Related papers: Scalable Machine Learning Algorithms using Path Si…
Gaussian concentration graph models and covariance graph models are two classes of graphical models that are useful for uncovering latent dependence structures among multivariate variables. In the Bayesian literature, graphs are often…
Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…
The modeling of high-dimensional spatio-temporal processes presents a fundamental dichotomy between the probabilistic rigor of classical geostatistics and the flexible, high-capacity representations of deep learning. While Gaussian…
Importance sampling of trajectories has proved a uniquely successful strategy for exploring rare dynamical behaviors of complex systems in an unbiased way. Carrying out this sampling, however, requires an ability to propose changes to…
The use of covariance kernels is ubiquitous in the field of spatial statistics. Kernels allow data to be mapped into high-dimensional feature spaces and can thus extend simple linear additive methods to nonlinear methods with higher order…
We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…
A popular approach to semi-supervised learning proceeds by endowing the input data with a graph structure in order to extract geometric information and incorporate it into a Bayesian framework. We introduce new theory that gives appropriate…
We present a novel framework for kernel learning with sequential data of any kind, such as time series, sequences of graphs, or strings. Our approach is based on signature features which can be seen as an ordered variant of sample…
Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified…
We develop a consistent method for estimating the parameters of a rich class of path-dependent SDEs, called signature SDEs, which can model general path-dependent phenomena. Path signatures are iterated integrals of a given path with the…
Representations of sequential data are commonly based on the assumption that observed sequences are realizations of an unknown underlying stochastic process, where the learning problem includes determination of the model parameters. In this…
We propose Path Signatures Logistic Regression (PSLR), a semi-parametric framework for classifying vector-valued functional data with scalar covariates. Classical functional logistic regression models rely on linear assumptions and fixed…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
Supervised learning has recently garnered significant attention in the field of computational physics due to its ability to effectively extract complex patterns for tasks like solving partial differential equations, or predicting material…
Graph learning has rapidly evolved into a critical subfield of machine learning and artificial intelligence (AI). Its development began with early graph-theoretic methods, gaining significant momentum with the advent of graph neural…
Machine learning techniques not only offer efficient tools for modelling dynamical systems from data, but can also be employed as frontline investigative instruments for the underlying physics. Nontrivial information about the original…
Over the past two decades, there has been a tremendous increase in the growth of representation learning methods for graphs, with numerous applications across various fields, including bioinformatics, chemistry, and the social sciences.…
Signature kernels have emerged as a powerful tool within kernel methods for sequential data. In the paper "The Signature Kernel is the solution of a Goursat PDE", the authors identify a kernel trick that demonstrates that, for continuously…
While Multimodal Large Language Models have achieved human-like performance on many visual and textual reasoning tasks, their proficiency in fine-grained spatial understanding, such as route tracing on maps remains limited. Unlike humans,…
Path signatures embed trajectories into tensor algebra and constitute a universal, non-parametric representation of paths; however, in the standard form, they collapse temporal structure into a single global object, which limits their…