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Sebastian Farquhar

### PhD, started 2017

Seb is a DPhil student supervised by Yarin Gal and part of the Centre for Doctoral Training in Cyber Security. He is interested in the pragmatic fundamentals of deep learning for their own sake as well as for their application to safe and secure machine learning systems. Before joining the research group, he worked in technology policy (including biosafety and AI policy), social-entrepreneurship, and strategy consulting. He has been working on startups in the effective altruism community since 2012. He has a Masters degree in Physics and Philosophy from the University of Oxford.

Publications while at OATML:

**Liberty or Depth: Deep Bayesian Neural Nets Do Not Need Complex Weight Posterior Approximations**

We challenge the longstanding assumption that the mean-field approximation for variational inference in Bayesian neural networks is severely restrictive, and show this is not the case in deep networks. We prove several results indicating that deep mean-field variational weight posteriors can induce similar distributions in function-space to those induced by shallower networks with complex weight posteriors. We validate our theoretical contributions empirically, both through examination of the weight posterior using Hamiltonian Monte Carlo in small models and by comparing diagonal- to structured-covariance in large settings. Since complex variational posteriors are often expensive and cumbersome to implement, our results suggest that using mean-field variational inference in a deeper model is both a practical and theoretically justified alternative to structured approximations.

Sebastian Farquhar, Lewis Smith, Yarin Gal

**NeurIPS, 2020**[Paper] [arXiv]

**Try Depth Instead of Weight Correlations: Mean-field is a Less Restrictive Assumption for Deeper Networks**

We challenge the longstanding assumption that the mean-field approximation for variational inference in Bayesian neural networks is severely restrictive. We argue mathematically that full-covariance approximations only improve the ELBO if they improve the expected log-likelihood. We further show that deeper mean-field networks are able to express predictive distributions approximately equivalent to shallower full-covariance networks. We validate these observations empirically, demonstrating that deeper models decrease the divergence between diagonal- and full-covariance Gaussian fits to the true posterior.

Sebastian Farquhar, Lewis Smith, Yarin Gal

**Contributed talk,**

*Workshop on Bayesian Deep Learning, NeurIPS 2019*[Workshop paper], [arXiv]

**Radial Bayesian Neural Networks: Beyond Discrete Support In Large-Scale Bayesian Deep Learning**

We propose Radial Bayesian Neural Networks (BNNs): a variational approximate posterior for BNNs which scales well to large models while maintaining a distribution over weight-space with full support. Other scalable Bayesian deep learning methods, like MC dropout or deep ensembles, have discrete support---they assign zero probability to almost all of the weight-space. Unlike these discrete support methods, Radial BNNs' full support makes them suitable for use as a prior for sequential inference. In addition, they solve the conceptual challenges with the a priori implausibility of weight distributions with discrete support. The Radial BNN is motivated by avoiding a sampling problem in 'mean-field' variational inference (MFVI) caused by the so-called 'soap-bubble' pathology of multivariate Gaussians. We show that, unlike MFVI, Radial BNNs are robust to hyperparameters and can be efficiently applied to a challenging real-world medical application without needing ad-hoc tweaks and inten... [full abstract]

Sebastian Farquhar, Michael Osborne, Yarin Gal

**The 23rd International Conference on Artificial Intelligence and Statistics (AISTATS)**[arXiv]

**A Systematic Comparison of Bayesian Deep Learning Robustness in Diabetic Retinopathy Tasks**

Evaluation of Bayesian deep learning (BDL) methods is challenging. We often seek to evaluate the methods' robustness and scalability, assessing whether new tools give 'better' uncertainty estimates than old ones. These evaluations are paramount for practitioners when choosing BDL tools on-top of which they build their applications. Current popular evaluations of BDL methods, such as the UCI experiments, are lacking: Methods that excel with these experiments often fail when used in application such as medical or automotive, suggesting a pertinent need for new benchmarks in the field. We propose a new BDL benchmark with a diverse set of tasks, inspired by a real-world medical imaging application on diabetic retinopathy diagnosis. Visual inputs (512x512 RGB images of retinas) are considered, where model uncertainty is used for medical pre-screening---i.e. to refer patients to an expert when model diagnosis is uncertain. Methods are then ranked according to metrics derived from expert-... [full abstract]

