The Susceptible-Infected-Susceptible (SIS) model is a widely used model for the spread of information and infectious diseases, particularly non-immunizing ones, on a graph. Given a highly contagious disease, a natural question is how to best vaccinate individuals to minimize the disease's extinction time. While previous works showed that the problem of optimal vaccination is closely linked to the NP-hard Spectral Radius Minimization (SRM) problem, they assumed that the graph is known, which is often not the case in practice. In this work, we consider the problem of minimizing the extinction time of an outbreak modeled by an SIS model where the graph on which the disease spreads is unknown and only the infection states of the vertices are observed. To this end, we split the problem into two: learning the graph and determining effective vaccination strategies. We propose a novel inclusion-exclusion-based learning algorithm and, unlike previous approaches, establish its sample complexity for graph recovery. We then detail an optimal algorithm for the SRM problem and prove that its running time is polynomial in the number of vertices for graphs with bounded treewidth. This is complemented by an efficient and effective polynomial-time greedy heuristic for any graph. Finally, we present experiments on synthetic and real-world data that numerically validate our learning and vaccination algorithms.

Real-time identification and quantification of greenhouse-gas emissions under transient atmospheric conditions is a critical challenge in environmental monitoring. We introduce a spatio-temporal inversion framework that embeds a deep-learning surrogate of computational fluid dynamics (CFD) within a sequential Monte Carlo algorithm to perform Bayesian inference of both emission rate and source location in dynamic flow fields. By substituting costly numerical solvers with a multilayer perceptron trained on high-fidelity CFD outputs, our surrogate captures spatial heterogeneity and temporal evolution of gas dispersion, while delivering near-real-time predictions. Validation on the Chilbolton methane release dataset demonstrates comparable accuracy to full CFD solvers and Gaussian plume models, yet achieves orders-of-magnitude faster runtimes. Further experiments under simulated obstructed-flow scenarios confirm robustness in complex environments. This work reconciles physical fidelity with computational feasibility, offering a scalable solution for industrial emissions monitoring and other time-sensitive spatio-temporal inversion tasks in environmental and scientific modeling.

Humans interpret the world around them in terms of cause and effect and communicate their understanding of the world to each other in causal terms. These causal aspects of human cognition are thought to underlie humans' ability to generalize and learn efficiently in new domains, an area where current machine learning systems are weak. Building human-like causal competency into machine learning systems may facilitate the construction of effective and interpretable AI. Indeed, the machine learning community has been importing ideas on causality formalized by the Structural Causal Model (SCM) framework, which provides a rigorous formal language for many aspects of causality and has led to significant advances. However, the SCM framework fails to capture some salient aspects of human causal cognition and has likewise not yet led to advances in machine learning in certain critical areas where humans excel. We contend that the problem of causality in the ``human niche'' -- for a social, autonomous, and goal-driven agent sensing and acting in the world in which humans live -- is quite different from the kind of causality captured by SCMs. For example, everyday objects come in similar types that have similar causal properties, and so humans readily generalize knowledge of one type of object (cups) to another related type (bowls) by drawing causal analogies between objects with similar properties, but such analogies are at best awkward to express in SCMs. We explore how such causal capabilities are adaptive in, and motivated by, the human niche. By better appreciating properties of human causal cognition and, crucially, how those properties are adaptive in the niche in which humans live, we hope that future work at the intersection of machine learning and causality will leverage more human-like inductive biases to create more capable, controllable, and interpretable systems.

Bayesian methods have recently been used to improve LoRA finetuning and, although they improve calibration, their effect on other metrics (such as accuracy) is marginal and can sometimes even be detrimental. Moreover, Bayesian methods also increase computational overheads and require additional tricks for them to work well. Here, we fix these issues by using a recently proposed variational algorithm called IVON. We show that IVON is easy to implement and has similar costs to AdamW, and yet it can also drastically improve many metrics by using a simple posterior pruning technique. We present extensive results on billion-scale LLMs (Llama and Qwen series) going way beyond the scale of existing applications of IVON. For example, we finetune a Llama-3.2-3B model on a set of commonsense reasoning tasks and improve accuracy over AdamW by 1.3% and reduce ECE by 5.4%, outperforming AdamW and other recent Bayesian methods like Laplace-LoRA and BLoB. Overall, our results show that variational learning with IVON can effectively improve LoRA finetuning.

Adaptation is the holy grail of intelligence, but even the best AI models (like GPT) lack the adaptivity of toddlers. So the question remains: how can machines adapt quickly? Despite a lot of progress on model adaptation to facilitate continual and federated learning, as well as model merging, editing, unlearning, etc., little is known about the mechanisms by which machines can naturally learn to adapt in a similar way as humans and animals. Here, we show that all such adaptation methods can be seen as different ways of `correcting' the approximate posteriors. More accurate posteriors lead to smaller corrections, which in turn imply quicker adaptation. The result is obtained by using a dual-perspective of the Bayesian Learning Rule of Khan and Rue (2023) where interference created during adaptation is characterized by the natural-gradient mismatch over the past data. We present many examples to demonstrate the use of posterior-correction as a natural mechanism for the machines to learn to adapt quickly.

