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One Formula to Rule Them All: The Unified Approach to Aggregation in Machine Learning
Learn how the arithmetic and geometric means, the minimum, maximum, and even median are related by a single formula.
When working with data, we often need to aggregate it in some way, such as calculating the (arithmetic) mean or median, or sometimes the minimum or maximum. Typically, there is only one correct method of aggregation that depends on the specific problem at hand. For example, if you want to calculate average sales, the objective is clear: you need to take the arithmetic mean.
However, there are situations where you can choose the type of aggregation. One example is the F₁ score, which is defined as the harmonic mean of precision and recall. This emphasizes the smaller of the two values more than the arithmetic mean does. While using the harmonic mean is a convention in this context, when aggregating models, you can freely choose your aggregation method.
Imagine you have trained three regression models and want to combine their predictions to derive a final answer. In this case, you can decide how to combine them — using the arithmetic mean, harmonic mean, minimum, maximum, or any method that yields the best performance.
