[mlpack] GSoC 2018 MVU+LRSDP Bugfix

[Abhijeet Krishnan]

Hi,

I am interested in working for mlpack for GSoC 2018, with an interest in
trying to get the MVU + LRSDP implementation working. I have built mlpack
and modified it (with help from zoq) to also build the MVU part of the
code. I am currently attempting to re-write the MVU code to match the
current APIs, since there were a number of compilation errors which I
believe were due to the LRSDP APIs being updated without also updating the
MVU code.

In terms of debugging the error, I have thought of the following approach -
1. Test the MVU code using the primal dual optimizer to verify if the error
is in MVU or in LRSDP
2a. If MVU+Primal Dual converges, the error is most likely in LRSDP
2b. If MVU+Primal Dual also does not converge, the error is most likely in
MVU (might also be in Primal Dual)
3. Wherever the error is, my plan is to be clear about how that algorithm
works (from reading the research papers) and to test the values the
function returns against some working implementation of it in another
package
4. If the error is in LRSDP, I don't think there is a reference
implementation. I will need to really dig into the code and algorithm to
find the error. I guess this is exactly why the issue is marked 10/10 in
difficulty.

I would like to know what approaches and efforts have been made previously
to solve this problem, in particular, if anyone has any intuition as to
where the problem might lie and what would be a good approach to solve it.

If anyone has any tips to share on debugging numerical algorithms, that
would also be welcome.

I am currently pursuing a PhD in CS from NC State University with plans of
conducting research in Generative Methods.
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