Thank you for clarification, Robin! My math was a very long time ago, so for me
it was not very obvious that specific optimization problem doesn't hold this
property (and thus cannot be globally optimized). But if anyone interested in
further reading I found some decent material on the subject:
http://www.stanford.edu/~boyd/cvxbook/bv_cvxbook.pdf
Again thank you all for fruitful (at least for me :-P) discussion!
> Subject: Re: Consistent repeatable results for distributed ALS-WR recommender
> From: robin.e...@xense.co.uk
> Date: Tue, 25 Jun 2013 09:10:23 +0100
> To: user@mahout.apache.org
>
> I think Sean has put it well but just to emphasise the point:
>
> - optimisation problems are either convex or non-convex
> - if you have a convex problem then the fundamental result that everyone
> should know is that if you find a local minimum it is also the global minimum
> - if you don't have a convex problem (or you can't prove that it is convex)
> then you cannot be sure the minimum you have found is a global minimum
>
> So if you know something is non-convex (e.g. ALS, k-means, convnets) you
> usually have to trade off something. You could try and find a global minimum
> but that may take an impossibly long-time. The other trade-off is to that you
> accept a local minimum and hope that it is close to the global. Which local
> minimum you get will depend on what your initialisation values are - if you
> try different initialisation values you may get a different local minimum. So
> a common practice is to run several sets of iterations using different
> initial values - often randomly generated - and take the best minimum. And of
> course you know the best one by evaluating the objective function and
> choosing the one that gives the lowest value.
>
> Robin
> On 24 Jun 2013, at 20:44, Michael Kazekin <kazm...@hotmail.com> wrote:
>
> > Thanks a lot!
> > Do you know by any chance what are the underlying reasons for including
> > such mandatory random seed initialization?
> > Do you see any sense in providing another option, such as filling them with
> > zeroes in order to ensure the consistency and repeatability? (for example
> > we might want to track and compare the generated recommendation lists for
> > different parameters, such as the number of features or number of
> > iterations etc.)
> > M.
> >
> >
> >> Date: Mon, 24 Jun 2013 19:51:44 +0200
> >> Subject: Re: Consistent repeatable results for distributed ALS-WR
> >> recommender
> >> From: s...@apache.org
> >> To: user@mahout.apache.org
> >>
> >> The matrices of the factorization are initalized randomly. If you fix the
> >> random seed (would require modification of the code) you should get exactly
> >> the same results.
> >> Am 24.06.2013 13:49 schrieb "Michael Kazekin" <kazm...@hotmail.com>:
> >>
> >>> Hi!
> >>> Should I assume that under same dataset and same parameters for factorizer
> >>> and recommender I will get the same results for any specific user?
> >>> My current understanding that theoretically ALS-WR algorithm could
> >>> guarantee this, but I was wondering could be there any numeric method
> >>> issues and/or implementation-specific concerns.
> >>> Would appreciate any highlight on this issue.
> >>> Mike.
> >>>
> >>>
> >>>
> >
>
