Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: More data speeds up training time in learning halfspaces over sparse
  vectors   The increased availability of data in recent years has led several authors to
ask whether it is possible to use data as a {\em computational} resource. That
is, if more data is available, beyond the sample complexity limit, is it
possible to use the extra examples to speed up the computation time required to
perform the learning task?
  We give the first positive answer to this question for a {\em natural
supervised learning problem} --- we consider agnostic PAC learning of
halfspaces over $3$-sparse vectors in $\{-1,1,0\}^n$. This class is
inefficiently learnable using $O\left(n/\epsilon^2\right)$ examples. Our main
contribution is a novel, non-cryptographic, methodology for establishing
computational-statistical gaps, which allows us to show that, under a widely
believed assumption that refuting random $\mathrm{3CNF}$ formulas is hard, it
is impossible to efficiently learn this class using only
$O\left(n/\epsilon^2\right)$ examples. We further show that under stronger
hardness assumptions, even $O\left(n^{1.499}/\epsilon^2\right)$ examples do not
suffice. On the other hand, we show a new algorithm that learns this class
efficiently using $\tilde{\Omega}\left(n^2/\epsilon^2\right)$ examples. This
formally establishes the tradeoff between sample and computational complexity
for a natural supervised learning problem.

17
The categories of this paper are: q-fin
2
The categories of this paper are: math
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph