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In the first part of this paper, we consider a family of continuous-time dynamical systems coupled with diffusion-transmutation processes. Under certain conditions, such randomly perturbed dynamical systems can be interpreted as an averaged…

When dealing with datasets containing a billion instances or with simulations that require a supercomputer to execute, computational resources become part of the equation. We can improve the efficiency of learning and inference by…

The research on and application of artificial intelligence (AI) has triggered a comprehensive scientific, economic, social and political discussion. Here we argue that statistics, as an interdisciplinary scientific field, plays a…

Generative AI systems have entered everyday academic, professional, and personal life with remarkable speed, yet most users encounter them as mysterious artifacts rather than intelligible systems. This chapter discusses large language…

Topic modelling has been a successful technique for text analysis for almost twenty years. When topic modelling met deep neural networks, there emerged a new and increasingly popular research area, neural topic models, with over a hundred…

A comprehensive artificial intelligence system needs to not only perceive the environment with different `senses' (e.g., seeing and hearing) but also infer the world's conditional (or even causal) relations and corresponding uncertainty.…

We develop a statistical framework for conducting inference on collections of time-varying covariance operators (covariance flows) over a general, possibly infinite dimensional, Hilbert space. We model the intrinsically non-linear structure…

The problem of statistical inference in its various forms has been the subject of decades-long extensive research. Most of the effort has been focused on characterizing the behavior as a function of the number of available samples, with far…

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such…

Large Language Models (LLMs) have emerged as transformative tools in artificial intelligence (AI), exhibiting remarkable capabilities across diverse tasks such as text generation, reasoning, and decision-making. While their success has…

In this paper we provide a comprehensive study of statistical inference in linear and allied models which exhibit some analytic perturbations in their design and covariance matrices. We also indicate a few potential applications. In the…

We present a study of morphological irregularity. Following recent work, we define an information-theoretic measure of irregularity based on the predictability of forms in a language. Using a neural transduction model, we estimate this…

The field of Machine Learning research is divided into subject areas, where each area tries to solve a specific problem, using specific methods. In recent years, borders have almost been erased, and many areas inherit methods from other…

The power of machine learning (ML) provides the possibility of analyzing experimental measurements with an unprecedented sensitivity. However, it still remains challenging to probe the subtle effects directly related to physical observables…

Mathematical reasoning and optimization are fundamental to artificial intelligence and computational problem-solving. Recent advancements in Large Language Models (LLMs) have significantly improved AI-driven mathematical reasoning, theorem…

Machine learning operates at the intersection of statistics and computer science. This raises the question as to its underlying methodology. While much emphasis has been put on the close link between the process of learning from data and…

Neuroscience has recently made much progress, expanding the complexity of both neural-activity measurements and brain-computational models. However, we lack robust methods for connecting theory and experiment by evaluating our new big…

A grand challenge in machine learning is the development of computational algorithms that match or outperform humans in perceptual inference tasks that are complicated by nuisance variation. For instance, visual object recognition involves…

Tensors are ubiquitous in statistics and data analysis. The central object that links data science to tensor theory and algebra is that of a model with latent variables. We provide an overview of tensor theory, with a particular emphasis on…

A density matrix describes the statistical state of a quantum system. It is a powerful formalism to represent both the quantum and classical uncertainty of quantum systems and to express different statistical operations such as measurement,…