Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Exponential Lower Bound on the Complexity of Regularization Paths   For a variety of regularized optimization problems in machine learning,
algorithms computing the entire solution path have been developed recently.
Most of these methods are quadratic programs that are parameterized by a single
parameter, as for example the Support Vector Machine (SVM). Solution path
algorithms do not only compute the solution for one particular value of the
regularization parameter but the entire path of solutions, making the selection
of an optimal parameter much easier.
  It has been assumed that these piecewise linear solution paths have only
linear complexity, i.e. linearly many bends. We prove that for the support
vector machine this complexity can be exponential in the number of training
points in the worst case. More strongly, we construct a single instance of n
input points in d dimensions for an SVM such that at least \Theta(2^{n/2}) =
\Theta(2^d) many distinct subsets of support vectors occur as the
regularization parameter changes.

35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an