Hmm, Will Xt*X be positive definite in all cases? For example it's not if X has linearly independent rows? (I'm not going to guarantee 100% that I haven't missed something there.)
Even though your data is huge, if it was generated by some synthetic process, maybe it is very low rank? QR decomposition is pretty good here, yes. -- Sean Owen | Director, Data Science | London On Thu, Mar 6, 2014 at 3:05 PM, Debasish Das <debasish.da...@gmail.com> wrote: > Hi Sebastian, > > Yes Mahout ALS and Oryx runs fine on the same matrix because Sean calls QR > decomposition. > > But the ALS objective should give us strictly positive definite matrix..I > am thinking more on it.. > > There are some random factor assignment step but that also initializes > factors with normal(0,1)...which I think is not a big deal... > > About QR decomposition, jblas has Solve.solve and > Solve.solvePositive...solve should also run fine but it does a LU > factorization and better way will be to do a QR decomposition. > > Seems breeze has QR decomposition and we can make use of that...But QR by > default is also not correct since if the matrix is positive definite BLAS > psov (Solve.solvePositive) is much faster due to cholesky computation.. > > I believe we need a singular value check and based on that we should call > solvePositive/solve or qr from breeze.. > > There is also a specialized version of TSQR (tall and skinny QR > decomposition) from Chris which might be good to evaluate as well: > > https://github.com/ccsevers/scalding-linalg > > I am going to debug it further and try to understand why I am getting non > positive definite matrix and publish the findings... > > Any suggestions on how to proceed further on this ? Should I ask for a PR > and we can discuss more on it ? > > Thanks. > Deb > > On Thu, Mar 6, 2014 at 6:47 AM, Sebastian Schelter <s...@apache.org> wrote: > >> I'm not sure about the mathematical details, but I found in some >> experiments with Mahout that the matrix there was also not positive >> definite. Therefore, we chose QR decomposition to solve the linear system. >> >> >> --sebastian >> >> >> On 03/06/2014 03:44 PM, Debasish Das wrote: >> >>> Hi, >>> >>> I am running ALS on a sparse problem (10M x 1M) and I am getting the >>> following error: >>> >>> org.jblas.exceptions.LapackArgumentException: LAPACK DPOSV: Leading minor >>> of order i of A is not positive definite. >>> at org.jblas.SimpleBlas.posv(SimpleBlas.java:373) >>> at org.jblas.Solve.solvePositive(Solve.java:68) >>> >>> This error from blas shows up if the hessian matrix is not positive >>> definite... >>> >>> I checked that rating matrix is all > 0 but of course like netflix they >>> are >>> not bounded within 1 and 5.... >>> >>> Is there some sort of specific initialization of factor matrices done >>> which >>> can make the hessian matrix non positive definite ? >>> >>> I am printing out the eigen vectors and fullXtX matrix to understand it >>> more but any help will be appreciated. >>> >>> Thanks. >>> Deb >>> >>> >>
