Until recently, transcriptomics was limited to bulk RNA sequencing, obscuring the underlying expression patterns of individual cells in favor of a global average. Thanks to technological advances, we can now profile gene expression across thousands or millions of individual cells in parallel. This new type of data has led to the intriguing discovery that individual cell profiles can reflect the imprint of time or dynamic processes. However, synthesizing this information to reconstruct dynamic biological phenomena from data that are noisy, heterogenous, and sparse---and from processes that may unfold asynchronously---poses a complex computational and statistical challenge. Here, we develop a full generative model for probabilistically reconstructing trees of cellular differentiation from single-cell RNA-seq data. Specifically, we extend the framework of the classical Dirichlet diffusion tree to simultaneously infer branch topology and latent cell states along continuous trajectories over the full tree. In tandem, we construct a novel Markov chain Monte Carlo sampler that interleaves Metropolis-Hastings and message passing to leverage model structure for efficient inference. Finally, we demonstrate that these techniques can recover latent trajectories from simulated single-cell transcriptomes. While this work is motivated by cellular differentiation, we derive a tractable model that provides flexible densities for any data (coupled with an appropriate noise model) that arise from continuous evolution along a latent nonparametric tree.

Recently, techniques for applying convolutional neural networks to graph-structured data have emerged. Graph convolutional neural networks (GCNNs) have been used to address node and graph classification and matrix completion. Although the performance has been impressive, the current implementations have limited capability to incorporate uncertainty in the graph structure. Almost all GCNNs process a graph as though it is a ground-truth depiction of the relationship between nodes, but often the graphs employed in applications are themselves derived from noisy data or modelling assumptions. Spurious edges may be included; other edges may be missing between nodes that have very strong relationships. In this paper we adopt a Bayesian approach, viewing the observed graph as a realization from a parametric family of random graphs. We then target inference of the joint posterior of the random graph parameters and the node (or graph) labels. We present the Bayesian GCNN framework and develop an iterative learning procedure for the case of assortative mixed-membership stochastic block models. We present the results of experiments that demonstrate that the Bayesian formulation can provide better performance when there are very few labels available during the training process.

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.

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.