Neural Information Processing Systems http://nips.cc/

Open source code is available athttps://github.

We then introduce our method, which builds on and adapts the work of Conrad et al. (2016) and Teymur et al. (2016), and provide a

Probabilistic solvers provide a flexible and efficient framework for simulation, uncertainty quantification, and inference in dynamical systems.

Probabilistic numerics casts numerical tasks, such the numerical solution of differential equations, as inference problems to be solved.

Consider an edge computing setting in which a user submits queries for the solution of a linear system to an edge processor, which is subject to time-varying computing availability. The edge processor applies a probabilistic linear solver (PLS) so as to be able to respond to the user's query within the allotted time and computing budget. Feedback to the user is in the form of an uncertainty set. Due to model misspecification, the uncertainty set obtained via a direct application of PLS does not come with coverage guarantees with respect to the true solution of the linear system. This work introduces a new method to calibrate the uncertainty sets produced by PLS with the aim of guaranteeing long-term coverage requirements. The proposed method, referred to as online conformal prediction-PLS (OCP-PLS), assumes sporadic feedback from cloud to edge. This enables the online calibration of uncertainty thresholds via online conformal prediction (OCP), an online optimization method previously studied in the context of prediction models. The validity of OCP-PLS is verified via experiments that bring insights into trade-offs between coverage, prediction set size, and cloud usage.

Filtering-based probabilistic numerical solvers for ordinary differential equations (ODEs), also known as ODE filters, have been established as efficient methods for quantifying numerical uncertainty in the solution of ODEs. In practical applications, however, the underlying dynamical system often contains uncertain parameters, requiring the propagation of this model uncertainty to the ODE solution. In this paper, we demonstrate that ODE filters, despite their probabilistic nature, do not automatically solve this uncertainty propagation problem. To address this limitation, we present a novel approach that combines ODE filters with numerical quadrature to properly marginalize over uncertain parameters, while accounting for both parameter uncertainty and numerical solver uncertainty. Experiments across multiple dynamical systems demonstrate that the resulting uncertainty estimates closely match reference solutions. Notably, we show how the numerical uncertainty from the ODE solver can help prevent overconfidence in the propagated uncertainty estimates, especially when using larger step sizes. Our results illustrate that probabilistic numerical methods can effectively quantify both numerical and parametric uncertainty in dynamical systems.

Koch and Oesterreicher's model of "N\"ahe und Distanz" (N\"ahe = immediacy, conceptual orality; Distanz = distance, conceptual literacy) is constantly used in German linguistics. However, there is no statistical foundation for use in corpus linguistic analyzes, while it is increasingly moving into empirical corpus linguistics. Theoretically, it is stipulated, among other things, that written texts can be rated on a scale of conceptual orality and literacy by linguistic features. This article establishes such a scale based on PCA and combines it with automatic analysis. Two corpora of New High German serve as examples. When evaluating established features, a central finding is that features of conceptual orality and literacy must be distinguished in order to rank texts in a differentiated manner. The scale is also discussed with a view to its use in corpus compilation and as a guide for analyzes in larger corpora. With a theory-driven starting point and as a "tailored" dimension, the approach compared to Biber's Dimension 1 is particularly suitable for these supporting, controlling tasks.