Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact high-dimensional asymptotics for Support Vector Machine   The Support Vector Machine (SVM) is one of the most widely used
classification methods. In this paper, we consider the soft-margin SVM used on
data points with independent features, where the sample size $n$ and the
feature dimension $p$ grows to $\infty$ in a fixed ratio $p/n\rightarrow
\delta$. We propose a set of equations that exactly characterizes the
asymptotic behavior of support vector machine. In particular, we give exact
formulas for (1) the variability of the optimal coefficients, (2) the
proportion of data points lying on the margin boundary (i.e. number of support
vectors), (3) the final objective function value, and (4) the expected
misclassification error on new data points, which in particular implies the
exact formula for the optimal tuning parameter given a data generating
mechanism. We first establish these formulas in the case where the label
$y\in\{+1,-1\}$ is independent of the feature $x$. Then the results are
generalized to the case where the label $y\in\{+1,-1\}$ is allowed to have a
general dependence on the feature $x$ through a linear combination $a_0^Tx$.
These formulas for the non-smooth hinge loss are analogous to the recent
results in \citep{sur2018modern} for smooth logistic loss. Our approach is
based on heuristic leave-one-out calculations.

36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
19
The categories of this paper are: eess
21
The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th