Uncertainty estimation is important for ensuring safety and robustness of AI systems, especially for high-risk applications. While much progress has recently been made in this area, most research has focused on un-structured prediction, such as image classification and regression tasks. However, while task-specific forms of confidence score estimation have been investigated by the speech and machine translation communities, limited work has investigated general uncertainty estimation approaches for structured prediction. Thus, this work aims to investigate uncertainty estimation for structured prediction tasks within a single unified and interpretable probabilistic ensemble-based framework. We consider uncertainty estimation for sequence data at the token-level and complete sequence-level, provide interpretations for, and applications of, various measures of uncertainty and discuss the challenges associated with obtaining them. This work also explores the practical challenges associated with obtaining uncertainty estimates for structured predictions tasks and provides baselines for token-level error detection, sequence-level prediction rejection, and sequence-level out-of-domain input detection using ensembles of auto-regressive transformer models trained on the WMT'14 English-French and WMT'17 English-German translation and LibriSpeech speech recognition datasets.

A Machine can only learn if it is biased in some way. Typically the bias is supplied by hand, for example through the choice of an appropriate set of features. However, if the learning machine is embedded within an {\em environment} of related tasks, then it can {\em learn} its own bias by learning sufficiently many tasks from the environment. In this paper two models of bias learning (or equivalently, learning to learn) are introduced and the main theoretical results presented. The first model is a PAC-type model based on empirical process theory, while the second is a hierarchical Bayes model.

A large fraction of the electronic health records (EHRs) consists of clinical measurements collected over time, such as lab tests and vital signs, which provide important information about a patient's health status. These sequences of clinical measurements are naturally represented as time series, characterized by multiple variables and large amounts of missing data, which complicate the analysis. In this work, we propose a novel kernel which is capable of exploiting both the information from the observed values as well the information hidden in the missing patterns in multivariate time series (MTS) originating e.g. from EHRs. The kernel, called TCK$_{IM}$, is designed using an ensemble learning strategy in which the base models are novel mixed mode Bayesian mixture models which can effectively exploit informative missingness without having to resort to imputation methods. Moreover, the ensemble approach ensures robustness to hyperparameters and therefore TCK$_{IM}$ is particularly well suited if there is a lack of labels - a known challenge in medical applications. Experiments on three real-world clinical datasets demonstrate the effectiveness of the proposed kernel.

Weak supervision is a popular method for building machine learning models without relying on ground truth annotations. Instead, it generates probabilistic training labels by estimating the accuracies of multiple noisy labeling sources (e.g., heuristics, crowd workers). Existing approaches use latent variable estimation to model the noisy sources, but these methods can be computationally expensive, scaling superlinearly in the data. In this work, we show that, for a class of latent variable models highly applicable to weak supervision, we can find a closed-form solution to model parameters, obviating the need for iterative solutions like stochastic gradient descent (SGD). We use this insight to build FlyingSquid, a weak supervision framework that runs orders of magnitude faster than previous weak supervision approaches and requires fewer assumptions. In particular, we prove bounds on generalization error without assuming that the latent variable model can exactly parameterize the underlying data distribution. Empirically, we validate FlyingSquid on benchmark weak supervision datasets and find that it achieves the same or higher quality compared to previous approaches without the need to tune an SGD procedure, recovers model parameters 170 times faster on average, and enables new video analysis and online learning applications.

One-shot neural architecture search allows joint learning of weights and network architecture, reducing computational cost. We limit our search space to the depth of residual networks and formulate an analytically tractable variational objective that allows for obtaining an unbiased approximate posterior over depths in one-shot. We propose a heuristic to prune our networks based on this distribution. We compare our proposed method against manual search over network depths on the MNIST, Fashion-MNIST, SVHN datasets. We find that pruned networks do not incur a loss in predictive performance, obtaining accuracies competitive with unpruned networks. Marginalising over depth allows us to obtain better-calibrated test-time uncertainty estimates than regular networks, in a single forward pass.

