Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sketching Transformed Matrices with Applications to Natural Language
  Processing   Suppose we are given a large matrix $A=(a_{i,j})$ that cannot be stored in
memory but is in a disk or is presented in a data stream. However, we need to
compute a matrix decomposition of the entry-wisely transformed matrix,
$f(A):=(f(a_{i,j}))$ for some function $f$. Is it possible to do it in a space
efficient way? Many machine learning applications indeed need to deal with such
large transformed matrices, for example word embedding method in NLP needs to
work with the pointwise mutual information (PMI) matrix, while the entrywise
transformation makes it difficult to apply known linear algebraic tools.
Existing approaches for this problem either need to store the whole matrix and
perform the entry-wise transformation afterwards, which is space consuming or
infeasible, or need to redesign the learning method, which is application
specific and requires substantial remodeling.
  In this paper, we first propose a space-efficient sketching algorithm for
computing the product of a given small matrix with the transformed matrix. It
works for a general family of transformations with provable small error bounds
and thus can be used as a primitive in downstream learning tasks. We then apply
this primitive to a concrete application: low-rank approximation. We show that
our approach obtains small error and is efficient in both space and time. We
complement our theoretical results with experiments on synthetic and real data.

7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
2
The categories of this paper are: math
32
The categories of this paper are: atom-ph
25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph