coursera machine learning assignment week 6

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Coursera: Machine Learning (Week 6) Quiz - Machine Learning System Design | Andrew NG

▸ machine learning system design :.

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

0.16 Precision is 0.087 and recall is 0.85, so F1 score is (2 * precision * recall) / (precision + recall) = 0.158.

You should use a “low bias” algorithm with many parameters, as it will be able to make use of the large dataset provided. If the model has too few parameters, it will underfit the large training set.

It is important that the features contain sufficient information, as otherwise no amount of data can solve a learning problem in which the features do not contain enough information to make an accurate prediction.

As we saw with neural networks, polynomial features can still be insufficient to capture the complexity of the data, especially if the features are very high-dimensional. Instead, you should use a complex model with many parameters to fit to the large training set.

• We train a learning algorithm with a small number of parameters (that is thus unlikely to overfit).

Even with a very large dataset, some regularization is still likely to help the algorithm’s performance, so you should use cross-validation to select the appropriate regularization parameter.

The problem of skewed classes is unrelated to training with large datasets.

You should use a complex, “low bias” algorithm, as it will be able to make use of the large dataset provided. If the model is too simple, it will underfit the large training set.

This is a nice project commencement briefing.

• The classifier is likely to have unchanged precision and recall, but higher accuracy.
• The classifier is likely to now have higher recall.

Increasing the threshold means more y = 0 predictions. This will decrease both true and false positives, so precision will increase.

• The classifier is likely to have unchanged precision and recall, and thus the same F1 score.

Increasing the threshold means more y = 0 predictions. This increase will decrease the number of true positives and increase the number of false negatives, so recall will decrease.

• The classifier is likely to now have lower precision.
• The classifier is likely to have unchanged precision and recall, but lower accuracy.

Recall = (true positives) / (true positives + false negatives) Decreasing the threshold means less y = 0 predictions. This will increase true positives and decrease the number of false negatives, so recall will increase.

• The classifier is likely to now have higher precision.
• The classifier is likely to now have lower recall.

Lowering the threshold means more y = 1 predictions. This will increase both true and false positives, so precision will decrease.

For data with skewed classes like these spam data, we want to achieve a high F1 score, which requires high precision and high recall.

Since 99% of the examples are y = 0, always predicting 0 gives an accuracy of 99%. Note, however, that this is not a good spam system, as you will never catch any spam.

The classifier achieves 99% accuracy on the training set because of how skewed the classes are. We can expect that the cross-validation set will be skewed in the same fashion, so the classifier will have approximately the same accuracy .

The classifier achieves 99% accuracy on the training set because of how skewed the classes are. We can expect that the cross-validation set will be skewed in the same fashion, so the classifier will have approximately the same accuracy.

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A sufficiently large training set will not be overfit, as the model cannot overfit some of the examples without doing poorly on the others.

You can and should adjust the threshold in logistic regression using cross validation data.

If the model is underfitting the training data, it has not captured the information in the examples you already have. Adding further examples will not help any more.

It is not recommended to spend a lot of time collecting a large data

You can always achieve high accuracy on skewed datasets by predicting the most the same output (the most common one) for every input. Thus the F1 score is a better way to measure performance.

This process of error analysis is crucial in developing high performance learning systems, as the space of possible improvements to your system is very large, and it gives you direction about what to work on next.

#5 "Using a very large training set makes it unlikely for model to overfit the training data." This one is correct.

Thanks for the feedback. I really appreciate your feedback. I verified it and made the correction in the post.

#3 The classifier is likely to now have higher precision should not be selected Increasing the threshold means more y = 0 predictions. This will decrease both true and false positives, so precision will increase, not decrease.

If you check carefully, There are 2 different questions marked as Q3. 1) Increase Threshold to 0.9 (from 0.5) [Correct answers are:] > a) The classifier is likely to now have higher precision b) The classifier is likely to now have lower recall. 2) Decrease Threshold to 0.3 (from 0.5) [Correct answers are:] > a) The classifier is likely to now have higher recall. b) The classifier is likely to now have lower precision.

