Predictive Inference by Maximizing Conditional Probability

Predictive Inference in Large Language Models

A predictive model is designed to generate an output, $y$, that minimizes a given loss function, $L(y)$, which measures the error of the prediction. Which of the following expressions correctly represents the formal definition of the model's predicted value, $\hat{y}$?

Formal Prediction Expressions for Different Objectives

A predictive model's output, $\hat{y}$, is formally defined as the argument that optimizes an objective function. Match each modeling objective to the correct formal expression that represents it.