arXiv:2606. 15332v1 Announce Type: new Abstract: The signature transform is a principled feature map for continuous-time paths, valued for its uniqueness and universality.
arXiv:2410. 02628v5 Announce Type: replace Abstract: Learning conditional distributions $\pi^*(\cdot|x)$ is a central problem in machine learning, which is typically approached via supervised methods with paired data $(x,y) \sim \pi^*$.
arXiv:2606. 30230v1 Announce Type: cross Abstract: Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the one assumed during training.
arXiv:2507. 06637v2 Announce Type: replace-cross Abstract: We propose Path Signatures Logistic Regression (PSLR), a semi-parametric framework for classifying vector-valued functional data with scalar covariates.
arXiv:2606. 02232v1 Announce Type: new Abstract: Learning a Markov transition model is not merely conditional density estimation: the learned object must be a valid transition kernel before it is iterated in downstream dynamics.
arXiv:2411. 08314v5 Announce Type: replace Abstract: Learning to transform conditional probability densities over time is a fundamental challenge spanning probabilistic modeling and the natural sciences.
arXiv:2603. 14798v2 Announce Type: replace-cross Abstract: We propose a machine-learning algorithm for Bayesian inverse problems in the function-space regime.
arXiv:2605. 15407v3 Announce Type: replace-cross Abstract: We consider amortized Bayesian inference for nonlinear inverse problems using only samples from the joint distribution of parameters and observations, including problems with unknown functions in a Banach space.
arXiv:2605. 25826v2 Announce Type: replace-cross Abstract: We develop a branched signature kernel solver for linear and nonlinear ordinary differential equations driven by a \emph{single observed trajectory} of a possibly rough forcing signal--a setting common within earthquake engineering, finance, biology, and structural health monitoring, where only one forcing realization is available, and the solver must respect the underlying physical law without an ensemble of realizations.
arXiv:2602. 19126v2 Announce Type: replace Abstract: We propose a robust Bayesian formulation of random feature (RF) regression that accounts explicitly for prior and likelihood misspecification via Huber-style contamination sets.
arXiv:2602. 13362v2 Announce Type: replace-cross Abstract: A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty.
arXiv:2607. 06252v1 Announce Type: cross Abstract: Many problems in science and engineering are difficult to model accurately, either due to unknown physical mechanisms, poorly quantified measurement uncertainty, or prohibitive computational costs of high-fidelity simulations.
arXiv:2607. 18804v1 Announce Type: new Abstract: In the \emph{latent posterior model} of transformer behavior, the next-token distribution arises from a posterior over latent predictive models conditioned on the context, mixed to generate continuations.