Joint Expectation and Correlation#

Introduction#

This section quantifies the degree in which two random variables are related to each other. For a simple example, consider you are a boss of a cafe, and you want to know if coffee and cheese cake sales are related to each other. Then we can model the number of coffee and cheese cake sold as random variables \(X\) and \(Y\) respectively, if the correlation between \(X\) and \(Y\) is high, then we should include both coffee and cheese cake on the same day’s menu.

Another example is in ensemble learning in machine learning , it is typical to ensemble different models’ predictions to get a better prediction. In this case, we can use the correlation between each model’s prediction to decide how much weight to give to each model’s prediction via a weighted average. We also want to ensure that the models are not too correlated with each other, otherwise the ensemble will not be better than the best model.

But how do we measure the correlation between two random variables? This is what we will discuss in this section.

Further Readings#