Homework Help is Here – Start Your Trial Now!
Math
Calculus
Problem 2. Mean Absolute Error - Adding a Data Point Suppose we have a dataset y₁ ≤ Y2 < ... < Yn and want to minimize absolute loss on it for the prediction h. As we've seen before, the corresponding empirical risk is mean absolute error, n Rabs(h) = | Yi - h n Suppose that Rabs(a) = Rabs (α + 3) = a) b) M, where M is the minimum value of Rabs(h) and a is some constant. Suppose we add to the dataset a new data point yn+1 whose value is a + 1. For this new larger dataset: What is the minimum of Rabs(h)? At what value of h is this minimum achieved? Your should only involve the variables n, M, a, and constants. Let n be odd. Let ya and yɩ be two values in our dataset such that ya < yɩ and that the slope of Rabs(h) is the same between h Ya and h = y. Specifically, let d be the slope of Rabs (h) between Ya and yb. = 1 = Suppose we introduce a new value q to our dataset such that q> y. In our new dataset of n + 1 values, the slope of Rabs (h) is still the same between h == Ya and h Yb, but it's no longer equal to d. What is the slope of Rabs (h) between h = Ya and h = y in our new dataset? Your answer should depend on d, n, q, and/or one or more constants.

Problem 2. Mean Absolute Error - Adding a Data Point Suppose we have a dataset y₁ ≤ Y2 < ... < Yn and want to minimize absolute loss on it for the prediction h. As we've seen before, the corresponding empirical risk is mean absolute error, n Rabs(h) = | Yi - h n Suppose that Rabs(a) = Rabs (α + 3) = a) b) M, where M is the minimum value of Rabs(h) and a is some constant. Suppose we add to the dataset a new data point yn+1 whose value is a + 1. For this new larger dataset: What is the minimum of Rabs(h)? At what value of h is this minimum achieved? Your should only involve the variables n, M, a, and constants. Let n be odd. Let ya and yɩ be two values in our dataset such that ya < yɩ and that the slope of Rabs(h) is the same between h Ya and h = y. Specifically, let d be the slope of Rabs (h) between Ya and yb. = 1 = Suppose we introduce a new value q to our dataset such that q> y. In our new dataset of n + 1 values, the slope of Rabs (h) is still the same between h == Ya and h Yb, but it's no longer equal to d. What is the slope of Rabs (h) between h = Ya and h = y in our new dataset? Your answer should depend on d, n, q, and/or one or more constants.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
See similar textbooks
icon
Related questions
Question
Problem 2. Mean Absolute Error - Adding a Data Point Suppose we have a dataset y₁ ≤ Y2 < ... < Yn and want to minimize absolute loss on it for the prediction h. As we've seen before, the corresponding empirical risk is mean absolute error, n Rabs(h) = | Yi - h n Suppose that Rabs(a) = Rabs (α + 3) = a) b) M, where M is the minimum value of Rabs(h) and a is some constant. Suppose we add to the dataset a new data point yn+1 whose value is a + 1. For this new larger dataset: What is the minimum of Rabs(h)? At what value of h is this minimum achieved? Your should only involve the variables n, M, a, and constants. Let n be odd. Let ya and yɩ be two values in our dataset such that ya < yɩ and that the slope of Rabs(h) is the same between h Ya and h = y. Specifically, let d be the slope of Rabs (h) between Ya and yb. = 1 = Suppose we introduce a new value q to our dataset such that q> y. In our new dataset of n + 1 values, the slope of Rabs (h) is still the same between h == Ya and h Yb, but it's no longer equal to d. What is the slope of Rabs (h) between h = Ya and h = y in our new dataset? Your answer should depend on d, n, q, and/or one or more constants.
Transcribed Image Text:Problem 2. Mean Absolute Error - Adding a Data Point Suppose we have a dataset y₁ ≤ Y2 < ... < Yn and want to minimize absolute loss on it for the prediction h. As we've seen before, the corresponding empirical risk is mean absolute error, n Rabs(h) = | Yi - h n Suppose that Rabs(a) = Rabs (α + 3) = a) b) M, where M is the minimum value of Rabs(h) and a is some constant. Suppose we add to the dataset a new data point yn+1 whose value is a + 1. For this new larger dataset: What is the minimum of Rabs(h)? At what value of h is this minimum achieved? Your should only involve the variables n, M, a, and constants. Let n be odd. Let ya and yɩ be two values in our dataset such that ya < yɩ and that the slope of Rabs(h) is the same between h Ya and h = y. Specifically, let d be the slope of Rabs (h) between Ya and yb. = 1 = Suppose we introduce a new value q to our dataset such that q> y. In our new dataset of n + 1 values, the slope of Rabs (h) is still the same between h == Ya and h Yb, but it's no longer equal to d. What is the slope of Rabs (h) between h = Ya and h = y in our new dataset? Your answer should depend on d, n, q, and/or one or more constants.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:
9781305071742
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Functions and Change: A Modeling Approach to Coll…
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS