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Formal Definition of the Predicted Value (ŷ)
The predicted value, denoted as , is formally determined as the argument that optimizes a specific objective function. This is expressed in the general form $\hat{y}$ = arg ..., where arg typically represents either argmin (argument of the minimum) or argmax (argument of the maximum). The choice between argmin and argmax depends on whether the objective is to minimize a loss function or maximize a likelihood function, respectively.
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Ch.3 Prompting - Foundations of Large Language Models
Foundations of Large Language Models
Foundations of Large Language Models Course
Computing Sciences
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Objective Function in Machine Learning
Least Squares Approach
Formal Definition of the Predicted Value (ŷ)
A real estate company uses a machine learning model to estimate the market value of houses. For a specific house with 3 bedrooms and 2,000 square feet of living space, the model calculates an estimated value of $450,000. The house later sells for an actual price of $465,000. In the context of this predictive model, what does the $450,000 figure represent?
Analyzing Model Predictions
Conditional Probability Pr^t(y|c, z)
Analyzing a Predictive Model's Performance
Linear Regression Analytic Solution
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Predictive Inference by Maximizing Conditional Probability
Predictive Inference in Large Language Models
A predictive model is designed to generate an output, , that minimizes a given loss function, , which measures the error of the prediction. Which of the following expressions correctly represents the formal definition of the model's predicted value, ?
Formal Prediction Expressions for Different Objectives
A predictive model's output, , is formally defined as the argument that optimizes an objective function. Match each modeling objective to the correct formal expression that represents it.