Mixed-membership (MM) models such as Latent Dirichlet Allocation (LDA) have been applied to microbiome compositional data to identify latent subcommunities of microbial species. However, microbiome compositional data, especially those collected from the gut, typically display substantial cross-sample heterogeneities in the subcommunity composition which current MM methods do not account for. To address this limitation, we incorporate the logistic-tree normal (LTN) model -- using the phylogenetic tree structure -- into the LDA model to form a new MM model. This model allows variation in the composition of each subcommunity around some ``centroid'' composition. Incorporation of auxiliary P\'olya-Gamma variables enables a computationally efficient collapsed blocked Gibbs sampler to carry out Bayesian inference under this model. We compare the new model and LDA and show that in the presence of large cross-sample heterogeneity, under the LDA model the resulting inference can be extremely sensitive to the specification of the total number of subcommunities as it does not account for cross-sample heterogeneity. As such, the popular strategy in other applications of MM models of overspecifying the number of subcommunities -- and hoping that some meaningful subcommunities will emerge among artificial ones -- can lead to highly misleading conclusions in the microbiome context. In contrast, by accounting for such heterogeneity, our MM model restores the robustness of the inference in the specification of the number of subcommunities and again allows meaningful subcommunities to be identified under this strategy.

Causal inference using observational text data is becoming increasingly popular in many research areas. This paper presents the Bayesian Topic Regression (BTR) model that uses both text and numerical information to model an outcome variable. It allows estimation of both discrete and continuous treatment effects. Furthermore, it allows for the inclusion of additional numerical confounding factors next to text data. To this end, we combine a supervised Bayesian topic model with a Bayesian regression framework and perform supervised representation learning for the text features jointly with the regression parameter training, respecting the Frisch-Waugh-Lovell theorem. Our paper makes two main contributions. First, we provide a regression framework that allows causal inference in settings when both text and numerical confounders are of relevance. We show with synthetic and semi-synthetic datasets that our joint approach recovers ground truth with lower bias than any benchmark model, when text and numerical features are correlated. Second, experiments on two real-world datasets demonstrate that a joint and supervised learning strategy also yields superior prediction results compared to strategies that estimate regression weights for text and non-text features separately, being even competitive with more complex deep neural networks.

Driving is an intuitive task that requires skills, constant alertness and vigilance for unexpected events. The driving task also requires long concentration spans focusing on the entire task for prolonged periods, and sophisticated negotiation skills with other road users, including wild animals. These requirements are particularly important when approaching intersections, overtaking, giving way, merging, turning and while adhering to the vast body of road rules. Modern motor vehicles now include an array of smart assistive and autonomous driving systems capable of subsuming some, most, or in limited cases, all of the driving task. The UK Department of Transport's response to the Safe Use of Automated Lane Keeping System consultation proposes that these systems are tested for compliance with relevant traffic rules. Building these smart automotive systems requires software developers with highly technical software engineering skills, and now a lawyer's in-depth knowledge of traffic legislation as well. These skills are required to ensure the systems are able to safely perform their tasks while being observant of the law. This paper presents an approach for deconstructing the complicated legalese of traffic law and representing its requirements and flow. The approach (de)constructs road rules in legal terminology and specifies them in structured English logic that is expressed as Boolean logic for automation and Lawmaps for visualisation. We demonstrate an example using these tools leading to the construction and validation of a Bayesian Network model. We strongly believe these tools to be approachable by programmers and the general public, and capable of use in developing Artificial Intelligence to underpin motor vehicle smart systems, and in validation to ensure these systems are considerate of the law when making decisions.

Knowing the position of the robot in the world is crucial for navigation. Nowadays, Bayesian filters, such as Kalman and particle-based, are standard approaches in mobile robotics. Recently, end-to-end learning has allowed for scaling-up to high-dimensional inputs and improved generalization. However, there are still limitations to providing reliable laser navigation. Here we show a proof-of-concept of the predictive processing-inspired approach to perception applied for localization and navigation using laser sensors, without the need for odometry. We learn the generative model of the laser through self-supervised learning and perform both online state-estimation and navigation through stochastic gradient descent on the variational free-energy bound. We evaluated the algorithm on a mobile robot (TIAGo Base) with a laser sensor (SICK) in Gazebo. Results showed improved state-estimation performance when comparing to a state-of-the-art particle filter in the absence of odometry. Furthermore, conversely to standard Bayesian estimation approaches our method also enables the robot to navigate when providing the desired goal by inferring the actions that minimize the prediction error.

Probabilistic generative models are attractive for scientific modeling because their inferred parameters can be used to generate hypotheses and design experiments. This requires that the learned model provide an accurate representation of the input data and yield a latent space that effectively predicts outcomes relevant to the scientific question. Supervised Variational Autoencoders (SVAEs) have previously been used for this purpose, where a carefully designed decoder can be used as an interpretable generative model while the supervised objective ensures a predictive latent representation. Unfortunately, the supervised objective forces the encoder to learn a biased approximation to the generative posterior distribution, which renders the generative parameters unreliable when used in scientific models. This issue has remained undetected as reconstruction losses commonly used to evaluate model performance do not detect bias in the encoder. We address this previously-unreported issue by developing a second order supervision framework (SOS-VAE) that influences the decoder to induce a predictive latent representation. This ensures that the associated encoder maintains a reliable generative interpretation. We extend this technique to allow the user to trade-off some bias in the generative parameters for improved predictive performance, acting as an intermediate option between SVAEs and our new SOS-VAE. We also use this methodology to address missing data issues that often arise when combining recordings from multiple scientific experiments. We demonstrate the effectiveness of these developments using synthetic data and electrophysiological recordings with an emphasis on how our learned representations can be used to design scientific experiments.

