Question: In this question we will perform the backward pass algorithm on the formula a. Calculate the following partial derivatives of f. (i) b. Calculate the

In this question we will perform the backward pass algorithm on the formula

A11 A12 [A21 A22] b||(b + b) is a scalar. = Here,a. Calculate the following partial derivatives of f.

(i) A = X = X = ||AX|| b = Ax = [A111+A122]

b. Calculate the following partial derivatives of b1.

(i)

A211 + A222] = and f =

(ii)

(iii)

c. Calculate the following partial derivatives of f.

(i)

(ii)

(iii)

d. Now we consider the general case where A is an n × d matrix, and x is a d × 1 vector. As before, f = 1/2 ||Ax||2. 

(i) Find ∂f/∂A in terms of A and x only. 

(ii) Find ∂f/∂x in terms of A and x only.

A11 A12 [A21 A22] b||(b + b) is a scalar. = Here, A = X = X = ||AX|| b = Ax = [A111+A122] A211 + A222] = and f =

Step by Step Solution

★★★★★

3.42 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a b i x 1 x 2 ii 0 0 iii A 11 A 12 c Ca... View full answer

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 Artificial Intelligence A Modern approach Questions!

Q:

Prove (where A is an nn matrix and so defines a transformation of any n-dimensional space V with respect to B, B where B is a basis) that dim(R(A) N (A)) = dim(R(A)) - dim(R(A2)). Conclude (a) N (A)...

Q:

Show that if A is an n square matrix and each row (column) sums to c then c is a characteristic root of A. ("Characteristic root" is a synonym for eigenvalue.)

Q:

Let A be an n n matrix and x Rn. (a) A scalar c can also be considered as a l l matrix C = (c), and a vector be Rn can be considered as an n 1 matrix B. Although the matrix multiplication CB is...

Q:

I have Five-questions for each question there's an exact example with a solution. Question 1: For the function ay) := 11:23:2 + 16:3y+ 9:2y+ 533 + 18y compute the following partial derivatives and...

Q:

Test 3 Math 273 July 12, 2012 Name: Problem Value 1 10 2 10 3 10 4 10 5 10 Total 50 Score Show all appropriate work. z z and where x y sh is ar stu ed d vi y re aC s ou ou rc rs e eH w er as o. co m...

Q:

Calculate the following partial derivatives: d1/ S, and d2/ S Now, using 2) above calculate / S(SN(d1)). For the partial of N(d1), just use N'(d1). Note that d1 is also a function of S so you will...

Q:

computer science 1 . ) Give an implementation level description of a Turing machine. You can check for an empty tapecell as a _ character. Convert from decimal to Unary: You are given a 2 - digit...

Q:

computer science 1 . ) Give an implementation level description of a Turing machine. You can check for an empty tapecell as a _ character. Convert from decimal to Unary: You are given a 2 - digit...

Q:

computer science 1 . ) Give an implementation level description of a Turing machine. You can check for an empty tapecell as a _ character. Convert from decimal to Unary: You are given a 2 - digit...

Q:

computer science 1 . ) Give an implementation level description of a Turing machine. You can check for an empty tapecell as a _ character. Convert from decimal to Unary: You are given a 2 - digit...

Q:

The Flower Family Trust is a discretionary trust created by Graeme Flower (the trustee) in 2012 for the benefit of his children and grandchildren. During the year ended 30 June 2021, the Flower...

Q:

1. The United States Federal personal income tax is calculated based on filing status and taxable income. There are four filing statuses: single filers (0) , married filing jointly or qualified...

Q:

Show that the rth moment about the origin of the gamma distribution is r = r( + r) () . [Hint: Substitute y = x/ in the integral defining r and then use the gamma function to evaluate the integral.]

Q:

Why do heterosexuals place so much emphasis on sex?

Q:

For the environment shown in Figure 17.1, find all the threshold values for R(s) such that the optimal policy changes when the threshold is crossed. You will need a way to calculate the optimal...

Q:

Select a specific member of the set of policies that are optimal for R(s) > 0 as shown in Figure 17.2(b), and calculate the fraction of time the agent spends in each state, in the limit, if the...

Q:

Recall the definition of value of information in Section 16.6. a. Prove that the value of information is nonnegative and order independent. b. Explain why it is that some people would prefer not to...

Q:

(NOTE: ENTER YOUR ANSWER WITHOUT THE $ AND COMMA, ROUNDED TO THE NEAREST DOLLAR, for instance as 10023, not as $10,022.78. Make sure you include negative sign in front of your answer if the answer is...

Q:

Chelsea Household Renovations (CHR) is a rapidly growing company that has not been profitable despite increases in sales. It has hired you as a consultant to find ways to improve inaccurate cost...

Q:

What is the value or price today of a bond with 8 years to maturity, a coupon rate of 6.20%, a required rate of return by bond investors of 8.60%, and a par value of $1,000? Assume semi-annual coupon...