Over the past decades, there has been a surge of interest in studying low-dimensional structures within high-dimensional data. Statistical factor models $-$ i.e., low-rank plus diagonal covariance structures $-$ offer a powerful framework for modeling such structures. However, traditional methods for fitting statistical factor models, such as principal component analysis (PCA) or maximum likelihood estimation assuming the data is Gaussian, are highly sensitive to heavy tails and outliers in the observed data. In this paper, we propose a novel expectation-maximization (EM) algorithm for robustly fitting statistical factor models. Our approach is based on Tyler's M-estimator of the scatter matrix for an elliptical distribution, and consists of solving Tyler's maximum likelihood estimation problem while imposing a structural constraint that enforces the low-rank plus diagonal covariance structure. We present numerical experiments on both synthetic and real examples, demonstrating the robustness of our method for direction-of-arrival estimation in nonuniform noise and subspace recovery.

Adapting to the addressee is crucial for successful explanations, yet poses significant challenges for dialogsystems. We adopt the approach of treating explanation generation as a non-stationary decision process, where the optimal strategy varies according to changing beliefs about the explainee and the interaction context. In this paper we address the questions of (1) how to track the interaction context and the relevant listener features in a formally defined computational partner model, and (2) how to utilize this model in the dynamically adjusted, rational decision process that determines the currently best explanation strategy. We propose a Bayesian inference-based approach to continuously update the partner model based on user feedback, and a non-stationary Markov Decision Process to adjust decision-making based on the partner model values. We evaluate an implementation of this framework with five simulated interlocutors, demonstrating its effectiveness in adapting to different partners with constant and even changing feedback behavior. The results show high adaptivity with distinct explanation strategies emerging for different partners, highlighting the potential of our approach to improve explainable AI systems and dialogsystems in general.

Photoplethysmography (PPG) signals encode information about relative changes in blood volume that can be used to assess various aspects of cardiac health non-invasively, e.g.\ to detect atrial fibrillation (AF) or predict blood pressure (BP). Deep networks are well-equipped to handle the large quantities of data acquired from wearable measurement devices. However, they lack interpretability and are prone to overfitting, leaving considerable risk for poor performance on unseen data and misdiagnosis. Here, we describe the use of two scalable uncertainty quantification techniques: Monte Carlo Dropout and the recently proposed Improved Variational Online Newton. These techniques are used to assess the trustworthiness of models trained to perform AF classification and BP regression from raw PPG time series. We find that the choice of hyperparameters has a considerable effect on the predictive performance of the models and on the quality and composition of predicted uncertainties. E.g. the stochasticity of the model parameter sampling determines the proportion of the total uncertainty that is aleatoric, and has varying effects on predictive performance and calibration quality dependent on the chosen uncertainty quantification technique and the chosen expression of uncertainty. We find significant discrepancy in the quality of uncertainties over the predicted classes, emphasising the need for a thorough evaluation protocol that assesses local and adaptive calibration. This work suggests that the choice of hyperparameters must be carefully tuned to balance predictive performance and calibration quality, and that the optimal parameterisation may vary depending on the chosen expression of uncertainty.

We introduce NeuralSurv, the first deep survival model to incorporate Bayesian uncertainty quantification. Our non-parametric, architecture-agnostic framework flexibly captures time-varying covariate-risk relationships in continuous time via a novel two-stage data-augmentation scheme, for which we establish theoretical guarantees. For efficient posterior inference, we introduce a mean-field variational algorithm with coordinate-ascent updates that scale linearly in model size. By locally linearizing the Bayesian neural network, we obtain full conjugacy and derive all coordinate updates in closed form. In experiments, NeuralSurv delivers superior calibration compared to state-of-the-art deep survival models, while matching or exceeding their discriminative performance across both synthetic benchmarks and real-world datasets. Our results demonstrate the value of Bayesian principles in data-scarce regimes by enhancing model calibration and providing robust, well-calibrated uncertainty estimates for the survival function.

Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is large or when the underlying function contains multi-scale features that are difficult to represent by a stationary kernel. To address the former, training of GPs with large-scale data is often performed through inducing point approximations (also known as sparse GP regression (GPR)), where the size of the covariance matrices in GPR is reduced considerably through a greedy search on the data set. To aid the latter, deep GPs have gained traction as hierarchical models that resolve multi-scale features by combining multiple GPs. Posterior inference in deep GPs requires a sampling or, more usual, a variational approximation. Variational approximations lead to large-scale stochastic, non-convex optimisation problems and the resulting approximation tends to represent uncertainty incorrectly. In this work, we combine variational learning with MCMC to develop a particle-based expectation-maximisation method to simultaneously find inducing points within the large-scale data (variationally) and accurately train the GPs (sampling-based). The result is a highly efficient and accurate methodology for deep GP training on large-scale data. We test our method on standard benchmark problems.

