[mlpack] MVU Bug Fix GSOC

[Ryan Curtin]

On Sun, Mar 18, 2018 at 08:15:57PM +0000, LI Xuran wrote:
> Dear Ryan,
> 
> 
>  I am currently working on my proposal for the Fixes to MVU and low-rank semidefinite programs and have come up with the following ideas:
> 1.generate random simple dataset, and compare normal MVU with MVU +LRSDP on it. do visualization of the procedure and the result in 2d/3d.
> 2. write unit tests and substitution for the original code in mlpack's MVU implementation and check their correctness over processing of the above datasets.
> 3. base on the observation of the result of 1 and 2, create datasets that particularly points out the issue ... and check step by step on that sample
> 4.(or maybe datasets with a special property such that it should always converge by an implementation of MVU + LRSDP  and check if the expected result  is met )
> 
> do you think any of the above ideas worth a try?

Hi Daniel,

This sounds like a good start.  A key point is that MVU does converge
with regular SDP solvers, so a sanity check might be to implement MVU
with mlpack's PrimalDualSolver and see if this works, to be sure that
there are no bugs in the MVU implementation itself.

The debugging of the LRSDP is likely to be very difficult, and I'd
suggest that you spend a long time reading about semidefinite
programming as well as the Monteiro-Burer papers about LRSDP, in order
to formulate a plan of action for how to debug the solver when it is not
converging.

Thanks,

Ryan

-- 
Ryan Curtin    | "Do I sound like I'm ordering a pizza?"
ryan at ratml.org |   - John McClane