Approximating Likelihood Ratios with Calibrated Discriminative Classifiers
作者： Gilles Louppe , Kyle Cranmer , Juan Pavez
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摘要: 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 tie parameters $\theta$ an underlying theory and measurement apparatus high-dimensional observations $\mathbf{x}\in \mathbb{R}^p$. However, often do not provide way evaluate function given observation $\mathbf{x}$, which motivates new class likelihood-free inference algorithms. this paper, we show ratios invariant under specific dimensionality reduction maps $\mathbb{R}^p \mapsto \mathbb{R}$. As direct consequence, discriminative classifiers can be approximate statistic when only model data available. This leads machine learning-based approach complementary Approximate Bayesian Computation, does require prior on parameters. Experimental results artificial problems with known exact likelihoods illustrate potential proposed method.
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