Accurately estimating human internal states, such as personality traits or behavioral patterns, is critical for enhancing the effectiveness of human-robot interaction, particularly in group settings. These insights are key in applications ranging from social navigation to autism diagnosis. However, prior methods are limited by scalability and passive observation, making real-time estimation in complex, multi-human settings difficult. In this work, we propose a practical method for active human personality estimation in groups, with a focus on applications related to Autism Spectrum Disorder (ASD). Our method combines a personality-conditioned behavior model, based on the Eysenck 3-Factor theory, with an active robot information gathering policy that triggers human behaviors through a receding-horizon planner. The robot's belief about human personality is then updated via Bayesian inference. We demonstrate the effectiveness of our approach through simulations, user studies with typical adults, and preliminary experiments involving participants with ASD. Our results show that our method can scale to tens of humans and reduce personality prediction error by 29.2% and uncertainty by 79.9% in simulation. User studies with typical adults confirm the method's ability to generalize across complex personality distributions. Additionally, we explore its application in autism-related scenarios, demonstrating that the method can identify the difference between neurotypical and autistic behavior, highlighting its potential for diagnosing ASD. The results suggest that our framework could serve as a foundation for future ASD-specific interventions.

Variational Autoencoders (VAEs) are well-established as a principled approach to probabilistic unsupervised learning with neural networks. Typically, an encoder network defines the parameters of a Gaussian distributed latent space from which we can sample and pass realizations to a decoder network. This model is trained to reconstruct its inputs and is optimized through the evidence lower bound. In recent years, discrete latent spaces have grown in popularity, suggesting that they may be a natural choice for many data modalities (e.g. text). In this tutorial, we provide a rigorous, yet practical, introduction to discrete variational autoencoders -- specifically, VAEs in which the latent space is made up of latent variables that follow a categorical distribution. We assume only a basic mathematical background with which we carefully derive each step from first principles. From there, we develop a concrete training recipe and provide an example implementation, hosted at https://github.com/alanjeffares/discreteVAE.

In industrial automation, radar is a critical sensor in machine perception. However, the angular resolution of radar is inherently limited by the Rayleigh criterion, which depends on both the radar's operating wavelength and the effective aperture of its antenna array.To overcome these hardware-imposed limitations, recent neural network-based methods have leveraged high-resolution LiDAR data, paired with radar measurements, during training to enhance radar point cloud resolution. While effective, these approaches require extensive paired datasets, which are costly to acquire and prone to calibration error. These challenges motivate the need for methods that can improve radar resolution without relying on paired high-resolution ground-truth data. Here, we introduce an unsupervised radar points enhancement algorithm that employs an arbitrary LiDAR-guided diffusion model as a prior without the need for paired training data. Specifically, our approach formulates radar angle estimation recovery as an inverse problem and incorporates prior knowledge through a diffusion model with arbitrary LiDAR domain knowledge. Experimental results demonstrate that our method attains high fidelity and low noise performance compared to traditional regularization techniques. Additionally, compared to paired training methods, it not only achieves comparable performance but also offers improved generalization capability. To our knowledge, this is the first approach that enhances radar points output by integrating prior knowledge via a diffusion model rather than relying on paired training data. Our code is available at https://github.com/yyxr75/RadarINV.

Bayesian inference with Markov Chain Monte Carlo (MCMC) is challenging when the likelihood function is irregular and expensive to compute. We explore several sampling algorithms that make use of subset evaluations to reduce computational overhead. We adapt the subset samplers for this setting where gradient information is not available or is unreliable. To achieve this, we introduce data-driven proxies in place of Taylor expansions and define a novel computation-cost aware adaptive controller. We undertake an extensive evaluation for a challenging disease modelling task and a configurable task with similar irregularity in the likelihood surface. We find our improved version of Hierarchical Importance with Nested Training Samples (HINTS), with adaptive proposals and a data-driven proxy, obtains the best sampling error in a fixed computational budget. We conclude that subset evaluations can provide cheap and naturally-tempered exploration, while a data-driven proxy can pre-screen proposals successfully in explored regions of the state space. These two elements combine through hierarchical delayed acceptance to achieve efficient, exact sampling.

In many scientific and industrial applications, we are given a handful of instances (a 'small ensemble') of a spatially distributed quantity (a 'field') but would like to acquire many more. For example, a large ensemble of global temperature sensitivity fields from a climate model can help farmers, insurers, and governments plan appropriately. When acquiring more data is prohibitively expensive -- as is the case with climate models -- statistical emulation offers an efficient alternative for simulating synthetic yet realistic fields. However, parameter inference using maximum likelihood estimation (MLE) is computationally prohibitive, especially for large, non-stationary fields. Thus, many recent works train neural networks to estimate parameters given spatial fields as input, sidestepping MLE completely. In this work we focus on a popular class of parametric, spatially autoregressive (SAR) models. We make a simple yet impactful observation; because the SAR parameters can be arranged on a regular grid, both inputs (spatial fields) and outputs (model parameters) can be viewed as images. Using this insight, we demonstrate that image-to-image (I2I) networks enable faster and more accurate parameter estimation for a class of non-stationary SAR models with unprecedented complexity.