What is entropy in machine learning?

Simply put, entropy in machine learning is related to randomness in the information being processed in your machine learning project. However, let’s be more specific. In this article, we will explain what entropy is in machine learning and what it means to you and your ML projects.

Almost everyone has heard the entropy term at least once, perhaps during physics class in high school. You can find many different definitions of entropy, but for the sake of this article, let’s use the most straightforward one:

Entropy is the measure of disorder and randomness in a closed [atomic or molecular] system. [1]

In other words, a high value of entropy means that the randomness in your system is high, meaning it is difficult to predict the state of atoms or molecules in it. On the other hand, if the entropy is low, predicting that state is much easier. And with this short introduction done, now, it’s so much easier to explain what entropy in machine learning is.

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Entropy in machine learning

We’ve just told you that entropy in physics is a measurement of randomness in an isolated system. It’s quite similar when it comes to machine learning! Here, entropy is also a measure of randomness.

However, here, you measure the disorder of the information processed in your ML project.

Again, a short introduction. You have to understand that every piece of information has a specific value and can be used to draw conclusions from it. In fact, that’s what the entire data science field is based on. The easier it is to draw valuable conclusions from a piece of information, the lower the entropy in machine learning.

Let’s use a simple example–flipping a coin. There can be two outcomes. However, they are difficult to predict because there is no direct relation between the flipping itself and the outcome. Whatever you do, it’s 50-50. In such a situation, entropy is high–getting conclusions from the information is difficult. But there is one more lesson to draw.

You see, each coin toss is an event. Some events are rare (there is a low probability of them happening), e.g., you toss a coin ten times, and it’s tails ten times. Such events are called more surprising. Now, surprising events typically entail more information than other, common events with high probability.

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Tge decision tree

Entropy is frequently used in one of the most common machine learning techniques – decision trees. As you know from our other blog posts, decision trees are used to predict an outcome based on historical data. They are used primarily for classification and regression problems. The decision trees are usually based on a sequence of the ‘if-then-else’ statements and a root, which is the initial question/problem you want to solve.

In machine learning, decision trees are based primarily on nodes (where the data splits) and leaves (where you get the decision or the outcome). Decision trees help managers and companies make the best decisions based on available information. Therefore our ultimate goal is to get to the point where entropy is as low as possible.

Source: opendatascience.com

And that’s the whole point of calculating entropy. It allows you to discern whether your result is based on a solid foundation. The lower the entropy in machine learning, the more accurate the decision/prediction you can make. Moreover, thanks to calculating entropy, you can decide which variables are the most efficient to split on, making your decision tree more effective and accurate.

Of course, we’ve just scratched the surface of entropy in machine learning. There are specific formulas that allow you to calculate entropy with amazing precision and principles you have to stick to. It’s a story for a different article, though.

What you should remember from this article is this – entropy measures disorder in the information processes in your machine learning project. The lower this disorder is the more accurate results/predictions you can get. Therefore, we can state that entropy is directly related to achieving high accuracy of your ML endeavors, making it critical.

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References

[1] Interesting Engineering.com. An infinite disoder. The physics of entropy. URL: https://interestingengineering.com/an-infinite-disorder-the-physics-of-entropy. Accessed Jul 10, 2021.