Question: 2. (Linear regression) Recall in linear regression, we have data pairs (X1,y1),(Xn,Yn) and we solve the following objective: ^+argRvminXY22. Here X,Y are the compact form

2. (Linear regression) Recall in linear regression, we have data pairs (X1,y1),(Xn,Yn) and we solve the following objective: ^+argRvminXY22. Here X,Y are the compact form to represent the data: XRnp with its i-th row vector to be Xi. and Y is a vector where its i-th coordinate is Yi=yi. (a) (6') Solve ^. (You should represent ^ in the form of X and Y.) (b) (10) Recall the standard model (with fixed design): Y=X+ E, where N(0,2I), is the ground-truth model, and X is considered as fixed. Calculate the following excess risk of the learned model ^: ER(^)=n1EX^X22. Hint: You may want to use the fact that Tr(AB)=Tr(BA). You msy assume XX is full rank

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!

Math 104A Homework #4 Instructor: Lihui Chai 1. Write a code to compute a natural spline S(x) which interpolates a collection of given points (x0 , y0 ), (x1 , y1 ), ..., (xn , yn ) where x0

Only accurate answers will be accepted! Suppose you have bivariate data (x1, y1), . . . ,(xn, yn). A common model is that there is a linear relationship between x and y, so in principle the data...

ML in a nutshell Optimization, and machine learning, are intimately connected. At a very coarse level, ML works as follows. First, you come up somehow with a very complicated model y = M(x, 0), which...

Final Exam MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the problem. 1) The average age of the students in a statistics class is 22...

answer with step by step explanation 4. Consider the non-linear regression problem of fitting the function class y = f (x) = 0(x)'0 = Zio big; (x) where o (x)" = [do (x) , ..., PM-1 (x)] are...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

Mickey's Amusements manufactures ride vehicles for roller coasters. One of their products is a seat with a harness for coasters that have inversions. Mickey's uses a standard cost system for all...

If n Z+, prove that (a) (2n) = 2(n) when n is even; and (b) (2n) = (n) when n is odd.

The threshold of data sufficiency is related to each of the following except: Question 7 options: The standard of proof The nature of an engagement The availability of data All of the above are...

Vulcan Companys contribution format income statement for June is given below: Vulcan Company Income Statement For the Month Ended June 30 Sales $ 900,000 Variable expenses 408,000 Contribution margin...