Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gradient flows and randomised thresholding: sparse inversion and
  classification   Sparse inversion and classification problems are ubiquitous in modern data
science and imaging. They are often formulated as non-smooth minimisation
problems. In sparse inversion, we minimise, e.g., the sum of a data fidelity
term and an L1/LASSO regulariser. In classification, we consider, e.g., the sum
of a data fidelity term and a non-smooth Ginzburg--Landau energy. Standard
(sub)gradient descent methods have shown to be inefficient when approaching
such problems. Splitting techniques are much more useful: here, the target
function is partitioned into a sum of two subtarget functions -- each of which
can be efficiently optimised. Splitting proceeds by performing optimisation
steps alternately with respect to each of the two subtarget functions.
  In this work, we study splitting from a stochastic continuous-time
perspective. Indeed, we define a differential inclusion that follows one of the
two subtarget function's negative subgradient at each point in time. The choice
of the subtarget function is controlled by a binary continuous-time Markov
process. The resulting dynamical system is a stochastic approximation of the
underlying subgradient flow. We investigate this stochastic approximation for
an L1-regularised sparse inversion flow and for a discrete Allen-Cahn equation
minimising a Ginzburg--Landau energy. In both cases, we study the longtime
behaviour of the stochastic dynamical system and its ability to approximate the
underlying subgradient flow at any accuracy. We illustrate our theoretical
findings in a simple sparse estimation problem and also in a low-dimensional
classification problem.

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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
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The categories of this paper are: econ
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
19
The categories of this paper are: eess
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The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex