Q3 Regression Consider the lasso criterion as seen in the lectures L = YTY - BTXTY + ½ß³ XTXẞ + \||B||1. In this problem, you will consider the case with only one explanatory variable. The columns X and Y are centered so there is no intercept in the model. The parameter ẞ is a scalar and so are the quantities XTX,XTY and YTY. These scalars have values XTX = 2.5, XTY = -0.5 and YTY = 2.5. A) Write the ordinary least squares estimate B = B) Using the given quantities and the result of B, write the lasso criterion as a function of ẞß and λ (both scalars). The criterion is L = By doing derivative of L and solving the corresponding system, determine the lasso coefficient as a function of A. That is ¹ = ¹ (A)= D) The value of A at which the path ẞL (A) shrinks to zero is
Q3 Regression Consider the lasso criterion as seen in the lectures L = YTY - BTXTY + ½ß³ XTXẞ + \||B||1. In this problem, you will consider the case with only one explanatory variable. The columns X and Y are centered so there is no intercept in the model. The parameter ẞ is a scalar and so are the quantities XTX,XTY and YTY. These scalars have values XTX = 2.5, XTY = -0.5 and YTY = 2.5. A) Write the ordinary least squares estimate B = B) Using the given quantities and the result of B, write the lasso criterion as a function of ẞß and λ (both scalars). The criterion is L = By doing derivative of L and solving the corresponding system, determine the lasso coefficient as a function of A. That is ¹ = ¹ (A)= D) The value of A at which the path ẞL (A) shrinks to zero is
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Q3 Regression
Consider the lasso criterion as seen in the lectures L = YTY - BTXTY + ½ß³ XTXẞ + \||B||1. In this
problem, you will consider the case with only one explanatory variable. The columns X and Y are centered
so there is no intercept in the model.
The parameter ẞ is a scalar and so are the quantities XTX,XTY and YTY. These scalars have values
XTX = 2.5, XTY = -0.5 and YTY = 2.5.
A) Write the ordinary least squares estimate B
=
B) Using the given quantities and the result of B, write the lasso criterion as a function of ẞß and λ (both
scalars). The criterion is L =
By doing derivative of L and solving the corresponding system, determine the lasso coefficient as a
function of A. That is ¹ = ¹ (A)=
D) The value of A at which the path ẞL (A) shrinks to zero is
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