Extracting low-dimensional summary statistics from large datasets is essential for efficient (likelihood-free) inference. We characterise different classes of summaries and demonstrate their importance for correctly analysing dimensionality reduction algorithms. We propose obtaining summaries by minimising the expected posterior entropy (EPE) under the prior predictive distribution of the model. Many existing methods are equivalent to or are special or limiting cases of minimising the EPE. We develop a method to obtain high-fidelity summaries that minimise the EPE; we apply it to benchmark and real-world examples. We both offer a unifying perspective for obtaining informative summaries and provide concrete recommendations for practitioners.

Many real-world processes have complex tail dependence structures that cannot be characterized using classical Gaussian processes. More flexible spatial extremes models exhibit appealing extremal dependence properties but are often exceedingly prohibitive to fit and simulate from in high dimensions. In this paper, we develop a new spatial extremes model that has flexible and non-stationary dependence properties, and we integrate it in the encoding-decoding structure of a variational autoencoder (XVAE), whose parameters are estimated via variational Bayes combined with deep learning. The XVAE can be used as a spatio-temporal emulator that characterizes the distribution of potential mechanistic model output states and produces outputs that have the same statistical properties as the inputs, especially in the tail. As an aside, our approach also provides a novel way of making fast inference with complex extreme-value processes. Through extensive simulation studies, we show that our XVAE is substantially more time-efficient than traditional Bayesian inference while also outperforming many spatial extremes models with a stationary dependence structure. To further demonstrate the computational power of the XVAE, we analyze a high-resolution satellite-derived dataset of sea surface temperature in the Red Sea, which includes 30 years of daily measurements at 16703 grid cells. We find that the extremal dependence strength is weaker in the interior of Red Sea and it has decreased slightly over time.

Neural networks have achieved remarkable performance across various problem domains, but their widespread applicability is hindered by inherent limitations such as overconfidence in predictions, lack of interpretability, and vulnerability to adversarial attacks. To address these challenges, Bayesian neural networks (BNNs) have emerged as a compelling extension of conventional neural networks, integrating uncertainty estimation into their predictive capabilities. This comprehensive primer presents a systematic introduction to the fundamental concepts of neural networks and Bayesian inference, elucidating their synergistic integration for the development of BNNs. The target audience comprises statisticians with a potential background in Bayesian methods but lacking deep learning expertise, as well as machine learners proficient in deep neural networks but with limited exposure to Bayesian statistics. We provide an overview of commonly employed priors, examining their impact on model behavior and performance. Additionally, we delve into the practical considerations associated with training and inference in BNNs. Furthermore, we explore advanced topics within the realm of BNN research, acknowledging the existence of ongoing debates and controversies. By offering insights into cutting-edge developments, this primer not only equips researchers and practitioners with a solid foundation in BNNs, but also illuminates the potential applications of this dynamic field. As a valuable resource, it fosters an understanding of BNNs and their promising prospects, facilitating further advancements in the pursuit of knowledge and innovation.

Motion planning under sensing uncertainty is critical for robots in unstructured environments to guarantee safety for both the robot and any nearby humans. Most work on planning under uncertainty does not scale to high-dimensional robots such as manipulators, assumes simplified geometry of the robot or environment, or requires per-object knowledge of noise. Instead, we propose a method that directly models sensor-specific aleatoric uncertainty to find safe motions for high-dimensional systems in complex environments, without exact knowledge of environment geometry. We combine a novel implicit neural model of stochastic signed distance functions with a hierarchical optimization-based motion planner to plan low-risk motions without sacrificing path quality. Our method also explicitly bounds the risk of the path, offering trustworthiness. We empirically validate that our method produces safe motions and accurate risk bounds and is safer than baseline approaches.

We study the convergence of $Q$-learning with linear function approximation. Our key contribution is the introduction of a novel multi-Bellman operator that extends the traditional Bellman operator. By exploring the properties of this operator, we identify conditions under which the projected multi-Bellman operator becomes contractive, providing improved fixed-point guarantees compared to the Bellman operator. To leverage these insights, we propose the multi $Q$-learning algorithm with linear function approximation. We demonstrate that this algorithm converges to the fixed-point of the projected multi-Bellman operator, yielding solutions of arbitrary accuracy. Finally, we validate our approach by applying it to well-known environments, showcasing the effectiveness and applicability of our findings.