For #4: If you always predict spam (output y=1y=1), your classifier will have a recall of 100% and precision of 1%. Correct Since every prediction is y = 1, there are no false negatives, so recall is 100%. Furthermore, the precision will be the fraction of examples with are positive, which is 1%. If you always predict non-spam (output y=0y=0), your classifier will have an accuracy of 99%. Correct Since 99% of the examples are y = 0, always predicting 0 gives an accuracy of 99%. Note, however, that this is not a good spam system, as you will never catch any spam. If you always predict non-spam (output y=0y=0), your classifier will have a recall of 0%. Correct Since every prediction is y = 0, there will be no true positives, so recall is 0%.

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Coursera: Machine Learning (Week 4) [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

• ex3.m - Octave/MATLAB script that steps you through part 1
• ex3 nn.m - Octave/MATLAB script that steps you through part 2
• ex3data1.mat - Training set of hand-written digits
• ex3weights.mat - Initial weights for the neural network exercise
• 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
• [*] lrCostFunction.m - Logistic regression cost function
• [*] oneVsAll.m - Train a one-vs-all multi-class classifier
• [*] predictOneVsAll.m - Predict using a one-vs-all multi-class classifier
• [*] predict.m - Neural network prediction function
• Video - YouTube videos featuring Free IOT/ML tutorials

lrCostFunction.m :

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

predict.m :

54 comments.

hey! In predict.m file theta should be = 25*401 not 26*401; wrong: % theta dimensions = S_(j+1) x ((S_j)+1) % theta1 = 26 x 401 % theta2 = 10 x 26 correct: % theta dimensions = S_(j+1) x ((S_j)+1) % theta1 = 25 x 401 % theta2 = 10 x 26

correct me.If I am wrong.

Thanks Bhupesh. You are right.

Hi Akshay I still did not understand how we arrived at the theta sizes. We only know the activation nodes in the first layer = 400 and in the last layer (output) = 10. We have no information relating to the second layer. Can you please elaborate? Thanks

@Unknown details for the layer2 is given in the question itself. I have also mentioned in the comments in code as below. (please read the question carefully once again.) % layer1 (input) = 400 nodes + 1bias % layer2 (hidden) = 25 nodes + 1bias % layer3 (output) = 10 nodes

Got it, thanks very much.

predict.m is not working

What error you are getting?

Hey, could you explain how "[prob, p] = max(a3,[],2);" is working in predict.m

Hi Iam getting error =: nonconformant arguments (op1 is 1x1, op2 is 1x2) at line using the code grad(1) = (1/m) * (X(:,1)'*(h_x-y)); in IrCostFunction

Mentioned error says there is some matrix dimension mismatch in variable op1 & op2. I don't see any variables as op1 & op2 in my code. Please check once again.

Hi Akshay I am having the same problem too when trying to submit my solutions. The error message is: !! Submission failed: product: nonconformant arguments (op1 is 20x3, op2 is 3x1) Function: lrCostFunction LineNumber: 46 Appreciate your help to troubleshoot this? Thanks

I got the same error and after I have figured it out. It is because of wrong implementation of sigmoid. you might have writing code as g = 1/(1+exp(-z)) but z can be matrix so operation should be element wise. find out correct implementation. ex = exp(z.*(-1)); din = 1.+ex; g = 1./din;

Sigmoid function is missing in predictOneVsAll

Sigmoid is not used as we need to get the maximum value of Theta*x as h(x) =Sigmoid(1/(1+e^theta*x)). this E (0,1) To predict the value to highest we need theta*x as maximum. Hence sigmoid is not used.

will you please tell me what is t here? @(t)(lrCostFunction(t, X, (y == c), lambda)

why do to separate grad into two line? like seen below grad(1) = (1/m) * (X(:,1)'*(h_x-y)); grad(2:end) = (1/m) * (X(:,2:end)'*(h_x-y)) + (lambda/m)*theta(2:end); Just writing it as grad = (1/m) * (X'*(h_x-y)) + (lambda/m)*theta; works fine or am i missing something here?

As per the theory, we don't do regularization for first term. and we apply regularization from 2nd term onward. that's why we have to do it separately. Watch the related theory video once again carefully.

