week 5 assignment

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Coursera: Machine Learning (Week 5) [Assignment Solution] - Andrew NG

Recommended Machine Learning Courses: Coursera: Machine Learning    Coursera: Deep Learning Specialization Coursera: Machine Learning with Python Coursera: Advanced Machine Learning Specialization Udemy: Machine Learning LinkedIn: Machine Learning Eduonix: Machine Learning edX: Machine Learning Fast.ai: Introduction to Machine Learning for Coders

• ex4.m - Octave/MATLAB script that steps you through the exercise
• ex4data1.mat - Training set of hand-written digits
• ex4weights.mat - Neural network parameters for exercise 4
• submit.m - Submission script that sends your solutions to our servers
• displayData.m - Function to help visualize the dataset
• fmincg.m - Function minimization routine (similar to fminunc)
• sigmoid.m - Sigmoid function
• computeNumericalGradient.m - Numerically compute gradients
• checkNNGradients.m - Function to help check your gradients
• debugInitializeWeights.m - Function for initializing weights
• predict.m - Neural network prediction function
• [*] sigmoidGradient.m - Compute the gradient of the sigmoid function
• [*] randInitializeWeights.m - Randomly initialize weights
• [*] nnCostFunction.m - Neural network cost function
• Video - YouTube videos featuring Free IOT/ML tutorials

sigmoidGradient.m :

Randinitializeweights.m :, check-out our free tutorials on iot (internet of things):.

nnCostFunction.m :

61 comments.

Hi, I am clear up to how to calculate partial derivatives. But, I am having doubt after calculating delta values. I have got delta-2 values in the dimension 10 X 25 and delta-1 with dimension 25X400. This is I have got for first row of input layer. So, for 5000 rows how these delta values will be calculated? Thanks.

Dimensions of delta should be similar as to corresponding Z dimensions not similar to theta's dimensions.

please clear why you have used different variables in cost fumctiof and Backpropagation

Just to keep two implementations separate for easy understanding of users.

Your Program is not running. When I try to run this program sigmoidGradient.m it says error in line 9. Now what is the error ?

Hi Sarthak, You should also post the error you are getting. All above programs are working and tested by me multiple times.

The program is giving the following error when runnning the nnCostFunction.m Error using == Matrix dimensions must agree. Error in nnCostFunction (line 87) y_Vec = (1:num_labels)==y; % m x num_labels == 5000 x 10

Hi Andrew,when I tried to test the sigmoid gradient descent by inputing the code g = sigmoid(z).*(1-sigmoid(z)); I got the following error: undefined function or variable 'z'. Please why is this happening?

Hi, I am not Andrew. I am Akshay. I think you are doing this assignment in Octave and that's why you are facing this issue. Chethan Bhandarkar has provided solution for it. Please check it out: https://www.apdaga.com/2018/06/coursera-machine-learning-week-2.html?showComment=1563986935868#c4682866656714070064 Thanks

You'll be getting this error because you are running your program sigmoidGradient.m The variable z is defined in the main ex4.m file. So run the ex4.m file after running the sigmoidGradient.m file.

Hi Akshay,the link you sent is for week2 and referring to week5

In the link I have provided, Go and check the comment by "Chethan Bhandarkar" She has provided the solution for the similar to your problem.

Hi Akshay, I have a quick Q about the delta2 calculation in the 'nnCostFunction.m' delta2 = (Theta2' * delta3) .* [1; sigmoidGradient(z2)]; % (hidden_layer_size+1) x 1 == 26 x 1 Why do you use a '1' --> .* [1; sigmoidGradient(z2)]; and just not multiply by the --> .* sigmoidGradient(z2) ? thank you in advance Bruno

