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.

Student Perspectives: Multi-agent sequential decision making

A post by Conor Newton, PhD student on the Compass programme.


My research focuses on designing decentralised algorithms for the multi-agent variant of the Multi-Armed Bandit problem. This research is jointly supervised by Henry Reeve and Ayalvadi Ganesh.

(Image credit: Microsoft Research)

Many real-world optimisation problems involve repeated rather than one-off decisions. A decision maker (who we refer to as an agent) is required to repeatedly perform actions from a set of available options. After taking an action, the agent will receive a reward based on the action performed. The agent can then use this feedback to inform later decisions. Some examples of such problems are:

  • Choosing advertisements to display on a website each time a page is loaded to maximise click-through rate.
  • Calibrating the temperature to maximise the yield from a chemical reaction.
  • Distributing a budget between university departments to maximise research output.
  • Choosing the best route to commute to work.

In each case there is a fundamental trade-off between exploitation and exploration. On the one hand, the agent should act in ways which exploit the knowledge they have accumulated to promote their short term reward, whether that’s the yield of a chemical process or click-through rate on advertisements. On the other hand, the agent should explore new actions in order to increase their understanding of their environment in ways which may translate into future rewards. (more…)

PhD Compass application deadline: 16 March 2022

EPSRC PhD in Computational Statistics and Data Science is now recruiting for its next available fully-funded home fees places to start September 2022.

We will be prioritising applicants who wish to work with the following potential supervisors:

Professor Nicky Welton – Professor Welton works in the the department of Population Health Sciences in the Bristol Medical School.  Her work as a Compass supervisor can include supervision in the areas of Medical Statistics and Health Economics, in particular methods for combining evidence from multiple sources to answer healthcare policy questions.

Dr Sidarth Jaggi – Dr Jaggi is an Associate Professor in the Institute of Statistical Science and a Turing Fellow.  His Compass PhD supervision can cover areas such as high-dimensional statistics, and robust machine learning.

Dr Rihuan Ke – Dr Ke is a Lecturer in the School of Mathematics.  His research is on machine learning and mathematical image analysis. He has been developing statistical learning approaches and data-driven models for solving problems in computation and data science, and in particular for large scale image analysis. The typical approaches that he takes are to combine mathematical structures and statistical knowledge with modern deep learning techniques, to enable automatic analysis of the intrinsic structure of imaging data and exploiting rich information encoded in the data for the underlying tasks. In his projects, he is also interested in relevant applications in material sciences, medical imaging, and remote sensing. He is supervising PhD projects in deep learning, image analysis, and more generally data science.

EMAIL for more information or APPLY HERE

Compass Guest Lecture: Dr Kamélia Daudel, Postdoctoral researcher Department of Statistics, University of Oxford

Student Perspectives: The role of energy demand forecasting in decarbonisation


My work focuses on addressing the growing need for reliable, day-ahead energy demand forecasts in smart grids. In particular, we have been developing structured ensemble models for probabilistic forecasting that are able to incorporate information from a number of sources. I have undertaken this EDF-sponsored project with the help of my supervisors Matteo Fasiolo (UoB) and Yannig Goude (EDF) and in collaboration Christian Capezza (University of Naples Federico II).



One of the largest challenges society faces is climate change. Decarbonisation will lead to both a considerable increase in demand for electricity and a change in the way it is produced. Reliable demand forecasts will play a key role in enabling this transition. Historically, electricity has been produced by large, centralised power plants. This allows production to be relatively easily tailored to demand with little need for large-scale storage infrastructure. However, renewable methods are typically decentralised, less flexible and supply is subject to weather conditions or other unpredictable factors. A consequence of this is that electricity production will less able to react to sudden changes in demand, instead it will need to be generated in advance and stored. To limit the need for large-scale and expensive electricity storage and transportation infrastructure, smart grid management systems can instead be employed. This will involve, for example, smaller, more localised energy storage options. This increases the reliance on accurate demand forecasts to inform storage management decisions, not only at the aggregate level, but possibly down at the individual household level. The recent impact of the Covid-19 pandemic also highlighted problems in current forecasting methods which struggled to cope with the sudden change in demand patterns. These issues call attention to the need to develop a framework for more flexible energy forecasting models that are accurate at the household level. At this level, demand is characterised by a low signal-to-noise ratio, with frequent abrupt changepoints in demand dynamics. This can be seen in Figure 1 below.


Figure 1: Demand profiles for two different customers. Portuguese smart meter data [4].
The challenges posed by forecasting at a low level of aggregation motivate the use of an ensemble approach that can incorporates information from several models and across households. In particular, we propose an additive stacking structure where we can borrow information across households by constructing a weighted combination of experts, which is generally referred to as stacking regressions [2].


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