Student Perspectives: Application of Density Ratio Estimation to Likelihood-Free problems

A post by Jack Simons, PhD student on the Compass programme.


I began my PhD with my supervisors, Dr Song Liu and Professor Mark Beaumont with the intention of combining their respective fields of research; Density Ratio Estimation (DRE), and Simulation Based Inference (SBI):

  • DRE is a rapidly growing paradigm in machine learning which (broadly) provides efficient methods of comparing densities without the need to compute each density individually. For a comprehensive yet accessible overview of DRE in Machine Learning see [1].
  • SBI is a group of methods which seek to solve Bayesian inference problems when the likelihood function is intractable. If you wish for a concise overview of the current work, as well as motivation then I recommend [2].

Last year we released a paper, Variational Likelihood-Free Gradient Descent [3] which combined these fields. This blog post seeks to condense, and make more accessible, the contents of the paper.

Motivation: Likelihood-Free Inference

Let’s begin by introducing likelihood-free inference. We wish to do inference on the posterior distribution of parameters \theta for a specific observation x=x_{\mathrm{obs}}, i.e. we wish to infer p(\theta|x_{\mathrm{obs}}) which can be decomposed via Bayes’ rule as

p(\theta|x_{\mathrm{obs}}) = \frac{p(x_{\mathrm{obs}}|\theta)p(\theta)}{\int p(x_{\mathrm{obs}}|\theta)p(\theta) \mathrm{d}\theta}.

The likelihood-free setting is that, additional to the usual intractability of the normalising constant in the denominator, the likelihood, p(x|\theta), is also intractable. In lieu of this, we require an implicit likelihood which describes the relation between data x and parameters \theta in the form of a forward model/simulator (hence simulation based inference!). (more…)

Compass students attending APTS Week in Durham

Between 4th and 8th of April 2022 Compass CDT students are attending APTS Week 2 in Durham.

Academy for PhD Training in Statistics (APTS) organises, through a collaboration between major UK statistics research groups, four residential weeks of training each year for first-year PhD students in statistics and applied probability nationally. Compass students attend all four APTS courses hosted by prestigious UK Universities.

For their APTS Week in Durham Compass students will be attending the following modules:

  • Applied Stochastic Processes (Nicholas Georgiou and Matt Roberts): This module will introduce students to two important notions in stochastic processes — reversibility and martingales — identifying the basic ideas, outlining the main results and giving a flavour of some of the important ways in which these notions are used in statistics.
  • Statistical Modelling (Helen Ogden): The aim of this module is to introduce important aspects of statistical modelling, including model selection, various extensions to generalised linear models, and non-linear models.


DataScience@work seminars 2022 announced

We are delighted to announce the confirmed DataScience@work seminars for 2022. Huge thanks to our invited speakers who will be joining us in person and online over the coming months!

The Compass DataScience@work seminar invites speakers from industry, government and third-sector to provide our PhD students with their perspective on the realities of being a data scientist in industry: from the methods and techniques they use to build applications, to working as part of a wider organisation, and how to build a career in their sector.

Find out more on our DataScience@work seminar here.

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