Copulas are a powerful statistical tool that captures dependencies across data dimensions. When applying Copulas, we can estimate multivariate distribution functions by initially estimating independent marginals, an easy task, and then a single copulating function, $C$, to connect the marginals, a hard task. For two-dimensional data, a copula is a two-increasing function of the form $C: (u,v)\in \mathbf{I}^2 \rightarrow \mathbf{I}$, where $\mathbf{I} = [0, 1]$. In this paper, we show how Neural Networks (NNs) can approximate any two-dimensional copula non-parametrically. Our approach, denoted as 2-Cats, is inspired by the Physics-Informed Neural Networks and Sobolev Training literature. Not only do we show that we can estimate the output of a 2d Copula better than the state-of-the-art, our approach is non-parametric and respects the mathematical properties of a Copula $C$.

Exact computation of the partition function is known to be intractable, necessitating approximate inference techniques. Existing methods for approximate inference are slow to converge for many benchmarks. The control of accuracy-complexity trade-off is also non-trivial in many of these methods. We propose a novel incremental build-infer-approximate (IBIA) framework for approximate inference that addresses these issues. In this framework, the probabilistic graphical model is converted into a sequence of clique tree forests (SCTF) with bounded clique sizes. We show that the SCTF can be used to efficiently compute the partition function. We propose two new algorithms which are used to construct the SCTF and prove the correctness of both. The first is an algorithm for incremental construction of CTFs that is guaranteed to give a valid CTF with bounded clique sizes and the second is an approximation algorithm that takes a calibrated CTF as input and yields a valid and calibrated CTF with reduced clique sizes as the output. We have evaluated our method using several benchmark sets from recent UAI competitions and our results show good accuracies with competitive runtimes.

This article presents a comprehensive review of the Active Simultaneous Localization and Mapping (A-SLAM) research conducted over the past decade. It explores the formulation, applications, and methodologies employed in A-SLAM, particularly in trajectory generation and control-action selection, drawing on concepts from Information Theory (IT) and the Theory of Optimal Experimental Design (TOED). This review includes both qualitative and quantitative analyses of various approaches, deployment scenarios, configurations, path-planning methods, and utility functions within A-SLAM research. Furthermore, this article introduces a novel analysis of Active Collaborative SLAM (AC-SLAM), focusing on collaborative aspects within SLAM systems. It includes a thorough examination of collaborative parameters and approaches, supported by both qualitative and statistical assessments. This study also identifies limitations in the existing literature and suggests potential avenues for future research. This survey serves as a valuable resource for researchers seeking insights into A-SLAM methods and techniques, offering a current overview of A-SLAM formulation.

Bayesian optimization (BO) is a popular black-box function optimization method, which makes sequential decisions based on a Bayesian model, typically a Gaussian process (GP), of the function. To ensure the quality of the model, transfer learning approaches have been developed to automatically design GP priors by learning from observations on "training" functions. These training functions are typically required to have the same domain as the "test" function (black-box function to be optimized). In this paper, we introduce MPHD, a model pre-training method on heterogeneous domains, which uses a neural net mapping from domain-specific contexts to specifications of hierarchical GPs. MPHD can be seamlessly integrated with BO to transfer knowledge across heterogeneous search spaces. Our theoretical and empirical results demonstrate the validity of MPHD and its superior performance on challenging black-box function optimization tasks.

Uncertainties in the real world mean that is impossible for system designers to anticipate and explicitly design for all scenarios that a robot might encounter. Thus, robots designed like this are fragile and fail outside of highly-controlled environments. Causal models provide a principled framework to encode formal knowledge of the causal relationships that govern the robot's interaction with its environment, in addition to probabilistic representations of noise and uncertainty typically encountered by real-world robots. Combined with causal inference, these models permit an autonomous agent to understand, reason about, and explain its environment. In this work, we focus on the problem of a robot block-stacking task due to the fundamental perception and manipulation capabilities it demonstrates, required by many applications including warehouse logistics and domestic human support robotics. We propose a novel causal probabilistic framework to embed a physics simulation capability into a structural causal model to permit robots to perceive and assess the current state of a block-stacking task, reason about the next-best action from placement candidates, and generate post-hoc counterfactual explanations. We provide exemplar next-best action selection results and outline planned experimentation in simulated and real-world robot block-stacking tasks.