Unveiling the Deep Connection Between Maximum Likelihood Estimation and Loss Functions
This article delves into the intrinsic relationship between Maximum Likelihood Estimation (MLE) and commonly used loss functions. Starting with the fundamentals of MLE, the author meticulously explains its close connection to KL divergence. The article then uses Mean Squared Error (MSE) and Cross-Entropy as examples, demonstrating how these functions are naturally derived from MLE rather than being arbitrarily chosen. By assuming data distributions (e.g., Gaussian for linear regression, Bernoulli for logistic regression), maximizing the likelihood function via MLE directly leads to MSE and Cross-Entropy loss functions. This provides a clear path to understanding the theoretical underpinnings of loss functions, moving beyond mere intuition.
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