Geographic Information Systems (GIS) and related technologies have generated substantial interest among statisticians with regard to scalable methodologies for analyzing large spatial datasets. A variety of scalable spatial process models have been proposed that can be easily embedded within a hierarchical modeling framework to carry out Bayesian inference. While the focus of statistical research has mostly been directed toward innovative and more complex model development, relatively limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article discusses how point-referenced spatial process models can be cast as a conjugate Bayesian linear regression that can rapidly deliver inference on spatial processes. The approach allows exact sampling directly (avoids iterative algorithms such as Markov chain Monte Carlo) from the joint posterior distribution of regression parameters, the latent process and the predictive random variables, and can be easily implemented on statistical programming environments such as R.

Markov Chain Monte Carlo (MCMC) methods are promising solutions to sample from target distributions in high dimensions. While MCMC methods enjoy nice theoretical properties, like guaranteed convergence and mixing to the true target, in practice their sampling efficiency depends on the choice of the proposal distribution and the target at hand. This work considers using machine learning to adapt the proposal distribution to the target, in order to improve the sampling efficiency in the purely discrete domain. Specifically, (i) it proposes a new parametrization for a family of proposal distributions, called locally balanced proposals, (ii) it defines an objective function based on mutual information and (iii) it devises a learning procedure to adapt the parameters of the proposal to the target, thus achieving fast convergence and fast mixing. We call the resulting sampler as the Locally Self-Balancing Sampler (LSB). We show through experimental analysis on the Ising model and Bayesian networks that LSB is indeed able to improve the efficiency over a state-of-the-art sampler based on locally balanced proposals, thus reducing the number of iterations required to converge, while achieving comparable mixing performance.

Bayesian methods have become a popular way to incorporate prior knowledge and a notion of uncertainty into machine learning models. At the same time, the complexity of modern machine learning makes it challenging to comprehend a model's reasoning process, let alone express specific prior assumptions in a rigorous manner. While primarily interested in the former issue, recent developments in transparent machine learning could also broaden the range of prior information that we can provide to complex Bayesian models. Inspired by the idea of selfexplaining models, we introduce a corresponding concept for variational Gaussian Processes. On the one hand, our contribution improves transparency for these types of models. More importantly though, our proposed self-explaining variational posterior distribution allows to incorporate both general prior knowledge about a target function as a whole and prior knowledge about the contribution of individual features.

We consider the use of Gaussian process (GP) priors for solving inverse problems in a Bayesian framework. As is well known, the computational complexity of GPs scales cubically in the number of datapoints. We here show that in the context of inverse problems involving integral operators, one faces additional difficulties that hinder inversion on large grids. Furthermore, in that context, covariance matrices can become too large to be stored. By leveraging results about sequential disintegrations of Gaussian measures, we are able to introduce an implicit representation of posterior covariance matrices that reduces the memory footprint by only storing low rank intermediate matrices, while allowing individual elements to be accessed on-the-fly without needing to build full posterior covariance matrices. Moreover, it allows for fast sequential inclusion of new observations. These features are crucial when considering sequential experimental design tasks. We demonstrate our approach by computing sequential data collection plans for excursion set recovery for a gravimetric inverse problem, where the goal is to provide fine resolution estimates of high density regions inside the Stromboli volcano, Italy. Sequential data collection plans are computed by extending the weighted integrated variance reduction (wIVR) criterion to inverse problems. Our results show that this criterion is able to significantly reduce the uncertainty on the excursion volume, reaching close to minimal levels of residual uncertainty. Overall, our techniques allow the advantages of probabilistic models to be brought to bear on large-scale inverse problems arising in the natural sciences.

We introduce semiparametric Bayesian networks that combine parametric and nonparametric conditional probability distributions. Their aim is to incorporate the advantages of both components: the bounded complexity of parametric models and the flexibility of nonparametric ones. We demonstrate that semiparametric Bayesian networks generalize two well-known types of Bayesian networks: Gaussian Bayesian networks and kernel density estimation Bayesian networks. For this purpose, we consider two different conditional probability distributions required in a semiparametric Bayesian network. In addition, we present modifications of two well-known algorithms (greedy hill-climbing and PC) to learn the structure of a semiparametric Bayesian network from data. To realize this, we employ a score function based on cross-validation. In addition, using a validation dataset, we apply an early-stopping criterion to avoid overfitting. To evaluate the applicability of the proposed algorithm, we conduct an exhaustive experiment on synthetic data sampled by mixing linear and nonlinear functions, multivariate normal data sampled from Gaussian Bayesian networks, real data from the UCI repository, and bearings degradation data. As a result of this experiment, we conclude that the proposed algorithm accurately learns the combination of parametric and nonparametric components, while achieving a performance comparable with those provided by state-of-the-art methods.