I have entered same code u mentioned for nncostfunction and submit it but backward propagation part has not submitted. A1 = X; % 5000 x 401 Z2 = A1 * Theta1'; % m x hidden_layer_size == 5000 x 25 A2 = sigmoid(Z2); % m x hidden_layer_size == 5000 x 25 A2 = [ones(size(A2,1),1), A2]; % Adding 1 as first column in z = (Adding bias unit) % m x (hidden_layer_size + 1) == 5000 x 26 Z3 = A2 * Theta2'; % m x num_labels == 5000 x 10 A3 = sigmoid(Z3); % m x num_labels == 5000 x 10 % h_x = a3; % m x num_labels == 5000 x 10 y_Vec = (1:num_labels)==y; % m x num_labels == 5000 x 10 DELTA3 = A3 - y_Vec; % 5000 x 10 DELTA2 = (DELTA3 * Theta2) .* [ones(size(Z2,1),1) sigmoidGradient(Z2)]; % 5000 x 26 DELTA2 = DELTA2(:,2:end); % 5000 x 25 %Removing delta2 for bias node Theta1_grad = (1/m) * (DELTA2' * A1); % 25 x 401 Theta2_grad = (1/m) * (DELTA3' * A2); % 10 x 26 %%%%%%%%%%%% WORKING: DIRECT CALCULATION OF THETA GRADIENT WITH REGULARISATION %%%%%%%%%%% % %Regularization term is later added in Part 3 % Theta1_grad = (1/m) * Theta1_grad + (lambda/m) * [zeros(size(Theta1, 1), 1) Theta1(:,2:end)]; % 25 x 401 % Theta2_grad = (1/m) * Theta2_grad + (lambda/m) * [zeros(size(Theta2, 1), 1) Theta2(:,2:end)]; % 10 x 26 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%% Part 3: Adding Regularisation term in J and Theta_grad %%%%%%%%%%%%% reg_term = (lambda/(2*m)) * (sum(sum(Theta1(:,2:end).^2)) + sum(sum(Theta2(:,2:end).^2))); %scalar %Costfunction With regularization J = J + reg_term; %scalar %Calculating gradients for the regularization Theta1_grad_reg_term = (lambda/m) * [zeros(size(Theta1, 1), 1) Theta1(:,2:end)]; % 25 x 401 Theta2_grad_reg_term = (lambda/m) * [zeros(size(Theta2, 1), 1) Theta2(:,2:end)]; % 10 x 26 %Adding regularization term to earlier calculated Theta_grad Theta1_grad = Theta1_grad + Theta1_grad_reg_term; Theta2_grad = Theta2_grad + Theta2_grad_reg_term;

My first concern is "Why did you copied the code as it is ?". Understand the code and do it on your own. Above code is just for reference. I have tested all my codes multiple times and they are 100% correct.

HI Akshay, thanks for your great work, could you please explain the below code, DELTA2 = (DELTA3 * Theta2) .* [ones(size(Z2,1),1) sigmoidGradient(Z2)]; % 5000 x 26

Hi Akshay, My approach to this problem is somewhat similar to yours (i.e going from part 1 to part 3 in exact order). However the relative difference I am getting is far to high. Don't you think we should first calculate regularised cost function before implementing backpropogation? What difference will it make? Also I have used a slightly different function to generate randomized initial weights assuming it is random anyways. Can that cause any problem?

Hey, Why we are initialising epsilon as epsilon_init = sqrt(6)/(sqrt(L_in)+sqrt(L_out)); Why by 6?

Please refer theory lecture for that.

refer ex4 pdf file

y_Vec = (1:num_labels)==y; ...what is this line of code doing ..plz help me get a clear picture. i it converting y to a vector

This line of code does exact same operation as below: y_Vec = zeros(m,num_labels); for i = 1:m y_Vec(i,y(i)) = 1; end

yeah thats what you have also commented in the code as well, but brother will you please elaborate, why it is done and also please provide a picture if you can, i tried it but i cannot visualize it

%%%%% WORKING %%%%% % y_Vec = zeros(m,num_labels); % for i = 1:m % y_Vec(i,y(i)) = 1; % end %%%%%%%%%%%%%%%%%%% OR y_Vec = (1:num_labels)==y; ---------------------------------------------------------- % yVector = (1:num_labels)'==y(t); why it is in the code, what it is doing and how to visualize this, Brother?. Thanks From Gujarat?

Please read about vectorized implemention. vectorized implementation is faster than for loop because it does operations on the all elements of the matrix / array simultaneously. About the above code, It is "%Converting y into vector of 0's and 1's for multi-class classification" 1. Initialing y_Vec as Zero matrix 2. then as per the multiclass, it is assigning 1 for correct category. NOTE: each row in y_Vec correspond to one inplut example (x) each column in y_vec represent output category. (1 represent correct category, 0 means incorrect)

Cheers from brazil,my friend. This was of great help!!

Thank you very much for the appreciation.