Bayesian learning rule is a recently proposed variational inference method, which not only contains many existing learning algorithms as special cases but also enables the design of new algorithms. Unfortunately, when posterior parameters lie in an open constraint set, the rule may not satisfy the constraints and requires line-searches which could slow down the algorithm. In this paper, we fix this issue for the positive-definite constraint by proposing an improved rule that naturally handles the constraint. Our modification is obtained using Riemannian gradient methods, and is valid when the approximation attains a \emph{block-coordinate natural parameterization} (e.g., Gaussian distributions and their mixtures). Our method outperforms existing methods without any significant increase in computation. Our work makes it easier to apply the learning rule in the presence of positive-definite constraints in parameter spaces.

Modelling exchangeable relational data can be described by \textit{graphon theory}. Most Bayesian methods for modelling exchangeable relational data can be attributed to this framework by exploiting different forms of graphons. However, the graphons adopted by existing Bayesian methods are either piecewise-constant functions, which are insufficiently flexible for accurate modelling of the relational data, or are complicated continuous functions, which incur heavy computational costs for inference. In this work, we introduce a smoothing procedure to piecewise-constant graphons to form {\em smoothing graphons}, which permit continuous intensity values for describing relations, but without impractically increasing computational costs. In particular, we focus on the Bayesian Stochastic Block Model (SBM) and demonstrate how to adapt the piecewise-constant SBM graphon to the smoothed version. We initially propose the Integrated Smoothing Graphon (ISG) which introduces one smoothing parameter to the SBM graphon to generate continuous relational intensity values. We then develop the Latent Feature Smoothing Graphon (LFSG), which improves on the ISG by introducing auxiliary hidden labels to decompose the calculation of the ISG intensity and enable efficient inference. Experimental results on real-world data sets validate the advantages of applying smoothing strategies to the Stochastic Block Model, demonstrating that smoothing graphons can greatly improve AUC and precision for link prediction without increasing computational complexity.

Artificial Neural Networks (ANNs) implement a specific form of multi-variate extrapolation and will generate an output for any input pattern, even when there is no similar training pattern. Extrapolations are not necessarily to be trusted, and in order to support safety critical systems, we require such systems to give an indication of the training sample related uncertainty associated with their output. Some readers may think that this is a well known issue which is already covered by the basic principles of pattern recognition. We will explain below how this is not the case and how the conventional (Likelihood estimate of) conditional probability of classification does not correctly assess this uncertainty. We provide a discussion of the standard interpretations of this problem and show how a quantitative approach based upon long standing methods can be practically applied. The methods are illustrated on the task of early diagnosis of dementing diseases using Magnetic Resonance Imaging.

Normalizing flows (Rezende & Mohamed, 2015) are probabilistic models constructed as a sequence of successive transformations applied to some initial distribution. A key strength of normalizing flows is their expressive power as generative models, while enjoying an explicitly computable form of the likelihood function evaluated on the transformed space. This makes them especially well-equipped for variational inference (VI). Neural networks are often used as inspiration for finding effective transformations (Dinh et al., 2015; van den Berg et al., 2018). Continuous normalizing flows were later developed in Chen et al. (2018) as a means to perform maximum likelihood estimation and VI for large-scale probabilistic models derived from ordinary differential equations (ODEs).

Neural networks with binary weights are computation-efficient and hardware-friendly, but their training is challenging because it involves a discrete optimization problem. Surprisingly, ignoring the discrete nature of the problem and using gradient-based methods, such as Straight-Through Estimator, still works well in practice. This raises the question: are there principled approaches which justify such methods? In this paper, we propose such an approach using the Bayesian learning rule. The rule, when applied to estimate a Bernoulli distribution over the binary weights, results in an algorithm which justifies some of the algorithmic choices made by the previous approaches. The algorithm not only obtains state-of-the-art performance, but also enables uncertainty estimation for continual learning to avoid catastrophic forgetting. Our work provides a principled approach for training binary neural networks which justifies and extends existing approaches.