Angelos Filos, Sebastian Farquhar, Aidan Gomez, Tim G. J. Rudner, Zac Kenton, Lewis Smith, Milad Alizadeh, Arnoud de Kroon, Yarin Gal

*Preprint, 2019*

[Preprint] [BibTex] [Code]

*arXiv, 2019*

[arXiv]

**Spotlight talk,**

*Workshop on Bayesian Deep Learning, NeurIPS 2019*[Paper]

**A Unifying Bayesian View of Continual Learning**

Some machine learning applications require continual learning—where data comes in a sequence of datasets, each is used for training and then permanently discarded. From a Bayesian perspective, continual learning seems straightforward: Given the model posterior one would simply use this as the prior for the next task. However, exact posterior evaluation is intractable with many models, especially with Bayesian neural networks (BNNs). Instead, posterior approximations are often sought. Unfortunately, when posterior approximations are used, prior-focused approaches do not succeed in evaluations designed to capture properties of realistic continual learning use cases. As an alternative to prior-focused methods, we introduce a new approximate Bayesian derivation of the continual learning loss. Our loss does not rely on the posterior from earlier tasks, and instead adapts the model itself by changing the likelihood term. We call these approaches likelihood-focused. We then combine prior-... [full abstract]

Sebastian Farquhar, Yarin Gal

**NeurIPS 2018 workshop on Bayesian Deep Learning**[Paper] [BibTex]

**Differentially private continual learning**

Catastrophic forgetting can be a significant problem for institutions that must delete historic data for privacy reasons. For example, hospitals might not be able to retain patient data permanently. But neural networks trained on recent data alone will tend to forget lessons learned on old data. We present a differentially private continual learning framework based on variational inference. We estimate the likelihood of past data given the current model using differentially private generative models of old datasets. The differentially private training has no detrimental impact on our architecture's continual learning performance, and still outperforms the current state-of-the-art non-private continual learning.

Sebastian Farquhar, Yarin Gal

**Privacy in Machine Learning and Artificial Intelligence workshop, ICML, 2018**[Paper] [BibTex]

**Towards Robust Evaluations of Continual Learning**

Continual learning experiments used in current deep learning papers do not faithfully assess fundamental challenges of learning continually, masking weak-points of the suggested approaches instead. We study gaps in such existing evaluations, proposing essential experimental evaluations that are more representative of continual learning's challenges, and suggest a re-prioritization of research efforts in the field. We show that current approaches fail with our new evaluations and, to analyse these failures, we propose a variational loss which unifies many existing solutions to continual learning under a Bayesian framing, as either 'prior-focused' or 'likelihood-focused'. We show that while prior-focused approaches such as EWC and VCL perform well on existing evaluations, they perform dramatically worse when compared to likelihood-focused approaches on other simple tasks.

Sebastian Farquhar, Yarin Gal

**Lifelong Learning: A Reinforcement Learning Approach workshop, ICML, 2018**[arXiv] [BibTex]

Reproducibility and Code

**Code for Bayesian Deep Learning Benchmarks**

In order to make real-world difference with **Bayesian Deep Learning** (BDL) tools, the tools must scale to real-world settings. And for that we, the research community, must be able to evaluate our inference tools (and iterate quickly) with real-world benchmark tasks. We should be able to do this without necessarily worrying about application-specific domain knowledge, like the expertise often required in medical applications for example. We require benchmarks to test for inference robustness, performance, and accuracy, in addition to cost and effort of development. These benchmarks should be at a variety of scales, ranging from toy MNIST-scale benchmarks for fast development cycles, to large data benchmarks which are truthful to real-world applications, capturing their constraints.