Hi Akshay, Thanks for the guide. I had a question regarding the following code: Theta1_grad_reg_term = (lambda/m) * [zeros(size(Theta1, 1), 1) Theta1(:,2:end)]; % 25 x 401 Theta2_grad_reg_term = (lambda/m) * [zeros(size(Theta2, 1), 1) Theta2(:,2:end)]; % 10 x 26 I'm not sure why the zeros(size(Theta1, 1), 1) is combined with the Theta1. I know from the lectures the formula to calculate the reg term is just: lambda/m * Thetaij ^ (L). Can you help me get a better understanding? I wasn't able to finish this part before the due date.

As per the theory in lectures, you don't apply regularization on theta_0, so, to exclude theta_0 from regularization we have replaced it with 0. so, regularization effected will be nullified for theta_0. (since, 0 multiplied by anything is 0). In other words, we have applied regularization on 2nd entry to last entry using Theta1(:,2:end) and first entry i.e. theta_0 is replaced by 0 using zeros(size(Theta1, 1), 1))

Hey,i'm get this type of error in random.....m ਀warning: function 'randInitializeWeights' defined within script file 'C:\Users\admin\Desktop\ML i mportant\machine-learning-ex4\ex4\randInitializeWeights.m' error: 'L_out' undefined near line 14 column 11 error: called from randInitializeWeights at line 14 column 3

i know it doesn't matter much, but isn't it "sqrt(L_in+L_out)" not "sqrt(L_in)+sqrt(L_out)"

I have a similar question.

hi i am getting my answer as 0.0000 for everything be it forward propagation, backpropagation.. could you please tell where i can be wrong?

Maybe you should check your randomInitializeWeights

Thank you so much, clearly explained each line of code.Its very helpful.

Thanks for the appreciation 🙏🏻

Thank you, its really helping me a lot how to figure out the code and steps.

Hey Akshay it's a great work

I’m getting 0.0000 for all the answers and I have checked for errors, there are none.

Hi! In [y_Vec = zeros(m,num_labels); for i = 1:m y_Vec(i,y(i)) = 1; end] and [y_Vec = (1:num_labels)==y; ] Is y_Vec a 5000x10 matrix?? Why so?? Or should it be 10x1??

Yes, y_Vec is 5000x10 i.e. m x num_labels y_Vec = (1:num_labels)==y; % m x num_labels == 5000 x 10

Just wanna say thank you! Seeing the differences between the iterative and vectorized approaches helped a lot!

You are always welcome. Glad to know that my work helped you.

Hi.Thanks for your help.I had a question: I used this cost function (J = (1/m)*(-y'*log(h)-((1-y)')*log(1-h))) for my logistic regression assignment and it worked. I was wondering why can't I use the same thing here for neural network like (J = (1/m)* sum(sum((-y'*log(h)-((1-y)')*log(1-h)))) ) since the cost function formulas of both logistic regression and neural network look almost the same.

Here y and log(h) are two dimensional while in case of logistic regression they were one dimensional.

I'm getting the submission failed and the following error. Please help me!! unexpected error: Out of memory. The likely cause is an infinite recursion within the program. !! Please try again later.

Im the regularization for Theta_grad, why is the zeros necessary?

can u explain the step wise code used in each of the assignments

I have already written comments for important lines of code. Please refer those comments.

I highly appreciate you explainations within the code. And also you have given the code in a very much step by step manner making each and everyone understands the code and the logic involved in it. GOOD JOB

Thank you 😊

why do you considered h_x = a3 ?

because a3 is the output of 3rd layer and also the final output of the Neural Network. which mean a3 is the predicted output (Which is also denoted by h_x). That's why h_x = a3. For more & better clarification, go through the respective theory video from the course.

sh: 1: curl: not found [error] submission with curl() was not successful !! Submission failed: Grader sent no response Function: submitWithConfiguration>validateResponse FileName: /home/bhargava/Downloads/ex4/lib/submitWithConfiguration.m LineNumber: 156 Please correct your code and resubmit. I am getting this error. Can someone please help?

Could you explain DELTA2 = (DELTA3 * Theta2) .* [ones(size(Z2,1),1) sigmoidGradient(Z2)]; % 5000 x 26 Because DELTA3 = 5000x10 and Theta2 = 10x26, how does this product work?

The codes and comments were very helpful Thank you.

Thank you for your kind words.

