Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalization of variable elimination for separable inverse problems
  beyond least squares   In linear inverse problems, we have data derived from a noisy linear
transformation of some unknown parameters, and we wish to estimate these
unknowns from the data. Separable inverse problems are a powerful
generalization in which the transformation itself depends on additional unknown
parameters and we wish to determine both sets of parameters simultaneously.
When separable problems are solved by optimization, convergence can often be
accelerated by elimination of the linear variables, a strategy which appears
most prominently in the variable projection methods due to Golub, Pereyra, and
Kaufman. Existing variable elimination methods require an explicit formula for
the optimal value of the linear variables, so they cannot be used in problems
with Poisson likelihoods, bound constraints, or other important departures from
least squares.
  To address this limitation, we propose a generalization of variable
elimination in which standard optimization methods are modified to behave as
though a variable has been eliminated. We verify that this approach is a proper
generalization by using it to re-derive several existing variable elimination
techniques. We then extend the approach to bound-constrained and Poissonian
problems, showing in the process that many of the best features of variable
elimination methods can be duplicated in our framework. Tests on difficult
exponential sum fitting and blind deconvolution problems indicate that the
proposed approach can have significant speed and robustness advantages over
standard methods.

6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ex