Assessing the fairness of a decision making system with respect to a protected class, such as gender or race, is challenging when class membership labels are unavailable. Probabilistic models for predicting the protected class based on observable proxies, such as surname and geolocation for race, are sometimes used to impute these missing labels for compliance assessments. Empirically, these methods are observed to exaggerate disparities, but the reason why is unknown. In this paper, we decompose the biases in estimating outcome disparity via threshold-based imputation into multiple interpretable bias sources, allowing us to explain when over- or underestimation occurs. We also propose an alternative weighted estimator that uses soft classification, and show that its bias arises simply from the conditional covariance of the outcome with the true class membership. Finally, we illustrate our results with numerical simulations and a public dataset of mortgage applications, using geolocation as a proxy for race. We confirm that the bias of threshold-based imputation is generally upward, but its magnitude varies strongly with the threshold chosen. Our new weighted estimator tends to have a negative bias that is much simpler to analyze and reason about.

Ensembles of neural networks (NNs) have long been used to estimate predictive uncertainty; a small number of NNs are trained from different initialisations and sometimes on differing versions of the dataset. The variance of the ensemble's predictions is interpreted as its epistemic uncertainty. The appeal of ensembling stems from being a collection of regular NNs - this makes them both scalable and easily implementable. They have achieved strong empirical results in recent years, often presented as a practical alternative to more costly Bayesian NNs (BNNs). The departure from Bayesian methodology is of concern since the Bayesian framework provides a principled, widely-accepted approach to handling uncertainty. In this extended abstract we derive and implement a modified NN ensembling scheme, which provides a consistent estimator of the Bayesian posterior in wide NNs - regularising parameters about values drawn from a prior distribution.

This technical report describes the multi-label classification (MLC) search space in the MEKA software, including the traditional/meta MLC algorithms, and the traditional/meta/pre-processing single-label classification (SLC) algorithms. The SLC search space is also studied because is part of MLC search space as several methods use problem transformation methods to create a solution (i.e., a classifier) for a MLC problem. This was done in order to understand better the MLC algorithms. Finally, we propose a grammar that formally expresses this understatement.

Variational inference (VI) has become the method of choice for fitting many modern probabilistic models. However, practitioners are faced with a fragmented literature that offers a bewildering array of algorithmic options. First, the variational family. Second, the granularity of the updates e.g. whether the updates are local to each data point and employ message passing or global. Third, the method of optimization (bespoke or blackbox, closed-form or stochastic updates, etc.). This paper presents a new framework, termed Partitioned Variational Inference (PVI), that explicitly acknowledges these algorithmic dimensions of VI, unifies disparate literature, and provides guidance on usage. Crucially, the proposed PVI framework allows us to identify new ways of performing VI that are ideally suited to challenging learning scenarios including federated learning (where distributed computing is leveraged to process non-centralized data) and continual learning (where new data and tasks arrive over time and must be accommodated quickly). We showcase these new capabilities by developing communication-efficient federated training of Bayesian neural networks and continual learning for Gaussian process models with private pseudo-points. The new methods significantly outperform the state-of-the-art, whilst being almost as straightforward to implement as standard VI.

This work presents an approach to automatically induction for non-greedy decision trees constructed from neural network architecture. This construction can be used to transfer weights when growing or pruning a decision tree, allowing non-greedy decision tree algorithms to automatically learn and adapt to the ideal architecture. In this work, we examine the underpinning ideas within ensemble modelling and Bayesian model averaging which allow our neural network to asymptotically approach the ideal architecture through weights transfer. Experimental results demonstrate that this approach improves models over fixed set of hyperparameters for decision tree models and decision forest models.