Error in submitWithConfiguration (line 4) parts = parts(conf); Error in submit (line 35) submitWithConfiguration(conf);

Submission failed: unexpected error: Undefined function 'makeValidFieldName' for input arguments of type 'char'. I am getting this error after am submitting Can anyone help me out

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Programming in Java | Week 5

Session: JAN-APR 2024

Course name: Programming In Java

Course Link: Click Here

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These are NPTEL Programming In Java Week 5 Assignment 5 Answers

Q1. Which of the following is an incorrect statement about interfaces? a. Interfaces specifies what class must do but not how it does. b. Interfaces are specified public if they are to be accessed by any code in the program. c. All variables in interface are implicitly final and static. d. All variables are static and methods are public if interface is defined public.

Answer: d. All variables are static and methods are public if interface is defined public.

Q2. How do you access a static method of an interface? a. Using the interface name b. Using the method name directly c. Through an object of the interface d. Through an implementation class

Answer: a. Using the interface name

Q3. What is the output of the below Java program with an Interface? a. 1000 b. 2000 c. Compiler error d. None of the above

Answer: c. Compiler error

Q4. What happens when we access the same variable defined in two interfaces implemented by the same class? a. Compilation failure b. Runtime Exception c. The JVM is not able to identify the correct variable d. The interfaceName.variableName needs to be defined

Answer: d. The interfaceName.variableName needs to be defined

Q5. Predict the output of following Java program a. Got the Test Exception Inside finally block b. Got the Test Exception c. Inside finally block d. Compiler Error

Answer: a. Got the Test Exception Inside finally block

Q6. What happens if an exception is not caught in the catch block? a. The finally block handles it b. The exception is ignored c. The exception is thrown to the caller method d. The program terminates immediately

Answer: c. The exception is thrown to the caller method

Q7. What will be the output of the following Java program? a. Hello b. World c. HelloWorld d. Hello World

Answer: b. World

Q8. What is the output of the below Java code with Exceptions? a. Index 4 out of bounds for length 3 b. Index 4 out of bounds for length 3 Some exception c. Some exception d. No exception occurs

Answer: a. Index 4 out of bounds for length 3

Q9. What is the output of the Java code with FINALLY block and RETURN statement? a. inside TRY b. inside TRY inside FINALLY c. inside FINALLY d. Compiler error

Answer: b. inside TRY inside FINALLY

Q10. What is the purpose of the finally block in Java exception handling? a. To handle an exception b. To catch an exception c. To clean up resources after a try block d. None of the above

Answer: c. To clean up resources after a try block

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Session: JULY-DEC 2023

Course Name: Programming In Java

Programming Assignment

Question 1 An interface Number is defined in the following program. You have to declare a class A, which will implement the interface Number. Note that the method findSqr(n) will return the square of the number n.

Question 2 This program is to find the GCD (greatest common divisor) of two integers writing a recursive function findGCD(n1,n2). Your function should return -1, if the argument(s) is(are) other than positive number(s).

Question 3 Complete the code segment to catch the ArithmeticException in the following, if any. On the occurrence of such an exception, your program should print “Exception caught: Division by zero.” If there is no such exception, it will print the result of division operation on two integer values.

Question 4 In the following program, an array of integer data to be initialized. During the initialization, if a user enters a value other than integer value, then it will throw InputMismatchException exception. On the occurrence of such an exception, your program should print “You entered bad data.” If there is no such exception it will print the total sum of the array.

Question 5 In the following program, there may be multiple exceptions. You have to complete the code using only one try-catch block to handle all the possible exceptions. For example, if user’s input is 1, then it will throw and catch “java.lang.NullPointerException“.

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Session: JAN-APR 2023

Course Name: Programming in Java

Q1. Consider the following program. If the program is executed, then what will be the output? a. 22 b. 33 c. 23 d. 32

Answer: c. 23

Q2. Consider the following piece of code. ‘Which of the following statement(s) is/are true for the above code? a. Itis an empty interface. b. Itis a tag interface. c. It is a marker interface. d. Itis a nested interface.

Answer: a, b, c

Q3. What is the output of the following code? a. java 10 b. java 20 c. 10 java d. 20 java

Answer: a. java 10

Q4. ‘Which of the following statement(s) is/are true? a. All abstract methods defined in an interface must be implemented. b. The variables defined inside an interface are static and final by default. c. An interface is used to achieve full abstraction. d. Inside an interface, a constructor can be called using the super keyword with hierarchy.

