the problem is convex but the idea is not to use a map reduce but a subsample and solve it in memory on a reduced sample (i was actually thinking of simple bisect rather than trying to fit to anything), but that's not the point .
the point is how accurate the solution for a random subsample would reflect the actual optimum on the whole. On Fri, Dec 16, 2011 at 10:50 AM, Raphael Cendrillon <[email protected]> wrote: > Hi Dmitry, > > I have a feeling the objective may be very close to convex. In that case > there are faster approaches than random subsampling. > > A common strategy for example is to fit a quadratic onto the previously > evaluated lambda values, and then solve it for the minimum. > > This is an iterative approach, so wouldn't fit well within map reduce, but if > you are thinking of doing this as a preprocessing step it would be OK. > > On Dec 16, 2011, at 10:05 AM, Dmitriy Lyubimov <[email protected]> wrote: > >> Hi, >> >> I remember vaguely the discussion of finding the optimum for reg rate >> in ALS-WR stuff. >> >> Would it make sense to take a subsample (or, rather, a random >> submatrix) of the original input and try to find optimum for it >> somehow, similar to total order paritioner's distribution sampling? >> >> I have put ALS with regularization and ALS-WR (and will put the >> implicit feedback paper as well) into R code and i was wondering if it >> makes sense to find a better guess for lambda by just doing an R >> simulation on a randomly subsampled data before putting it into >> pipeline? or there's a fundamental problem with this approach? >> >> Thanks. >> -Dmitriy
