Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximating Likelihood Ratios with Calibrated Discriminative
  Classifiers   In many fields of science, generalized likelihood ratio tests are established
tools for statistical inference. At the same time, it has become increasingly
common that a simulator (or generative model) is used to describe complex
processes that tie parameters $\theta$ of an underlying theory and measurement
apparatus to high-dimensional observations $\mathbf{x}\in \mathbb{R}^p$.
However, simulator often do not provide a way to evaluate the likelihood
function for a given observation $\mathbf{x}$, which motivates a new class of
likelihood-free inference algorithms. In this paper, we show that likelihood
ratios are invariant under a specific class of dimensionality reduction maps
$\mathbb{R}^p \mapsto \mathbb{R}$. As a direct consequence, we show that
discriminative classifiers can be used to approximate the generalized
likelihood ratio statistic when only a generative model for the data is
available. This leads to a new machine learning-based approach to
likelihood-free inference that is complementary to Approximate Bayesian
Computation, and which does not require a prior on the model parameters.
Experimental results on artificial problems with known exact likelihoods
illustrate the potential of the proposed method.

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The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
4
The categories of this paper are: cond-mat
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: math
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The categories of this paper are: nucl-th
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The categories of this paper are: solv-int
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The categories of this paper are: hep-th
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The categories of this paper are: econ