nonparametric ABC [seminar]

Puzzle: How do you run ABC when you mistrust the model?! We somewhat considered this question in our misspecified ABC paper with David and Judith. An AISTATS 2022 paper by Harita Dellaporta (Warwick), Jeremias Knoblauch,  Theodoros Damoulas (Warwick), and François-Xavier Briol (formerly Warwick) is addressing this same question and Harita presented the paper at the One World ABC webinar yesterday.

It is inspired from Lyddon, Walker & Holmes (2018), who place a nonparametric prior on the generating model, in top of the assumed parametric model (with an intractable likelihood). This induces a push-forward prior on the pseudo-true parameter, that is, the value that brings the parametric family the closest possible to the true distribution of the data. Here defined as a minimum distance parameter, the maximum mean discrepancy (MMD). Choosing RKHS framework allows for a practical implementation, resorting to simulations for posterior realisations from a Dirichlet posterior and from the parametric model, and stochastic gradient for computing the pseudo-true parameter, which may prove somewhat heavy in terms of computing cost.

The paper also containts a consistency result in an ε-contaminated setting (contamination of the assumed parametric family). Comparisons like the above with a fully parametric Wasserstein-ABC approach show that this alter resists better misspecification, as could be expected since the later is not constructed for that purpose.

Next talk is on 23 June by Cosma Shalizi.

Recent Advances in Approximate Bayesian Inference [YSE, 15.2.22]

On June 15, the Young Statisticians Europe initiative is organising an on-line seminar on approximate Bayesian inference. With talks by

• Lorenzo Pacchiardi, University of Oxford, United Kingdom
• Emilia Pompe, University of Oxford, United Kingdom
• Łukasz Rajkowski, University of Warsaw, Poland
• Théo Moins, Inria Grenoble Rhône-Alpes, France

starting at 7:00 PT / 10:00 EST / 16:00 CET. The registration form is available here.

Concentration and robustness of discrepancy-based ABC [One World ABC ‘minar, 28 April]

Our next speaker at the One World ABC Seminar will be Pierre Alquier, who will talk about “Concentration and robustness of discrepancy-based ABC“, on Thursday April 28, at 9.30am UK time, with an abstract reported below.

Approximate Bayesian Computation (ABC) typically employs summary statistics to measure the discrepancy among the observed data and the synthetic data generated from each proposed value of the parameter of interest. However, finding good summary statistics (that are close to sufficiency) is non-trivial for most of the models for which ABC is needed. In this paper, we investigate the properties of ABC based on integral probability semi-metrics, including MMD and Wasserstein distances. We exhibit conditions ensuring the contraction of the approximate posterior. Moreover, we prove that MMD with an adequate kernel leads to very strong robustness properties.

One World ABC seminar [31.3.22]

The next One World ABC seminar is on Thursday 31 March, with David Warnes (from QUT) talking on Multifidelity multilevel Monte Carlo for approximate Bayesian computation It will take place at 10:30 CET (GMT+1).

Models of stochastic processes are widely used in almost all fields of science. However, data are almost always incomplete observations of reality. This leads to a great challenge for statistical inference because the likelihood function will be intractable for almost all partially observed stochastic processes. As a result, it is common to apply likelihood-free approaches that replace likelihood evaluations with realisations of the model and observation process. However, likelihood-free techniques are computationally expensive for accurate inference as they may require millions of high-fidelity, expensive stochastic simulations. To address this challenge, we develop a novel approach that combines the multilevel Monte Carlo telescoping summation, applied to a sequence of approximate Bayesian posterior targets, with a multifidelity rejection sampler that learns from low-fidelity, computationally inexpensive,
model approximations to minimise the number of high-fidelity, computationally expensive, simulations required for accurate inference. Using examples from systems biology, we demonstrate improvements of more than two orders of magnitude over standard rejection sampling techniques

One World ABC seminar [24.2.22]

The next One World ABC seminar is on Thursday 24 Feb, with Rafael Izbicki talking on Likelihood-Free Frequentist Inference – Constructing Confidence Sets with Correct Conditional Coverage. It will take place at 14:30 CET (GMT+1).

Many areas of science make extensive use of computer simulators that implicitly encode likelihood functions of complex systems. Classical statistical methods are poorly suited for these so-called likelihood-free inference (LFI) settings, outside the asymptotic and low-dimensional regimes. Although new machine learning methods, such as normalizing flows, have revolutionized the sample efficiency and capacity of LFI methods, it remains an open question whether they produce reliable measures of uncertainty. We present a statistical framework for LFI that unifies classical statistics with modern machine learning to: (1) efficiently construct frequentist confidence sets and hypothesis tests with finite-sample guarantees of nominal coverage (type I error control) and power; (2) provide practical diagnostics
for assessing empirical coverage over the entire parameter space. We refer to our framework as likelihood-free frequentist inference (LF2I). Any method that estimates a test statistic, like the likelihood ratio, can be plugged into our framework to create valid confidence sets and compute diagnostics, without costly Monte Carlo samples at fixed parameter settings. In this work, we specifically study the power of two test statistics (ACORE and BFF), which, respectively, maximize versus integrate an odds function over the parameter space. Our study offers multifaceted perspectives on the challenges in LF2I. This is joint work with Niccolo Dalmasso, David Zhao and Ann B. Lee.