Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Probabilistic low-rank matrix completion on finite alphabets   The task of reconstructing a matrix given a sample of observedentries is
known as the matrix completion problem. It arises ina wide range of problems,
including recommender systems, collaborativefiltering, dimensionality
reduction, image processing, quantum physics or multi-class classificationto
name a few. Most works have focused on recovering an unknown real-valued
low-rankmatrix from randomly sub-sampling its entries.Here, we investigate the
case where the observations take a finite number of values, corresponding for
examples to ratings in recommender systems or labels in multi-class
classification.We also consider a general sampling scheme (not necessarily
uniform) over the matrix entries.The performance of a nuclear-norm penalized
estimator is analyzed theoretically.More precisely, we derive bounds for the
Kullback-Leibler divergence between the true and estimated distributions.In
practice, we have also proposed an efficient algorithm based on lifted
coordinate gradient descent in order to tacklepotentially high dimensional
settings.

31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org