arXiv subjects

Louis Aslett

Publications and source records attributed to Louis Aslett.

3 recordsLinked to original sources

arXiv2026

A Distribution-to-Distribution Neural Probabilistic Forecasting Framework for Dynamical Systems

Probabilistic forecasting provides a principled framework for uncertainty quantification in dynamical systems by representing predictions as probability distributions rather than deterministic trajectories. However, existing forecasting approaches, whether physics-based or neural-network-based, remain fundamentally trajectory-oriented: predictive distributions are usually accessed through ensembles or sampling, rather than evolved directly as dynamical objects. A distribution-to-distribution (D2D) neural probabilistic forecasting framework is developed to operate directly on predictive distributions. The framework introduces a distributional encoding and decoding structure around a replaceable neural forecasting module, using kernel mean embeddings to represent input distributions and mixture density networks to parameterise output predictive distributions. This design enables recursive propagation of predictive uncertainty within a unified end-to-end neural architecture, with model training and evaluation carried out directly in terms of probabilistic forecast skill. The framework is demonstrated on the Lorenz63 chaotic dynamical system. Results show that the D2D model captures nontrivial distributional evolution under nonlinear dynamics, produces skillful probabilistic forecasts without explicit ensemble simulation, and remains competitive with, and in some cases outperforms, a simplified perfect model benchmark. These findings point to a new paradigm for probabilistic forecasting, in which predictive distributions are learned and evolved directly rather than reconstructed indirectly through ensemble-based uncertainty propagation.

stat.ML↗

arXiv2026

Privacy Guarantees in Posterior Sampling under Contamination

In recent years, differential privacy has been adopted by tech-companies and governmental agencies as the standard for measuring privacy in algorithms. In this article, we study differential privacy in Bayesian posterior sampling settings. We begin by considering differential privacy in the most common privatisation setting in which Laplace or Gaussian noise is injected into the output. In an effort to achieve better differential privacy, we consider adopting {\em Huber's contamination model} for use within privacy settings, and replace at random data points with samples from a heavy-tailed distribution ({\em instead} of injecting noise into the output). We derive bounds for the differential privacy level $(ε,δ)$ of our approach, without requiring bounded observation and parameter spaces, a restriction commonly imposed in the literature. We further consider for our approach the effect of sample size on the privacy level and the rate at which $(ε,δ)$ converges to zero. Asymptotically, our contamination approach is fully private with no information loss. We also provide examples of inference models for which our approach applies, with theoretical convergence rate analysis and simulation studies.

math.ST↗

arXiv2025

Statistical Disaggregation -- a Monte Carlo Approach for Imputation under Constraints

Equality-constrained models naturally arise in problems in which measurements are taken at different levels of resolution. The challenge in this setting is that the models usually induce a joint distribution which is intractable. Resorting to instead sampling from the joint distribution by means of a Monte Carlo approach is also challenging. For example, a naive rejection sampling does not work when the probability mass of the constraint is zero. A typical example of such constrained problems is to learn energy consumption for a higher resolution level based on data at a lower resolution, e.g., to decompose a daily reading into readings at a finer level. We introduce a novel Monte Carlo sampling algorithm based on Langevin diffusions and rejection sampling to solve the problem of sampling from equality-constrained models. Our method has the advantage of being exact for linear constraints and naturally deals with multimodal distributions on arbitrary constraints. We test our method on statistical disaggregation problems for electricity consumption datasets, and our approach provides better uncertainty estimation and accuracy in data imputation compared with other naive/unconstrained methods.

stat.CO↗