Q5. Which of the following statement(s) is/are true? 1. A class can extend more than one class. 2. A class can extend only one class but many interfaces. 3. An interface can extend many interfaces. 4. An interface can implement many interfaces. 5. A class can extend one class and implement many interfaces. a. 1 and 2 b. 2 and 4 c. 3 and 5 d. 3 and 4

Answer: c. 3 and 5

Q6. ‘Which of the following statement(s) is/are true? a. Abstract class can have abstract and non-abstract methods. b. Abstract class can have final, non-final, static and non-static vanables. c. Interface has only static and final vaniables. d. Interface can provide the implementation of an abstract class.

Q7. Consider the following piece of code. What is the output of the above code? a. A b. B c. BC d. AC

Answer: c. BC

Q8. The class at the top of exception class hierarchy is ………….. a. Object b. Throwable c. Exception d. ArthmeticException

Answer: b. Throwable

Q9. Which of these class is superclass of every class in Java? a. Object class b. Abstract class c. String class d AmayList class

Answer: a. Object class

Q10. If the program is executed, then what will be the output? a. 012 b. 004 c. 024 d. 044

Answer: b. 004

Programming Assignment of Programming in Java

Complete the code segment to catch the ArithmeticException in the following, if any. On the occurrence of such an exception, your program should print “Exception caught: Division by zero.” If there is no such exception, it will print the result of division operation on two integer values.

In the following program, an array of integer data to be initialized. During the initialization, if a user enters a value other than integer value, then it will throw InputMismatchException exception. On the occurrence of such an exception, your program should print “You entered bad data.” If there is no such exception it will print the total sum of the array.

In the following program, there may be multiple exceptions. You have to complete the code using only one try-catch block to handle all the possible exceptions. For example, if user’s input is 1, then it will throw and catch “java.lang.NullPointerException“.

An interface Number is defined in the following program. You have to declare a class A, which will implement the interface Number. Note that the method findSqr(n) will return the square of the number n.

This program is to find the GCD (greatest common divisor) of two integers writing a recursive function findGCD(n1,n2). Your function should return -1, if the argument(s) is(are) other than positive number(s).

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Session: JULY-DEC 2022

Course Name: Programming in Java NPTEL

Q1. Consider the following program. If the program is executed, then what will be the output from the execution? a. 100 102 b. 20 22 C. 102 100 d. 22 20

Answer: a. 100 102

Q2. Consider the following program. If the program is executed, then what will be the output from the execution? a. 170 b. 130 c. 0 d. 260

Answer: a. 170

Q3. What is the output of the following code? a. Output: This is Explanation’s Print method This is Answer’s Print method b. Error: super.super’ is not allowed. c. Error: Compilation unsuccessful, as there is only one super class of Answer d. Output: This is Answer’s Print method This is Explanation’s Print method

Answer: b. Error: super.super’ is not allowed.

Q4. Which of the following is/are interface(s)? a. DriverManager b. Connection c. Statement d. ResultSet

Answer: b, c, d

Q5. Which of the following statement(s) is/are true? a. You can write a new instance method in the subclass that has the same signature as the one in the superclass, thus overriding it. b. You can write a new static method in the subclass that has the same signature as the one in the superclass, thus hiding it. c. A subclass inherits all of the public and protected members of its parent, no matter what package the subclass is in. d. You cannot declare new methods in the subclass that are not in the superclass.

Q6. Which of the following statement(s) is/are true? a. Static methods in interfaces are never inherited. b. You will get a compile-time error if you attempt to change an instance method in the superclass to a static method in the subelass. / c. You can prevent a class from being sub classed by using the final keyword in the class’s declaration. d. An abstract class can only be subclassed; it cannot be instantiated.

Answer:a, b, c, d

Q7. Consider the following piece of code: Which of the following statement(s) is/are correct? a. There is no main () method so the program is not compile successfully. b. The value of i will be printed as 22, as it is static and final by default. c. The value of I will be printed as 2. as it is initialized in class B. d. Compile time error

Answer: a. There is no main () method so the program is not compile successfully.

Q8. Which of the following statement(s) is/are true? a. A class can extend more than one class. b. An interface can extend many interfaces. c. An interface can implement many interfaces. d. A class can extend one class and implement many interfaces.

Answer: b, d

Q9. All classes in Java are inherited from which class? a. java.lang.class b. java.class.inherited c. java.class.object d. java.lang.Object

Q10. If the program is executed, then what will be the output from the execution? a. Output: 1020 b. Output : 30 c. Output: 2010 d. Error: Cl is abstract; cannot be instantiated.

Programming Assignment Solutions

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