Probabilistic Spatial Transformers for Bayesian Data Augmentation

High-capacity models require vast amounts of data, and data augmentation is a common remedy when this resource is limited. Standard augmentation techniques apply small hand-tuned transformations to existing data, which is a brittle process that realistically only allows for simple transformations. We propose a Bayesian interpretation of data augmentation where the transformations are modelled as latent variables to be marginalized, and show how these can be inferred variationally in an end-to-end fashion. This allows for significantly more complex transformations than manual tuning, and the marginalization implies a form of test-time data augmentation. The resulting model can be interpreted as a probabilistic extension of spatial transformer networks. Experimentally, we demonstrate improvements in accuracy and uncertainty quantification in image and time series classification tasks.Comment: Submitted to the International Conference on Machine Learning (ICML), 202

Last Layer Marginal Likelihood for Invariance Learning

Data augmentation is often used to incorporate inductive biases into models. Traditionally, these are hand-crafted and tuned with cross validation. The Bayesian paradigm for model selection provides a path towards end-to-end learning of invariances using only the training data, by optimising the marginal likelihood. We work towards bringing this approach to neural networks by using an architecture with a Gaussian process in the last layer, a model for which the marginal likelihood can be computed. Experimentally, we improve performance by learning appropriate invariances in standard benchmarks, the low data regime and in a medical imaging task. Optimisation challenges for invariant Deep Kernel Gaussian processes are identified, and a systematic analysis is presented to arrive at a robust training scheme. We introduce a new lower bound to the marginal likelihood, which allows us to perform inference for a larger class of likelihood functions than before, thereby overcoming some of the training challenges that existed with previous approaches

The Long Arc of Fairness:Formalisations and Ethical Discourse

In recent years, the idea of formalising and modelling fairness for algorithmic decision making (ADM) has advanced to a point of sophisticated specialisation. However, the relations between technical (formalised) and ethical discourse on fairness are not always clear and productive. Arguing for an alternative perspective, we review existing fairness metrics and discuss some common issues. For instance, the fairness of procedures and distributions is often formalised and discussed statically, disregarding both structural preconditions of the status quo and downstream effects of a given intervention. We then introduce dynamic fairness modelling, a more comprehensive approach that realigns formal fairness metrics with arguments from the ethical discourse. A dynamic fairness model incorporates (1) ethical goals, (2) formal metrics to quantify decision procedures and outcomes and (3) mid-term or long-term downstream effects. By contextualising these elements of fairness-related processes, dynamic fairness modelling explicates formerly latent ethical aspects and thereby provides a helpful tool to navigate trade-offs between different fairness interventions. To illustrate the framework, we discuss an example application -- the current European efforts to increase the number of women on company boards, e.g. via quota solutions -- and present early technical work that fits within our framework