Angelos Filos, Sebastian Farquhar, Aidan Gomez, Tim G. J. Rudner, Zac Kenton, Lewis Smith, Milad Alizadeh, Yarin Gal

Blog Posts

**22 OATML Conference and Workshop papers at NeurIPS 2020**

OATML group members and collaborators are proud to be presenting 22 papers at NeurIPS 2020. Group members are also co-organising various events around NeurIPS, including workshops, the NeurIPS Meet-Up on Bayesian Deep Learning and socials. …

Full post...Muhammed Razzak, Panagiotis Tigas, Angelos Filos, Atılım Güneş Baydin, Andrew Jesson, Andreas Kirsch, Clare Lyle, Freddie Kalaitzis, Jan Brauner, Jishnu Mukhoti, Lewis Smith, Lisa Schut, Mizu Nishikawa-Toomey, Oscar Key, Binxin (Robin) Ru, Sebastian Farquhar, Sören Mindermann, Tim G. J. Rudner, Yarin Gal, 04 Dec 2020

**Is Mean-field Good Enough for Variational Inference in Bayesian Neural Networks?**

NeurIPS 2020. *Tl,dr; the bigger your model, the easier it is to be approximately Bayesian.* When doing Variational Inference with large Bayesian Neural Networks, we feel practically forced to use the mean-field approximation. But ‘common knowledge’ tells us this is a bad approximation, leading to many expensive structured covariance methods. This work challenges ‘common knowledge’ regarding large neural networks, where the complexity of the network structure allows simple variational approximations to be effective. …

Sebastian Farquhar, Lewis Smith, Yarin Gal, 29 Nov 2020

**13 OATML Conference and Workshop papers at ICML 2020**

We are glad to share the following 13 papers by OATML authors and collaborators to be presented at this ICML conference and workshops …

Full post...Angelos Filos, Sebastian Farquhar, Tim G. J. Rudner, Lewis Smith, Lisa Schut, Tom Rainforth, Panagiotis Tigas, Pascal Notin, Andreas Kirsch, Clare Lyle, Joost van Amersfoort, Jishnu Mukhoti, Yarin Gal, 10 Jul 2020

**Beyond Discrete Support in Large-scale Bayesian Deep Learning**

Most of the scalable methods for Bayesian deep learning give approximate posteriors with ‘discrete support’, which is unsuitable for Bayesian updating. Mean-field variational inference could work, but we show that it fails in high dimensions because of the ‘soap-bubble’ pathology of multivariate Gaussians. We introduce a novel approximating posterior, Radial BNNs, that give you the distribution you intuitively imagine when you think about multi-variate Gaussians in high dimensions. Repo at https://github.com/SebFar/radial_bnn …

Full post...Sebastian Farquhar, Michael Osborne, Yarin Gal, 22 Apr 2020

**25 OATML Conference and Workshop papers at NeurIPS 2019**

We are glad to share the following 25 papers by OATML authors and collaborators to be presented at this NeurIPS conference and workshops. …

Full post...Angelos Filos, Sebastian Farquhar, Aidan Gomez, Tim G. J. Rudner, Zac Kenton, Lewis Smith, Milad Alizadeh, Tom Rainforth, Panagiotis Tigas, Andreas Kirsch, Clare Lyle, Joost van Amersfoort, Yarin Gal, 08 Dec 2019

**Bayesian Deep Learning Benchmarks**

In order to make real-world difference with **Bayesian Deep Learning** (BDL) tools, the tools must scale to real-world settings. And for that we, the research community, must be able to evaluate our inference tools (and iterate quickly) with real-world benchmark tasks. We should be able to do this without necessarily worrying about application-specific domain knowledge, like the expertise often required in medical applications for example. We require benchmarks to test for inference robustness, performance, and accuracy, in addition to cost and effort of development. These benchmarks should be at a variety of scales, ranging from toy MNIST-scale benchmarks for fast development cycles, to large data benchmarks which are truthful to real-world applications, capturing their constraints. …

Angelos Filos, Sebastian Farquhar, Aidan Gomez, Tim G. J. Rudner, Zac Kenton, Lewis Smith, Milad Alizadeh, Yarin Gal, 14 Jun 2019