Thankyou for your help it's really great of you , i just wanted to know 2 things (1) always i start with an programming assignment i get really confused and dont understand where and how to start , so i first refer to your code understand it thoroughly and proceed with the assignment , i wanted to know how correct it is to do (2) why have we used [prob , p] and and what are it's further intuations in the code , i mean why have we used 2 variables 'prob' & 'p'

Hi Rohan, (1) I think you should understand the problem first, then try to solve it your way. and if stuck in between or couldn't understand the problem then only you should check out my code for understanding purpose and then start solving your assignment. (Please don't just copy paste the code as it is) (2) In predict function, we calculate probability for each class (for multi-class problem) then find out the maximum probability. "prob" variable has value of probability and "p" variable has index of probability. more the probability means more matching. then we use variable "p" to represent predicted class (category). which is nothing but the index of the maximum probability (prob). I hope, I made it clear. If you still find it difficult to understand, please go through the theory lecture once again.

absolutely clear , thanks for the support

Hi Akshay Thanks for creating this amazing forum for us like minded people. Had a couple of queries: 1. Am not able to understand the variables of fmincg function (despite of using 'help'. It would be great if someone could help me with the same ! 2. What do the three dots (...) in the line preceding the fmincg function specify ? Why are they needed ? (tried running the function without them but it pointed out as syntax error ! Thanks in advance.

Thank you very much for your appreciation. 1. fmincg is explained a little bit in theory lecture. (Honestly, Even I have to check it in details) 2. Three dots (...) are nothing but "Lin Continuation character" in MATLAB. DESCRIPTION: Three or more periods at the end of a line continues the current command on the next line. If three or more periods occur before the end of a line, then MATLAB ignores the rest of the line and continues to the next line. This effectively makes a comment out of anything on the current line that follows the three periods.

None of the coed are working, getting 0/100

Hi Qwert123, I think you are doing something wrong. Because the codes were 100% working for me and they are still working for many of my viewers. (you can get idea from comments). And anyways, these codes are just for understanding. Get the idea from the above codes and make your own solution and try to submit. Thank you.

how were you able to solve onevsall.m predictOneVsAll.m and predict.m bc i am trying to understand the problem and i am not getting how should i solve it

Can anyone explain what "theta_t" is? Why and how they coose some random value "[-2; -1; 1; 2]" (in ex.m).

Sorry, I don't see any "theta_t" in my code.

Hi Akshay , It is showing error as unprecedented parameter name 'GrabObj'

Hi Akshay, In OneVsall.m,it is saying IrCostFunction is undefined. Why is it so?

Hello, Can you help me resolve this octave:7> oneVsAll.m error: 'X' undefined near line 11 column 10 error: called from oneVsAll at line 11 column 3

Instead of running oneVsAll.m file, please run the (.m) file in which all above function are called. Don't run those individual (.m) files in which the functions are defined.

Hi..... I used same to same implementation but the cost of my set is coming out to be 45.73 in contrast to the expected cost of 2.53. I am using the same logic as yours but I dont know why is this happening. Can you plz help me out?

Did you find the solution? Cos am having the same problem here.

I found the solution. His vectorizing formulas are wrong. He needed to use scalar multipication in some of them. Try the code below. It works %100 z = X * theta; % m x 1 h_x = sigmoid(z); % m x 1 reg_term = (lambda/(2*m)) .* sum(theta(2:end).^2); J = (1/m).*sum((-y.*log(h_x))-((1-y).*log(1-h_x))) + reg_term; % scalar grad(1) = (1/m). * (X(:,1)'*(h_x-y)); % 1 x 1 grad(2:end) = (1/m). * (X(:,2:end)'*(h_x-y)) + (lambda/m).*theta(2:end); % n x 1

@Ozan Kocabs All vectorized implemented formulas provided by me are 100% right. When you multiply a scalar (constant) with any matrix, you don't have to use ".*" (dot star), only "*" (star) is enough to multiply all the elements of the matrix by that constant. You might have some other mistake which caused the different cost value. Please check and find out the correct root cause of your problem. NOTE: For 2nd check, I ran my code once again and tested it just now and it is giving the correct output. ... Testing lrCostFunction() with regularization Cost: 2.534819 Expected cost: 2.534819 ...

