This paper proposes a causal discovery method for mixed bivariate data consisting of one continuous and one discrete variable. Existing constraint-based approaches are ineffective in the bivariate setting, as they rely on conditional independence tests that are not suited to bivariate data. Score-based methods either impose strong distributional assumptions or face challenges in fairly comparing causal directions between variables of different types, due to differences in their information content. We introduce a novel approach that determines causal direction by analyzing the monotonicity of the conditional density ratio of the continuous variable, conditioned on different values of the discrete variable. Our theoretical analysis shows that the conditional density ratio exhibits monotonicity when the continuous variable causes the discrete variable, but not in the reverse direction. This property provides a principled basis for comparing causal directions between variables of different types, free from strong distributional assumptions and bias arising from differences in their information content. We demonstrate its effectiveness through experiments on both synthetic and real-world datasets, showing superior accuracy compared to existing methods.

In this paper, we consider a score-based Integer Programming (IP) approach for solving the Bayesian Network Structure Learning (BNSL) problem. State-of-the-art BNSL IP formulations suffer from the exponentially large number of variables and constraints. A standard approach in IP to address such challenges is to employ row and column generation techniques, which dynamically generate rows and columns, while the complex pricing problem remains a computational bottleneck for BNSL. For the general class of $\ell_0$-penalized likelihood scores, we show how the pricing problem can be reformulated as a difference of submodular optimization problem, and how the Difference of Convex Algorithm (DCA) can be applied as an inexact method to efficiently solve the pricing problems. Empirically, we show that, for continuous Gaussian data, our row and column generation approach yields solutions with higher quality than state-of-the-art score-based approaches, especially when the graph density increases, and achieves comparable performance against benchmark constraint-based and hybrid approaches, even when the graph size increases.

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.

Kernel-based conditional independence (KCI) testing is a powerful nonparametric method commonly employed in causal discovery tasks. Despite its flexibility and statistical reliability, cubic computational complexity limits its application to large datasets. To address this computational bottleneck, we propose \textit{FastKCI}, a scalable and parallelizable kernel-based conditional independence test that utilizes a mixture-of-experts approach inspired by embarrassingly parallel inference techniques for Gaussian processes. By partitioning the dataset based on a Gaussian mixture model over the conditioning variables, FastKCI conducts local KCI tests in parallel, aggregating the results using an importance-weighted sampling scheme. Experiments on synthetic datasets and benchmarks on real-world production data validate that FastKCI maintains the statistical power of the original KCI test while achieving substantial computational speedups. FastKCI thus represents a practical and efficient solution for conditional independence testing in causal inference on large-scale data.

In this paper, an unsupervised Recurrent Wavelet Probabilistic Neural Network (RWPNN) is proposed, which aims at detecting anomalies in non-stationary environments by modelling the temporal features using a nonparametric density estimation network. The novel framework consists of two components, a Stacked Recurrent Encoder-Decoder (SREnc-Dec) module that captures temporal features in a latent space, and a Multi-Receptive-field Wavelet Probabilistic Network (MRWPN) that creates an ensemble probabilistic model to characterise the latent space. This formulation extends the standard wavelet probabilistic networks to wavelet deep probabilistic networks, which can handle higher data dimensionality. The MRWPN module can adapt to different rates of data variation in different datasets without imposing strong distribution assumptions, resulting in a more robust and accurate detection for Time Series Anomaly Detection (TSAD) tasks in the non-stationary environment. We carry out the assessment on 45 real-world time series datasets from various domains, verify the performance of RWPNN in TSAD tasks with several constraints, and show its ability to provide early warnings for anomalous events.

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.

Unsupervised domain adaptation (UDA) for time series data remains a critical challenge in deep learning, with traditional pseudo-labeling strategies failing to capture temporal patterns and channel-wise shifts between domains, producing sub-optimal pseudo-labels. As such, we introduce TransPL, a novel approach that addresses these limitations by modeling the joint distribution $P(\mathbf{X}, y)$ of the source domain through code transition matrices, where the codes are derived from vector quantization (VQ) of time series patches. Our method constructs class- and channel-wise code transition matrices from the source domain and employs Bayes' rule for target domain adaptation, generating pseudo-labels based on channel-wise weighted class-conditional likelihoods. TransPL offers three key advantages: explicit modeling of temporal transitions and channel-wise shifts between different domains, versatility towards different UDA scenarios (e.g., weakly-supervised UDA), and explainable pseudo-label generation. We validate TransPL's effectiveness through extensive analysis on four time series UDA benchmarks and confirm that it consistently outperforms state-of-the-art pseudo-labeling methods by a strong margin (6.1% accuracy improvement, 4.9% F1 improvement), while providing interpretable insights into the domain adaptation process through its learned code transition matrices.

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.