Deep Learning and Likelihood-Free Bayesian Inference for Intractable Stochastic Models

[A PhD position is available for this project. Scroll down to the recruitment section to apply.]

Mathematical and statistical models for real-world applications are complex. When applying statistical and machine learning methodology to adapt the model to our data, we want to obtain a realistic mathematical representation of the experiment under study. This means finding "best fitting" model parameters and quantify their uncertainties in a probabilistic way. However, what we typically face with realistically complex models is the inability to compute the likelihood function of the model parameters. This affects both frequentist and Bayesian procedures, to the point that exact inference is usually unavailable. A change of paradigm is given by simulations-based "likelihood-free" approaches. In this case, the only requirement is the ability to simulate artificial data from a " computer simulator", which is a software implementation of the mathematical model. Simulated data can then be used to compensate for the lack of an explicit likelihood function.  An important example of this approach is the class of Approximate Bayesian Computation (ABC) algorithms.

Several challenges can be considered for improving ABC towards make it more plug-and-play and accurate. One of these is about reducing the dimensionality of the data by specifying ad-hoc summary statistics. We intend to do so by constructing novel deep neuronal networks helping to automatically obtain these summary statistics, to produce a more reliable, plug-and-play methodology for likelihood-free inference (an initial effort is published here). More research questions can be formulated as it fits and the project is open to consider further ideas towards improving the construction of reliable simulations-based methods for Bayesian inference, and their interaction with neuronal networks. Special interest is for data arising from stochastic dynamical models, with emphasis on inference for stochastic differential equations (SDEs) observed with measurement error, and more generally models with "intractable likelihoods". The construction of appropriate bridge-proposals and particle filters for SDEs is also of interest.

While the project is of methodological nature, applications to real data case studies are foreseen, such as protein folding data, epidemic data and smart-city data such as such as precipitation, pollution data, temperature and humidity.

Here is a slightly more extended description with references.

PI is Umberto Picchini and the project is an international collaboration with Jes Frellsen (DTU Copenhagen)Andrew Golightly  (Newcastle University, UK) and Samuel Wiqvist (Lund, Sweden).

The project is funded by the Chalmers AI Research centre and by the Swedish Research Council (Vetenskapsrådet).

PhD student recruitment

Interested in this project?


CLICK HERE TO APPLY. The deadline is 6 March 2020

This is part of a large call to recruit overall 6 students across 6 projects.   


Please contact Umberto Picchini (link below) for further information or questions about this specific project.

Essential requirements:

  • strong interest in statistical inference and machine learning;
  • having taken courses in Bayesian inference and have some experience with corresponding computational methods (such as MCMC);
  • The student should be proficient with at least one programming language for data-science (e.g. R, Python, MATLAB, Julia);
  • Be willing to engage in an international collaboration involving some travelling abroad and online meetings with collaborators;
  • Proficiency with oral and written English.
Additional points of merit (NOT essential requirements. Please feel free to apply even without the experience below)
  • experience with inference for SDEs;
  • experience with inference via particle filters (sequential Monte Carlo);
  • experience with modern machine learning and deep learning software libraries, such as TensorFlow or PyTorch.

Published: Fri 13 Mar 2020.