Approximating Likelihood Ratios with Calibrated Discriminative Classifiers

By Kyle Cranmer, Juan Pavez, Gilles Louppe. 2015

273 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Probabilistic & Bayesian Methods

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Citations in the corpus

Your GAN is Secretly an Energy-based Model and You Should use Discriminator Driven Latent Sampling (2020, methodology): “Trained classiﬁers have similarly been used to correct probabilistic models in other contexts [21].”
The frontier of simulation-based inference (2019, methodology): “ST A TI ST IC S (33, 56) or the likelihood ratio (60, 62, 64).”
Learning in Implicit Generative Models (2016, background): “…approach unsupervised-as-supervised learning, Qin (1998) explore this for analysis of case-control in observational studies, both Neal (2008) and Cranmer et al. (2015) explore this approach for high-energy physics applications, Gutmann and Hyvärinen (2012) exploit it for learning un-normalised…”
Deep and Hierarchical Implicit Models (2017, background): “It is a key idea in GAN s (Mohamed & Lakshmi-narayanan, 2016; Uehara et al., 2016), and similar ideas have rearisen in statistics and physics (Gutmann et al., 2014; Cranmer et al., 2015).”
Jet Substructure Classification in High-Energy Physics with Deep Neural Networks (2016, background): “clude information from tracking detectors, nor do they offer performance parameterized [44, 45] in the mass of the decaying heavy state.”
Hierarchical Implicit Models and Likelihood-Free Variational Inference (2017, background): “It is a key idea in GANs [35, 54], and similar ideas have rearisen in statistics and physics [19, 8].”
Likelihood-free MCMC with Approximate Likelihood Ratios (2019, methodology): “Contributions We adapt the training procedure proposed by [3] to improve the quality of the approximated likelihood ratio (Section 2.1).”
sbi: A toolkit for simulation-based inference (2020, methodology): “The package carl (Louppe, Cranmer, & Pavez, 2016) implements the algorithm described in Cranmer, Pavez, & Louppe (2015).”
Efficient Probabilistic Inference in the Quest for Physics Beyond the Standard Model (2018, methodology): “In the ﬁrst, one uses a simulator indirectly to train a surrogate model endowed with a likelihood that can be used in traditional inference algorithms, for example approaches based on conditional density estimation [57, 71, 78, 86] and density ratio estimation [30, 35].”
Under Review as a Conference Paper at Iclr 2017 Learning in Implicit Generative Models (2017, background): “…approach unsupervised-assupervised learning, Qin (1998) explore this for analysis of case-control in observational studies, both Neal (2008) and Cranmer et al. (2015) explore this approach for high-energy physics applications, Gutmann and Hyvärinen (2012) exploit it for learning un-normalised…”
INFERNO: Inference-Aware Neural Optimisation (2018, methodology): “This can be approached via likelihood-free inference algorithms such as Approximate Bayesian Computation (ABC) [1], simplified synthetic likelihoods [2] or density estimation-by-comparison approaches [3].”
Adversarial Variational Optimization of Non-Differentiable Simulators (2017, methodology): “The prevalence and significance of this problem has motivated an active research effort in so-called likelihood-free inference algorithms such as Approximate Bayesian Computation (ABC) and density estimation-by-comparison algorithms (Beaumont et al., 2002; Marjoram et al., 2003; Sisson et al., 2007;”