an essential role in the construction of decision trees or tree induction. At present, iterative dichotomizes 3 (ID3), ASSISTANT, and C4.5 are some of the most prominent methods of tree induction that utilize information gain (Pranto, 2020). In this context, entropy refers to the state of data homogeneity in the segment, while information gain determines the effectiveness of each tree node in reducing entropy (Hillier, 2021). In other words, the most substantial factors of differentiation (or the tree nodes) have the largest information gain on the whole dataset (Verma, 2021). As a result, the concepts of entropy and information gain are essential to tree induction.

## Differences in Entropy and Information Gain between Different Decision Tree Types

Based on the nature of the three mentioned decision tree types, there are certain differences in entropy and information gain. First, the classification trees have the highest information gain on each node since they generally propose two mutually exclusive variants – Yes or No – and significantly lower entropy in the dataset (Mehta, 2019; Vala, 2021). On the other hand, regression trees frequently determine the numeric variable when there are nonlinear relationships between the nodes (Mehta, 2019; Vala, 2021). Moreover, it is plausible to use the “mean square error” parameter instead of entropy in regression trees since the objective is to predict a continuous variable (Prasad, 2021). Each node of a classification tree has a more direct and notable impact on data entropy and might specify the needed outcomes in just several nodes. In other words, classification trees emphasize information gain and entropy as their primary attributes of node effectiveness, while these concepts are less significant for regression trees.

## Conclusion

Similarly, information gain is a less relevant metric for probability trees since they reveal estimations as probability values and not assertive conclusions. The objective of probability trees is to calculate the estimation of a variable occurrence with little regard to the entropy of the data set (‘Probability tree,’ 2021). In other words, this estimated probability becomes the primary metric of the decision tree and reveals a less accurate value (e.g., no write-off in classification trees/ 0.15 chance of write-off in probability trees) (Provost and Fawcett, 2013). This difference is essential in the comparison of information gain between the two types. Ultimately, entropy and information gain are vital to determine the impact of tree nodes in classification trees, but their relevance is significantly lower in regression and probability tree-structured models.

## Reference List

Hillier, W. (2021). ‘What is a decision tree and how is it used?’ Career Foundry, Web.

Kurama, V. (2020). ‘An introduction to decision trees’, Paperspace Blog. Web.

Mehta, A. (2019). ‘A beginner’s guide to classification and regression trees”, Digital Vidya, Web.

Pranto, B. (2020). ‘Entropy calculation, information gain & decision tree learning”, Medium, Web.

Prasad, A. (2021). ‘Regression trees | decision tree for regression | machine learning”, Medium, Web.

‘Probability tree diagrams explained’ (2021). Web.

Provost, F. and Fawcett, T. (2013). Data science for business: What you need to know about data mining and data-analytical thinking. California: O’Reilly.

Vala, K. (2021). ‘How to get started with regression trees?’ Builtin, Web.

Verma, Y. (2021). ‘A complete guide to decision tree split using information gain’, Analytics India Mag, Web.