Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditional Sparse $\ell_p$-norm Regression With Optimal Probability   We consider the following conditional linear regression problem: the task is
to identify both (i) a $k$-DNF condition $c$ and (ii) a linear rule $f$ such
that the probability of $c$ is (approximately) at least some given bound $\mu$,
and $f$ minimizes the $\ell_p$ loss of predicting the target $z$ in the
distribution of examples conditioned on $c$. Thus, the task is to identify a
portion of the distribution on which a linear rule can provide a good fit.
Algorithms for this task are useful in cases where simple, learnable rules only
accurately model portions of the distribution. The prior state-of-the-art for
such algorithms could only guarantee finding a condition of probability
$\Omega(\mu/n^k)$ when a condition of probability $\mu$ exists, and achieved an
$O(n^k)$-approximation to the target loss, where $n$ is the number of Boolean
attributes. Here, we give efficient algorithms for solving this task with a
condition $c$ that nearly matches the probability of the ideal condition, while
also improving the approximation to the target loss. We also give an algorithm
for finding a $k$-DNF reference class for prediction at a given query point,
that obtains a sparse regression fit that has loss within $O(n^k)$ of optimal
among all sparse regression parameters and sufficiently large $k$-DNF reference
classes containing the query point.

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The categories of this paper are: math-ph
3
The categories of this paper are: physics
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The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org