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: where typically represents either (argument of the minimum) or (argument of the maximum). The choice between and 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
Components of Karim's Constrained Choice Problem
A farmer plans to grow two types of crops: wheat (W, measured in bushels) and corn (C, measured in bushels). The farmer's primary goal is to achieve the highest possible profit from their land. The market price gives a profit of $5 per bushel of wheat and $8 per bushel of corn. The farmer faces limitations on available land and water. Given this situation, which of the following expressions represents the farmer's objective function?
Formulating an Objective Function for a Diet Plan
Analyzing a Business Decision
In any problem where a decision-maker faces limitations on their choices, the function representing the goal they are trying to optimize must be a quantity they wish to maximize.
Evaluating Competing Policy Objectives
A decision-maker faces a problem where they must make a choice under certain limitations. Match each decision-maker's scenario with the correct mathematical expression that represents their primary goal.
A city's transportation department is designing a new public bus system. Their main goal is to reduce the average commute time for its citizens, but they must work within a specific budget and a limited number of buses. The mathematical formula that represents the average commute time, which the department is trying to minimize, is referred to as the ______.
A city planner is trying to determine the optimal allocation of funds between building new parks and repairing existing roads. The goal is to maximize the overall well-being of the city's residents, subject to a fixed annual budget. To solve this as a formal optimization problem, the planner must follow a series of logical steps. Arrange the following steps in the correct logical order for setting up this problem.
Evaluating a Public Health Objective Function
Interpreting a Firm's Objective
Prediction via Optimization
Preference for Divergence-Based Objective Functions
Formal Definition of the Predicted Value (ŷ)
Using Optimized Predictions as Learning Targets
General Formula for Prediction via Maximum Probability
A language model is given the input 'The ocean is...' and calculates the conditional probability for four candidate words to be the next word. Based on the values below, which word would a model that predicts by maximizing probability choose?
- P("deep" | "The ocean is...") = 0.75
- P("cold" | "The ocean is...") = 0.15
- P("running" | "The ocean is...") = 0.09
- P("quiet" | "The ocean is...") = 0.01
Evaluating a Prediction Strategy
Spam Filter Classification
Formal Definition of the Predicted Value (ŷ)
Learn After
Predictive Inference by Maximizing Conditional Probability
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.
Predictive Inference Formula in Large Language Models