Machine Learning Seminar

[Andreas Argyriou]

TTIC Machine Learning Seminar

There will be a machine learning seminar this Wednesday Nov. 9 at
11-12 am in room 530 at TTIC.
Rina Foygel from the Dept. of Statistics will present the following
work.
Seminar URL: https://groups.google.com/a/ttic.edu/group/machine-learning-seminar-2011/topics?hl=en&lnk

Title: Low-rank matrix reconstruction under non-uniform sampling and
non-independent noise

We consider the problem of approximately reconstructing a
partially-observed matrix, consisting of a low-rank or low-trace-norm
signal corrupted by arbitrary noise, where the sampled observations
may be selected non-uniformly across the matrix. For learning with
squared loss, we give learning guarantees for the matrix max-norm in a
broad setting, and compare to the many existing results that examine
trace-norm or rank-constrained learning under more strict assumptions.
For learning with absolute loss, we prove learning guarantees and
limitations of the weighted trace-norm, and propose an adaptation (the
"smoothed weighted trace-norm") that yields significantly better
theoretical guarantees and improves performance in experiments. Our
results also suggest that even if the true sampling distribution is
known (or is uniform), weighting by the empirical distribution may be
beneficial.