Question: Softmax Regression (or Multinomial Logistics Regression) The gradient for cross-entropy cost function: m Vo J(0) = 1 (Pk (i) m - yk (i))x(i) i=1 yk

Softmax Regression (or Multinomial Logistics Regression) The gradient for cross-entropy cost function: m Vo J(0) = 1 (Pk (i) m - yk (i))x(i) i=1 yk () = 1 if the ith instance belongs to class k; 0 otherwise. [10 points] Recall the multi-class Softmax Regression model on page 16 of Lecture 3-3. Assume we have K different classes. The posterior probability is PR = 6(S,(X) )k = TK_ s,(x) exp (5k (*)) for k = 1, 2, .... K, where Sk(x) = 0k . x, and input x is an n-dimension vector. 1) To learn this Softmax Regression model, how many parameters we need to estimate? What are these parameters? 2) Consider the cross-entropy cost function / (@) (see page 16 of Lecture 3-3) of m training samples ((*/ Vi))=1.2..m. Derive the gradient of ](@) regarding to Ox as shown in page 17 of Lecture 3-3

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!

Task 2: Multinomial logistic regression (softmax classifier) on MNIST dataset In this task, we will implement the generalization of binary logistic regression to classify multiple classes (10 digits)...

Assume we have K different classes in a multi-class Softmax Regression model. The for k=1,2,..., K, where Sk (x) = Ok.x, T - posterior probability is pk = 8(Sk(x))k exp (Sk(x)) 1 exp (sj(x)) j=1...

1 Softmax regression and logistic regression [10 points] In lecture 15, we introduced the softmax regression, which learns for each class c a pair (wc,bc) such that p(cx)=cexp(wcx+bc)exp(wcx+bc)....

D. What is the main difference between logistic regression and softmax regression? 1. Logistic regression is used for binary classification, while softmax regression is used for multi-class...

Question 3 . 1 We will first need to implement the softmax function, which is used as the predictor function by the softmax regression learner. In class we learned that the softmax function is...

CNN MeaningApplying to MNIST 0 . 0 / 1 . 0 point ( graded ) If we explicitly apply the cubic feature mapping to the original 7 8 4 - dimensional raw pixel features, the resulting representation would...

Derivatives. Partial solutions are ok! \f\fIndicator function - Indicator function 1{*} l{a true statement} =1 - l{s false statement} = 0 - We can rewrite the loss function of binary logistic...

6 . 1 . Run the program and complete the following exercises. ( 2 0 points ) ( 3 points ) We have learned two sklearn predefined models that solve linear problems with a regularization term adding to...

Run the program and complete the following exercises. ( 2 0 points ) ( 3 points ) We have learned two sklearn predefined models that solve linear problems with a regularization term adding to the...

DESC 620 Advanced Statistical Models in Business (Discrete Multivariate Analysis) Recommendations for our Final Class 1. Please take a look at the Ted Talk I mentioned to you in class, found at:...

A) In late 2012 the inflation rate in the U.S. was about 2%. In the Wall Street Journal, a columnist wrote: "Someone buying long-term bonds yielding 1.5% or 2%, and then seeing consumer price...

Determine the periodic payments PMT on the given loan or mortgage. (Round your answer to the nearest cent.) $800,000 borrowed at 8% for 7 years, with quarterly payments

"Option ARMs" were a cheap way to speculate on rising home prices because the borrower usually had to have a large down payment the borrower could pay a smaller amount than a conventional mortgage if...

A company issues 1,050 shares of its common stock for $33,600 cash. Prepare journal entries to record this event under each of the following separate situations.