Implication of Central Limit theorem and its application in machine Learning According to central limit theorem, irrespective of the distribution of the original/population dataset, the sampling distribution will follow normal distribution.
My Question is if the means of n samples of the population data follow normal distribution, what is this helping us in ? I tried to find examples in the context of Ml but found no good example. It would be of great help if you could help me understand the significance of CLT ( basically application of knowing that sampling distribution will have bell curve) in the context of ML with an example.
Are you familiar with hypothesis testing? Confidence Intervals ? Statistical Significance ? All of these concepts typically rely on the central limit theorem.
One concrete example I can think of relating to ML: Regression
Most approaches to regression typically assume that the error term that appears follows a Gaussian distribution. How do we justify this assumption ? Well the idea is that we can think of the error term as a sum of multiple different error terms.
Now even if these individual error terms do not follow a Gaussian distribution, we can model their sum as a Gaussian because of the Central Limit Theorem.