I dont know why it resulted in 5 different values in my results. It was like 5x1 matrice all resulting 45,73 and after i put some scalar multipication problem solved. I have just used your code once again and it worked. U are right. But i dont know why it didnt work at first. Thanks you mate. You are a life saver:)

Hi Akshay, I have used the same code as yours in predict.m Within the exercise code i am getting training exercise accuracy as expected (97.5%). Also the digit is also being recognized correctly. But when i am submitting the code for grading, i am getting the following error: !! Submission failed: unexpected error: Index exceeds the number of array elements (16). !! Please try again later. Thanks in advance for the help.

Please compare your code with the one given above and check if the dimensions are matching or not. Please use the comments given in each in above code. That will help you understand what that particular line of code signifies.

Could you please explain the line all_theta(c,:) = ... in onevsall. I got stuck for this an hour

I dont know , i am getting iteration and cost on output console here i am posting some of them. Please help as i am stuck there for more than one day. Iteration 16 | Cost: 1.018509e-01 Iteration 17 | Cost: 1.018509e-01 Iteration 18 | Cost: 1.018509e-01 Iteration 19 | Cost: 1.018509e-01 Iteration 20 | Cost: 1.018509e-01 Iteration 21 | Cost: 1.018509e-01 Iteration 22 | Cost: 1.018509e-01 Iteration 23 | Cost: 1.018509e-01 Iteration 24 | Cost: 1.018509e-01 Iteration 25 | Cost: 1.018509e-01 Iteration 26 | Cost: 1.018509e-01 all_theta = -0.5595 0.6192 -0.5504 -0.0935 -5.4744 -0.4716 1.2613 0.6349 0.0684 -0.3756 -1.6523 -1.4101

missing ';' in code?

Hi could you please help me? this is my code on lrcostfunction: H = sigmoid(X*theta); T = y.*log(H) + (1 - y).*log(1 - H); J = -1/m*sum(T) + lambda/(2*m)*sum(theta(2:end).^2); ta = [0; theta(2:end)]; grad = X'*(H - y)/m + lambda/m*ta; but im getting this error: >> lrCostFunction Not enough input arguments. Error in lrCostFunction (line 9) m = length(y); % number of training examples I try using your code to check if i was wrong but i got the same error could you help me? please

Hey, I have question and that is when we were calculating grad in week 3 assignment we include grad(1) = (1/m)* sum(X(:,1)'*(hx-y)); grad(2:end) = (1/m)* sum(X(:,2:end)'*(hx-y))+(lambda/m)*theta(2:end); Now, when we calculate in week 4 we remove "sum" in both equations, my question is why we remove sum and when I calculate with sum it's provides wrong answer.

I don't see any sum function used in calculating grad even in assignment 3. Here is the link for assignment 3 solution- https://www.apdaga.com/2018/06/coursera-machine-learning-week-3.html#costFunctionReg Please check it out.

Hi for the oneVsAll.m problem, how would the code look like if you don't use the fmincg function, I'm kinda lost on the process of how to get all_theta

can you send submit.m and submit confg file of the of this experiment

i am getting error at predict.m file error: called from predict at line 7 column 5

it might be some silly mistake near line 6 or 7. Please check. You will resolve it yourself.

I am trying to submit the whole package. All scripts so far are running and give me the correct answer, but when I submit to the test servers, I get an error on the size of a matrix !! Submission failed: unexpected error: Matrix dimensions must agree. !! Please try again later. How can I fix this error? Thanks

In predict.m why do we have to do a1 * Theta1' instead of Theta1 * a1'?

i am getting a very high cost function that is around 45.734819. plese tell me why i am getting this.

Hello Akshay, I have a question in relation to the prediction part. I understand the creation of all_theta, using the fmincg function to create theta parameters that fit the particular number from 1-10, but my question is, that once you multiply X * all_theta', you receive the 5000 x 10 matrix, which is the 5000 samples x (10) the value at each number prediction. How do we know, that the maximum value will be reflecting the number which is most likely thanks to our prediction. So why is it not the minimum value or etc. Why do we know that the column with the maximum value, will equal the number we predict.

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