Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Faster Uncertainty Quantification for Inverse Problems with Conditional
  Normalizing Flows   In inverse problems, we often have access to data consisting of paired
samples $(x,y)\sim p_{X,Y}(x,y)$ where $y$ are partial observations of a
physical system, and $x$ represents the unknowns of the problem. Under these
circumstances, we can employ supervised training to learn a solution $x$ and
its uncertainty from the observations $y$. We refer to this problem as the
"supervised" case. However, the data $y\sim p_{Y}(y)$ collected at one point
could be distributed differently than observations $y'\sim p_{Y}'(y')$,
relevant for a current set of problems. In the context of Bayesian inference,
we propose a two-step scheme, which makes use of normalizing flows and joint
data to train a conditional generator $q_{\theta}(x|y)$ to approximate the
target posterior density $p_{X|Y}(x|y)$. Additionally, this preliminary phase
provides a density function $q_{\theta}(x|y)$, which can be recast as a prior
for the "unsupervised" problem, e.g.~when only the observations $y'\sim
p_{Y}'(y')$, a likelihood model $y'|x$, and a prior on $x'$ are known. We then
train another invertible generator with output density $q'_{\phi}(x|y')$
specifically for $y'$, allowing us to sample from the posterior
$p_{X|Y}'(x|y')$. We present some synthetic results that demonstrate
considerable training speedup when reusing the pretrained network
$q_{\theta}(x|y')$ as a warm start or preconditioning for approximating
$p_{X|Y}'(x|y')$, instead of learning from scratch. This training modality can
be interpreted as an instance of transfer learning. This result is particularly
relevant for large-scale inverse problems that employ expensive numerical
simulations.

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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: econ
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The categories of this paper are: dg-ga