Mathematical Understanding of Bias Variance Tradeoff

Many of us have read about the Bias and Variance at various places in the AI literature but still many people struggle to explain it with respect to mathematical equation. People always comment about bias-variance whenever they build a model in order to figure out whether the model can be used or not in the real world and how good its performance will be. In this article, we will focus on the mathematical equation depicting Bias-Variance and try to understand different parts of this equation from a mathematical perspective. We will be using above assumptions in the equation below. As the main focus of this article is to understand the bias-variance equation from mathematical perspective, we will directly look at the equation without going into the derivation behind it(Please check the references, if you want to understand the derivation).