Real-world event sequences are often generated by different temporal point processes (TPPs) and thus have clustering structures. Nonetheless, in the modeling and prediction of event sequences, most existing TPPs ignore the inherent clustering structures of the event sequences, leading to the models with unsatisfactory interpretability. In this study, we learn structure-enhanced TPPs with the help of Gromov-Wasserstein (GW) regularization, which imposes clustering structures on the sequence-level embeddings of the TPPs in the maximum likelihood estimation framework.In the training phase, the proposed method leverages a nonparametric TPP kernel to regularize the similarity matrix derived based on the sequence embeddings. In large-scale applications, we sample the kernel matrix and implement the regularization as a Gromov-Wasserstein (GW) discrepancy term, which achieves a trade-off between regularity and computational efficiency.The TPPs learned through this method result in clustered sequence embeddings and demonstrate competitive predictive and clustering performance, significantly improving the model interpretability without compromising prediction accuracy.

Likelihood-free approaches are appealing for performing inference on complex dependence models, either because it is not possible to formulate a likelihood function, or its evaluation is very computationally costly. This is the case for several models available in the multivariate extremes literature, particularly for the most flexible tail models, including those that interpolate between the two key dependence classes of `asymptotic dependence' and `asymptotic independence'. We focus on approaches that leverage neural networks to approximate Bayes estimators. In particular, we explore the properties of neural Bayes estimators for parameter inference for several flexible but computationally expensive models to fit, with a view to aiding their routine implementation. Owing to the absence of likelihood evaluation in the inference procedure, classical information criteria such as the Bayesian information criterion cannot be used to select the most appropriate model. Instead, we propose using neural networks as neural Bayes classifiers for model selection. Our goal is to provide a toolbox for simple, fast fitting and comparison of complex extreme-value dependence models, where the best model is selected for a given data set and its parameters subsequently estimated using neural Bayes estimation. We apply our classifiers and estimators to analyse the pairwise extremal behaviour of changes in horizontal geomagnetic field fluctuations at three different locations.

Land cover classification involves the production of land cover maps, which determine the type of land through remote sensing imagery. Over recent years, such classification is being performed by machine learning classification models, which can give highly accurate predictions on land cover per pixel using large quantities of input training data. However, such models do not currently take account of input measurement uncertainty, which is vital for traceability in metrology. In this work we propose a Bayesian classification framework using generative modelling to take account of input measurement uncertainty. We take the specific case of Bayesian quadratic discriminant analysis, and apply it to land cover datasets from Copernicus Sentinel-2 in 2020 and 2021. We benchmark the performance of the model against more popular classification models used in land cover maps such as random forests and neural networks. We find that such Bayesian models are more trustworthy, in the sense that they are more interpretable, explicitly model the input measurement uncertainty, and maintain predictive performance of class probability outputs across datasets of different years and sizes, whilst also being computationally efficient.

Context: Astronomy and astrophysics demand rigorous handling of uncertainties to ensure the credibility of outcomes. The growing integration of artificial intelligence offers a novel avenue to address this necessity. This convergence presents an opportunity to create advanced models capable of quantifying diverse sources of uncertainty and automating complex data relationship exploration. What: We introduce a hierarchical Bayesian architecture whose probabilistic relationships are modeled by neural networks, designed to forecast stellar attributes such as mass, radius, and age (our main target). This architecture handles both observational uncertainties stemming from measurements and epistemic uncertainties inherent in the predictive model itself. As a result, our system generates distributions that encapsulate the potential range of values for our predictions, providing a comprehensive understanding of their variability and robustness. Methods: Our focus is on dating main sequence stars using a technique known as Chemical Clocks, which serves as both our primary astronomical challenge and a model prototype. In this work, we use hierarchical architectures to account for correlations between stellar parameters and optimize information extraction from our dataset. We also employ Bayesian neural networks for their versatility and flexibility in capturing complex data relationships. Results: By integrating our machine learning algorithm into a Bayesian framework, we have successfully propagated errors consistently and managed uncertainty treatment effectively, resulting in predictions characterized by broader uncertainty margins. This approach facilitates more conservative estimates in stellar dating. Our architecture achieves age predictions with a mean absolute error of less than 1 Ga for the stars in the test dataset.

We propose a method to explore the flavor structure of leptons using diffusion models, which are known as one of generative artificial intelligence (generative AI). We consider a simple extension of the Standard Model with the type I seesaw mechanism and train a neural network to generate the neutrino mass matrix. By utilizing transfer learning, the diffusion model generates 104 solutions that are consistent with the neutrino mass squared differences and the leptonic mixing angles. The distributions of the CP phases and the sums of neutrino masses, which are not included in the conditional labels but are calculated from the solutions, exhibit non-trivial tendencies. In addition, the effective mass in neutrinoless double beta decay is concentrated near the boundaries of the existing confidence intervals, allowing us to verify the obtained solutions through future experiments. An inverse approach using the diffusion model is expected to facilitate the experimental verification of flavor models from a perspective distinct from conventional analytical methods.