This article is the rejoinder for the paper "Probabilistic Integration: A Role in Statistical Computation?" to appear in Statistical Science with discussion [Briol et al., 2015]. We would first like to thank the reviewers and many of our colleagues who helped shape this paper, the editor for selecting our paper for discussion, and of course all of the discussants for their thoughtful, insightful and constructive comments. In this rejoinder, we respond to some of the points raised by the discussants and comment further on the fundamental questions underlying the paper: - Should Bayesian ideas be used in numerical analysis? Numerical analysis is concerned with the approximation of typically high or infinite-dimensional mathematical quantities using discretisations of the space on which these are defined. Different discretisation schemes lead to different numerical algorithms, whose stability and convergence properties need to be carefully assessed.

Food packaging labels provide important information for public health, such as allergens and use-by dates. Off-the-shelf Optical Character Verification (OCV) systems are good solutions for automating food label quality assessments, but are known to under perform on complex data. This paper proposes a Deep Learning based system that can identify inadequate images for OCV, due to their poor label quality, by employing state-of-the-art Convolutional Neural Network (CNN) architectures, and practical Bayesian inference techniques for automatic self-annotation. We propose a practical domain adaptation procedure based on k-means clustering of CNN latent variables, followed by a k-Nearest Neighbour classification for handling high label variability between different dataset distributions. Moreover, Supervised Learning has proven useful in such systems but manual annotation of large amounts of data is usually required. This is practically intractable in most real world problems due to time/labour constraints. In an attempt to address this issue, we introduce a self-annotating prediction model based on Self-Training of a Bayesian CNN, that leverages modern variational inference methods of deep models. In this context, we propose a new inverse uncertainty weighting technique that encourages the Self-Training model to learn from more informative data over time, potentially preventing it from becoming lazy by only selecting easy examples to learn from. An experimental study is presented illustrating the superior performance of the proposed approach over standard Self-Training, and highlighting the importance of predictive uncertainty estimates in safety-critical domains.

Deep neural networks (DNNs) provide state-of-the-art results for a multitude of applications, but the use of DNNs for multimodal audiovisual applications is still an unsolved problem. The current approaches that combine audiovisual information do not consider inherent uncertainty or leverage true classification confidence associated with each modality in the final decision. Our contribution in this work is to apply Bayesian variational inference to DNNs for audiovisual activity recognition and quantify model uncertainty along with principled confidence. We propose a novel approach that combines deterministic and variational layers to estimate model uncertainty and principled confidence. Our experiments with in- and out-of-distribution samples selected from a subset of the Moments-in-Time (MiT) dataset show more reliable confidence measure as compared to the non-Bayesian baseline. We also demonstrate the uncertainty estimates obtained from this framework can identify out-of-distribution data on the UCF101 and MiT datasets. In the multimodal setting, the proposed framework improved precision-recall AUC by 14.4% on the subset of MiT dataset as compared to non-Bayesian baseline.

Two major classes of numerical problems that arise in data analysis procedures are optimization and integration problems. It is not always possible to analytically compute the estimators associated with a given model, and we are often led to consider numerical solutions. One way to avoid that problem is to use simulation. Monte Carlo estimation refers to simulating hypothetical draws from a probability distribution, in order to calculate significant quantities of that distribution. The basic idea of Monte Carlo consist of writing the integral as an expected value with respect to some probability distribution, and then approximated using the method of moment estimator ($E[g(X)] \approx \overline{g(X)} \dfrac{1}{n}\sum g(X_{i})$).

In this work, we present our various contributions to the objective of building a decision support tool for the diagnosis of rare diseases. Our goal is to achieve a state of knowledge where the uncertainty about the patient's disease is below a predetermined threshold. We aim to reach such states while minimizing the average number of medical tests to perform. In doing so, we take into account the need, in many medical applications, to avoid, as much as possible, any misdiagnosis. To solve this optimization task, we investigate several reinforcement learning algorithm and make them operable in our high-dimensional and sparse-reward setting. We also present a way to combine expert knowledge, expressed as conditional probabilities, with real clinical data. This is crucial because the scarcity of data in the field of rare diseases prevents any approach based solely on clinical data. Finally we show that it is possible to integrate the ontological information about symptoms while remaining in our probabilistic reasoning. It enables our decision support tool to process information given at different level of precision by the user.