Yes in this case you end up with the least-squares solution. I don't
see a problem with that; it's a corner case anyway and the best you
can do. The QR decomposition will handle it either way, finding the
exact solution when it exists.
I think it's slower than Cholesky? (yes I am guessing that is
Yup, this would definitely be fine. I’d like to understand when this happens
though, I imagine it might be if a user / product has no ratings (though we
should certainly try to run well in that case).
Matei
On Mar 6, 2014, at 10:00 AM, Debasish Das wrote:
> Matei,
>
> If the data has linearl
But Sean, because that matrix is not invertible, you can’t solve it. That’s why
I’m saying, as long as it is solvable, it will be positive definite too, and in
that case solvePositive is optimized for this use case (I believe it does
Cholesky decomposition).
Matei
On Mar 6, 2014, at 9:58 AM,
Matei,
If the data has linearly dependent rows ALS should have a failback
mechanism. Either remove the rows and then call BLAS posv or call BLAS gesv
or Breeze QR decomposition.
I can share the analysis over email.
Thanks.
Deb
On Thu, Mar 6, 2014 at 9:39 AM, Matei Zaharia wrote:
> Xt*X should
Agree. For example you could have a user-feature matrix X =
1 0
1 0
and X' * X =
2 0
0 0
is not positive definite but is semidefinite.
So I think the code should be calling solveSymmetric not
solvePositive? the latter requires positive definite.
--
Sean Owen | Director, Data Science | London
Xt*X should mathematically always be positive semi-definite, so the only way
this might be bad is if it’s not invertible due to linearly dependent rows.
This might happen due to the initialization or possibly due to numerical
issues, though it seems unlikely. Maybe it also happens if some users
I do not think there is an advantage in projecting into only the
nonnegative quadrant (meaning all of X and Y are nonnegative right?)
The argument I have seen is simply interpretability but this doesn't
matter here.
I think it would be a great exercise to see if the QR decomposition is
as fast, an
Bound constraints in QR decomposition / BLAS posv other than projecting to
positive space at each iteration ?
Common usecases are feature generation from photos/videos etc...
I saw a paper on projecting to positive space from 70s...there are some
improvements later using projected gradients but t
Yes that will be really cool if the data has linearly independent rows ! I
have to debug it more but I got it running with jblas Solve.solve..
I will try breeze QR decomposition next.
Have you guys tried adding bound constraints in QR decomposition / BLAS
posv other than projecting to positive sp
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 decomposi
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,
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