The rapid digitalisation of contemporary society has profoundly impacted various facets of our lives, including healthcare, communication, business, and education. The ability to engage with new technologies and solve problems has become crucial, making CT skills, such as pattern recognition, decomposition, and algorithm design, essential competencies. In response, Switzerland is conducting research and initiatives to integrate CT into its educational system. This study aims to develop a comprehensive framework for large-scale assessment of CT skills, particularly focusing on AT, the ability to design algorithms. To achieve this, we first developed a competence model capturing the situated and developmental nature of CT, guiding the design of activities tailored to cognitive abilities, age, and context. This framework clarifies how activity characteristics influence CT development and how to assess these competencies. Additionally, we developed an activity for large-scale assessment of AT skills, offered in two variants: one based on non-digital artefacts (unplugged) and manual expert assessment, and the other based on digital artefacts (virtual) and automatic assessment. To provide a more comprehensive evaluation of students' competencies, we developed an IAS based on BNs with noisy gates, which offers real-time probabilistic assessment for each skill rather than a single overall score. The results indicate that the proposed instrument can measure AT competencies across different age groups and educational contexts in Switzerland, demonstrating its applicability for large-scale use. AT competencies exhibit a progressive development, with no overall gender differences, though variations are observed at the school level, significantly influenced by the artefact-based environment and its context, underscoring the importance of creating accessible and adaptable assessment tools.

Decision making under uncertainty is a cross-cutting challenge in science and engineering. Most approaches to this challenge employ probabilistic representations of uncertainty. In complicated systems accessible only via data or black-box models, however, these representations are rarely known. We discuss how to characterize and manipulate such representations using triangular transport maps, which approximate any complex probability distribution as a transformation of a simple, well-understood distribution. The particular structure of triangular transport guarantees many desirable mathematical and computational properties that translate well into solving practical problems. Triangular maps are actively used for density estimation, (conditional) generative modelling, Bayesian inference, data assimilation, optimal experimental design, and related tasks. While there is ample literature on the development and theory of triangular transport methods, this manuscript provides a detailed introduction for scientists interested in employing measure transport without assuming a formal mathematical background. We build intuition for the key foundations of triangular transport, discuss many aspects of its practical implementation, and outline the frontiers of this field.

Robots rely on motion planning to navigate safely and efficiently while performing various tasks. In this paper, we investigate motion planning through Bayesian inference, where motion plans are inferred based on planning objectives and constraints. However, existing Bayesian motion planning methods often struggle to explore low-probability regions of the planning space, where high-quality plans may reside. To address this limitation, we propose the use of heavy-tailed distributions -- specifically, Student's-$t$ distributions -- to enhance probabilistic inferential search for motion plans. We develop a novel sequential single-pass smoothing approach that integrates Student's-$t$ distribution with Monte Carlo sampling. A special case of this approach is ensemble Kalman smoothing, which depends on short-tailed Gaussian distributions. We validate the proposed approach through simulations in autonomous vehicle motion planning, demonstrating its superior performance in planning, sampling efficiency, and constraint satisfaction compared to ensemble Kalman smoothing. While focused on motion planning, this work points to the broader potential of heavy-tailed distributions in enhancing probabilistic decision-making in robotics.

We introduce squared families, which are families of probability densities obtained by squaring a linear transformation of a statistic. Squared families are singular, however their singularity can easily be handled so that they form regular models. After handling the singularity, squared families possess many convenient properties. Their Fisher information is a conformal transformation of the Hessian metric induced from a Bregman generator. The Bregman generator is the normalising constant, and yields a statistical divergence on the family. The normalising constant admits a helpful parameter-integral factorisation, meaning that only one parameter-independent integral needs to be computed for all normalising constants in the family, unlike in exponential families. Finally, the squared family kernel is the only integral that needs to be computed for the Fisher information, statistical divergence and normalising constant. We then describe how squared families are special in the broader class of $g$-families, which are obtained by applying a sufficiently regular function $g$ to a linear transformation of a statistic. After removing special singularities, positively homogeneous families and exponential families are the only $g$-families for which the Fisher information is a conformal transformation of the Hessian metric, where the generator depends on the parameter only through the normalising constant. Even-order monomial families also admit parameter-integral factorisations, unlike exponential families. We study parameter estimation and density estimation in squared families, in the well-specified and misspecified settings. We use a universal approximation property to show that squared families can learn sufficiently well-behaved target densities at a rate of $\mathcal{O}(N^{-1/2})+C n^{-1/4}$, where $N$ is the number of datapoints, $n$ is the number of parameters, and $C$ is some constant.

Continual learning (CL) refers to the ability to continuously learn and accumulate new knowledge while retaining useful information from past experiences. Although numerous CL methods have been proposed in recent years, it is not straightforward to deploy them directly to real-world decision-making problems due to their computational cost and lack of uncertainty quantification. To address these issues, we propose CL-BRUNO, a probabilistic, Neural Process-based CL model that performs scalable and tractable Bayesian update and prediction. Our proposed approach uses deep-generative models to create a unified probabilistic framework capable of handling different types of CL problems such as task- and class-incremental learning, allowing users to integrate information across different CL scenarios using a single model. Our approach is able to prevent catastrophic forgetting through distributional and functional regularisation without the need of retaining any previously seen samples, making it appealing to applications where data privacy or storage capacity is of concern. Experiments show that CL-BRUNO outperforms existing methods on both natural image and biomedical data sets, confirming its effectiveness in real-world applications.