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Can anyone help me transform this double sum into a big vector operation?
\[\frac{1}{m} * \sum_{i=1}^{m}{\sum_{k=1}^{k}{[y_{k}^{(i)}\log((h_{\theta}(x)^{(i)}))_k)  (1  y_{k}^{(i)})\log(1(h_{\theta}(x^{(i)}))_k)]}}\]
 2 years ago
 2 years ago
Can anyone help me transform this double sum into a big vector operation? \[\frac{1}{m} * \sum_{i=1}^{m}{\sum_{k=1}^{k}{[y_{k}^{(i)}\log((h_{\theta}(x)^{(i)}))_k)  (1  y_{k}^{(i)})\log(1(h_{\theta}(x^{(i)}))_k)]}}\]
 2 years ago
 2 years ago

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agdgdgdgwngoBest ResponseYou've already chosen the best response.1
think of the i's as the i'th row of a matrix, and the k as the k'th element of that row (vector)
 2 years ago

JamesJBest ResponseYou've already chosen the best response.0
I suggest you think exactly what all this notation means (which is not obvious to the rest of us with no context) and I imagine there is a way to convert this into an inner product calculation and/or matrix operation.
 2 years ago

agdgdgdgwngoBest ResponseYou've already chosen the best response.1
btw can we move the sum symbols around? so the k sum comes before the m sum?
 2 years ago

agdgdgdgwngoBest ResponseYou've already chosen the best response.1
I had one like this (with only the sigma from one to m) and made it into an inner product calculation, but the new sigma symbol is giving me hell :(
 2 years ago

agdgdgdgwngoBest ResponseYou've already chosen the best response.1
we're summing up all the vectors produced by that expression inside those brackets, and then we're summing up the elements of that one big vector.
 2 years ago

dmancineBest ResponseYou've already chosen the best response.0
This is from Neural Networks in the Stanford Machine Learning class. I think I got the inner sum vectorized. I made yi be a zerovector of size K, then set the y(i)th element be 1. Then I assigned the output activations to h (just to make it look more like the formula). Then the inner sum just became yi' * log(h) + (1yi') * log(1h). I guess I could omit the transposes and turn the multiplications into ".*". But I'm having a devil of a time creating a Y matrix where row i is the yi I gave above. I can create a 5000x10 matrix of zeros (easy). Then I want to use y (the 5000x1 label vector) as indices into each row of Y, and set those entries to 1. Something like Y(y) = 1, but that doesn't work. I'm reading about indexing right now to try to figure it out. I was able to figure out a vectorized cost function for last week's homework, so once I get this Y figured out I think I'll have it.
 2 years ago

ineedbiohelpandquickBest ResponseYou've already chosen the best response.1
How the thing go with the girl
 2 years ago

agdgdgdgwngoBest ResponseYou've already chosen the best response.1
@dmancine Yeah I finally figured it out. I used a for loop to construct that new y matrix, and then used another for loop to loop over each training example, but I cloned the vectorized computation of the cost for each example over so it's reasonably fast :P
 2 years ago

agdgdgdgwngoBest ResponseYou've already chosen the best response.1
I just set a new y matrix to be equal to a matrix of zeros of size m x num_labels and then I used a forloop. can't show actual code or we will get flamed for honor code stuff :D
 2 years ago

agdgdgdgwngoBest ResponseYou've already chosen the best response.1
I do think the whole thing can be vectorized into a oneliner, but I just want to get this assignment done :P
 2 years ago

agdgdgdgwngoBest ResponseYou've already chosen the best response.1
Finally got this assignment done (just now, which is about 2 hours before the due time!) I struggled to implement a forloop based backpropagation, but I became so frustrated with the 'nonconforming operands' errors that I just went with vectorization for the whole problem.
 2 years ago

agdgdgdgwngoBest ResponseYou've already chosen the best response.1
here's one way to transform that y matrix into an array of classification vectors: yi = eye(num_labels)(y,:);
 2 years ago

dmancineBest ResponseYou've already chosen the best response.0
Whew! 20 minutes to spare!
 2 years ago

dmancineBest ResponseYou've already chosen the best response.0
@agd, That's the formula I was trying to think of. I even thought about indexing into the eye matrix. I just couldn't get all the way to the end. Thanks! In the ex4.pdf he suggests using logical arrays might be helpful for this, and they were explained in the previous programming exercise. I haven't figured out how to use that, yet, either.
 2 years ago

agdgdgdgwngoBest ResponseYou've already chosen the best response.1
I never really figured out the logical arrays part either :P
 2 years ago

agdgdgdgwngoBest ResponseYou've already chosen the best response.1
wait..... argh I forgot to submit my completed work!!!!
 2 years ago

agdgdgdgwngoBest ResponseYou've already chosen the best response.1
oh the page was not refreshed :P yeah it's there
 2 years ago
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