Distribution Estimation

This lecture delves into the concept of distribution estimation, focusing on min-max loss functions and natural estimators. The instructor explains the importance of constraints in estimating distributions and introduces the notion of competitive analysis to design robust estimators. The lecture explores the derivation of a competitive estimator and its operational meaning in minimizing regret. Through a detailed example, the instructor illustrates how to construct a natural estimator based on observed symbols and probabilities. The discussion concludes with a comparison between the natural estimator and the competitive genie, emphasizing the need for reasonable constraints to ensure meaningful estimation.