Q7 - understanding co-ordinate descent

[bargava]

I didn't entirely understand what co-ordinate descent meant. This is what I believe it to be: Instead of descending "simultaneously" along all the co-ordinates as in gradient descent(in this eg: both u and v), we first descend along u, find the new u and then find v. So, when computing v, the new value of u is to be used. Am I right?

[yaser]

Originally Posted by bargava

I didn't entirely understand what co-ordinate descent meant. This is what I believe it to be: Instead of descending "simultaneously" along all the co-ordinates as in gradient descent(in this eg: both u and v), we first descend along u, find the new u and then find v. So, when computing v, the new value of u is to be used. Am I right?

Correct. After each update along one coordinate, you compute the derivative at the new point, then descend along the other coordinate. This is not an efficient method, and is meant for comparison with gradient descent.

[Darcy Daugela]

I am struggling to understand what I did wrong on this question.

The instructions are clear, I followed the method above (I think?), my answers to related questions (5 and 6) were correct, but my answer to question 7 is far far less than the correct answer. I got the answer level of accuracy in only 5 iterations (instead of 15), so I must have a serious problem with my algorithm.

I am wondering if I understand the term "only to reduce error". I took this to mean that after each step I recalculate the error, and if the error increased I do not apply the update. This helped rapid convergence significantly.

Upon researching why I got this answer wrong, I ran across some conflicting references that suggest "coordinate descent" can be much more efficient algorithm than GD because of some tricks to re-use parts of the calculation. I'm not sure what to think.

[yaser]

Originally Posted by Darcy Daugela

I am wondering if I understand the term "only to reduce error". I took this to mean that after each step I recalculate the error, and if the error increased I do not apply the update. This helped rapid convergence significantly.

I see where the misunderstanding is. The word 'only' is meant to qualify the previous part: move along the u coordinate only to reduce the error.' Having said that, evaluating the error then undoing the step is not indicated given the part that follows: '(assume first-order approximation holds like in gradient descent).'