[mlpack] MVU Bug Fix GSOC

[Ryan Curtin]

On Mon, Mar 26, 2018 at 08:23:20PM +0000, LI Xuran wrote:
> >I took a quick look at your proposal and I think it is relatively clear
> >and sufficiently detailed.  I am not clear on exactly what you mean by
> >"5.  it might also be useful to write an algorithm to pre-process the
> >dataset to make it smoother and convex"---note that the LRSDP algorithm
> >breaks the convexity of SDPs and it is a nonconvex optimization.
>
> Thanks a lot for the feedback! Yeah, you are right about the LRSDP is
> a nonconvex optimization, what I intend to say is that during the
> process of sample generation, it might be helpful if we can have some
> constraints (say convex and closed? I am not too sure about the detail
> constraints yet but there is a theorem in the paper of local minima
> specifying it )  on the data to guarantee that an optimal solution can
> always be reached on the sample created, both by LRSDP and a dual
> solver.
>
> I 've gone through the rest of papers and Posts about LRSDP on Github
> during the past few days, as I am interested in what effort have been
> made to debug it. Do you think the following  ideas would be helpful
> to the debug project:
>
>  1.  refactor the SDP class to allow detail constraints specified in input.
>  2.  create variable template to specify linear/sparse/dense
>  constraints on input or A(constraint matrix) and support evaluation
>  of Tr(A_i * UU^T)
>
>
> I didn't add these two to my proposal, but if you think implementing
> those would be useful than I can also look into it and take it as a
> part of the project. Maybe I can try to approach it during the
> community bound.

Hi Daniel,

I realize my response is past the deadline here, so the proposal can't
be modified.  Still I did want to ask for a little clarification of what
you mean to be sure I understand correctly.

For the refactoring you are proposing, can you tell me what more of what
you mean by "allow detail constraints specified in input"?

I think the MVU SDP can be expressed only with sparse and dense
constraints, which we already have implemented.  So I'm not sure what
advantage using variadic templates would get us; can you clarify that
please?

Thanks,

Ryan

-- 
Ryan Curtin    | "Happy premise #2: There is no giant foot trying
ryan at ratml.org | to squash me." - Kit Ramsey