Synthetic data generation plays a crucial role in medical research by mitigating privacy concerns and enabling large-scale patient data analysis. This study presents a beta-Variational Autoencoder Graph Convolutional Neural Network framework for generating synthetic Abdominal Aorta Aneurysms (AAA). Using a small real-world dataset, our approach extracts key anatomical features and captures complex statistical relationships within a compact disentangled latent space. To address data limitations, low-impact data augmentation based on Procrustes analysis was employed, preserving anatomical integrity. The generation strategies, both deterministic and stochastic, manage to enhance data diversity while ensuring realism. Compared to PCA-based approaches, our model performs more robustly on unseen data by capturing complex, nonlinear anatomical variations. This enables more comprehensive clinical and statistical analyses than the original dataset alone. The resulting synthetic AAA dataset preserves patient privacy while providing a scalable foundation for medical research, device testing, and computational modeling.

In-context learning (ICL) has emerged as a powerful paradigm for task adaptation in large language models (LLMs), where models infer underlying task structures from a few demonstrations. However, ICL remains susceptible to biases that arise from prior knowledge and contextual demonstrations, which can degrade the performance of LLMs. Existing bias calibration methods typically apply fixed class priors across all inputs, limiting their efficacy in dynamic ICL settings where the context for each query differs. To address these limitations, we adopt implicit sequential Bayesian inference as a framework for interpreting ICL, identify "surprise" as an informative signal for class prior shift, and introduce a novel method--Surprise Calibration (SC). SC leverages the notion of surprise to capture the temporal dynamics of class priors, providing a more adaptive and computationally efficient solution for in-context learning. We empirically demonstrate the superiority of SC over existing bias calibration techniques across a range of benchmark natural language processing tasks.

People regularly make inferences about objects in the world that they cannot see by flexibly integrating information from multiple sources: auditory and visual cues, language, and our prior beliefs and knowledge about the scene. How are we able to so flexibly integrate many sources of information to make sense of the world around us, even if we have no direct knowledge? In this work, we propose a neurosymbolic model that uses neural networks to parse open-ended multi-modal inputs and then applies a Bayesian model to integrate different sources of information to evaluate different hypotheses. We evaluate our model with a novel object guessing game called "What's in the Box?" where humans and models watch a video clip of an experimenter shaking boxes and then try to guess the objects inside the boxes. Through a human experiment, we show that our model correlates strongly with human judgments, whereas unimodal ablated models and large multi-modal neural model baselines showed poor correlation.

Developing agents capable of exploring, planning and learning in complex open-ended environments is a grand challenge in artificial intelligence (AI). Hierarchical reinforcement learning (HRL) offers a promising solution to this challenge by discovering and exploiting the temporal structure within a stream of experience. The strong appeal of the HRL framework has led to a rich and diverse body of literature attempting to discover a useful structure. However, it is still not clear how one might define what constitutes good structure in the first place, or the kind of problems in which identifying it may be helpful. This work aims to identify the benefits of HRL from the perspective of the fundamental challenges in decision-making, as well as highlight its impact on the performance trade-offs of AI agents. Through these benefits, we then cover the families of methods that discover temporal structure in HRL, ranging from learning directly from online experience to offline datasets, to leveraging large language models (LLMs). Finally, we highlight the challenges of temporal structure discovery and the domains that are particularly well-suited for such endeavours.

This textbook provides a systematic treatment of statistical machine learning for astronomical research through the lens of Bayesian inference, developing a unified framework that reveals connections between modern data analysis techniques and traditional statistical methods. We show how these techniques emerge from familiar statistical foundations. The consistently Bayesian perspective prioritizes uncertainty quantification and statistical rigor essential for scientific inference in astronomy. The textbook progresses from probability theory and Bayesian inference through supervised learning including linear regression with measurement uncertainties, logistic regression, and classification. Unsupervised learning topics cover Principal Component Analysis and clustering methods. We then introduce computational techniques through sampling and Markov Chain Monte Carlo, followed by Gaussian Processes as probabilistic nonparametric methods and neural networks within the broader statistical context. Our theory-focused pedagogical approach derives each method from first principles with complete mathematical development, emphasizing statistical insight and complementing with astronomical applications. We prioritize understanding why algorithms work, when they are appropriate, and how they connect to broader statistical principles. The treatment builds toward modern techniques including neural networks through a solid foundation in classical methods and their theoretical underpinnings. This foundation enables thoughtful application of these methods to astronomical research, ensuring proper consideration of assumptions, limitations, and uncertainty propagation essential for advancing astronomical knowledge in the era of large astronomical surveys.