Probabilistic Numerics and Uncertainty in Computations

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 uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data has led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimisers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.Comment: Author Generated Postprint. 17 pages, 4 Figures, 1 Tabl

Probabilistic machine learning and artificial intelligence.

How can a machine learn from experience? Probabilistic modelling provides a framework for understanding what learning is, and has therefore emerged as one of the principal theoretical and practical approaches for designing machines that learn from data acquired through experience. The probabilistic framework, which describes how to represent and manipulate uncertainty about models and predictions, has a central role in scientific data analysis, machine learning, robotics, cognitive science and artificial intelligence. This Review provides an introduction to this framework, and discusses some of the state-of-the-art advances in the field, namely, probabilistic programming, Bayesian optimization, data compression and automatic model discovery.The author acknowledges an EPSRC grant EP/I036575/1, the DARPA PPAML programme, a Google Focused Research Award for the Automatic Statistician and support from Microsoft Research.This is the author accepted manuscript. The final version is available from NPG at http://www.nature.com/nature/journal/v521/n7553/full/nature14541.html#abstract

Evaluating the methodology of social experiments

Welfare ; Econometric models

Computer Aided Verification

This open access two-volume set LNCS 11561 and 11562 constitutes the refereed proceedings of the 31st International Conference on Computer Aided Verification, CAV 2019, held in New York City, USA, in July 2019. The 52 full papers presented together with 13 tool papers and 2 case studies, were carefully reviewed and selected from 258 submissions. The papers were organized in the following topical sections: Part I: automata and timed systems; security and hyperproperties; synthesis; model checking; cyber-physical systems and machine learning; probabilistic systems, runtime techniques; dynamical, hybrid, and reactive systems; Part II: logics, decision procedures; and solvers; numerical programs; verification; distributed systems and networks; verification and invariants; and concurrency

Checking the price tag on catastrophe: The social cost of carbon under non-linear climate response. ESRI WP392, June 2011

Research into the social cost of carbon emissions — the marginal social damage from a tonne of emitted carbon — has tended to focus on “best guess” scenarios. Such scenarios generally ignore the potential for low-probability, high- damage events, which are critically important to determining optimal climate policy. This paper uses the FUND integrated assessment model to investigate the influence of three types of low-probability, high-impact climate responses on the social cost of carbon: the collapse of the Atlantic Ocean Meridional Overturning Circulation; large scale dissociation of oceanic methane hydrates; and climate sensitivities above “best guess” levels. We find that incorporating these events can increase the social cost of carbon by a factor of over 3

Enhancing sustainability in logistics through stochastic network routing mechanism optimization using ant colony algorithm

Stochastic networks are one of the most prevalent types of networks these days. Therefore, many researchers directed to study them and summarize the essential points and challenges they face in developing these types of networks, especially optimal route path selection. In this paper, a solution to this problem was addressed using the evolutionary algorithm ACO (Ant Colony Optimization), where the path with the lowest cost was obtained according to several scenarios studied in the research, which consider the fact that, the traffic information in the network is available either in a static or in a dynamic form in real-time. The proposed method presented contributions for real networks that can be used in many applications. The results are essential in solving the problem of choosing the optimal route. Also, they can be applied to various scenarios of the stochastic networks that exist in real life. Optimization improves logistics efficiency, which contributes to sustainability by minimizing fuel consumption, reducing emissions, and conserving resources

Parametric G-computation for Compatible Indirect Treatment Comparisons with Limited Individual Patient Data

Population adjustment methods such as matching-adjusted indirect comparison (MAIC) are increasingly used to compare marginal treatment effects when there are cross-trial differences in effect modifiers and limited patient-level data. MAIC is based on propensity score weighting, which is sensitive to poor covariate overlap and cannot extrapolate beyond the observed covariate space. Current outcome regression-based alternatives can extrapolate but target a conditional treatment effect that is incompatible in the indirect comparison. When adjusting for covariates, one must integrate or average the conditional estimate over the relevant population to recover a compatible marginal treatment effect. We propose a marginalization method based parametric G-computation that can be easily applied where the outcome regression is a generalized linear model or a Cox model. The approach views the covariate adjustment regression as a nuisance model and separates its estimation from the evaluation of the marginal treatment effect of interest. The method can accommodate a Bayesian statistical framework, which naturally integrates the analysis into a probabilistic framework. A simulation study provides proof-of-principle and benchmarks the method's performance against MAIC and the conventional outcome regression. Parametric G-computation achieves more precise and more accurate estimates than MAIC, particularly when covariate overlap is poor, and yields unbiased marginal treatment effect estimates under no failures of assumptions. Furthermore, the marginalized regression-adjusted estimates provide greater precision and accuracy than the conditional estimates produced by the conventional outcome regression, which are systematically biased because the measure of effect is non-collapsible. This article is protected by copyright. All rights reserved

a literature review

Fonseca, J., & Bacao, F. (2023). Tabular and latent space synthetic data generation: a literature review. Journal of Big Data, 10, 1-37. [115]. https://doi.org/10.1186/s40537-023-00792-7 --- This research was supported by two research grants of the Portuguese Foundation for Science and Technology (“Fundação para a Ciência e a Tecnologia”), references SFRH/BD/151473/2021 and DSAIPA/DS/0116/2019, and by project UIDB/04152/2020 - Centro de Investigação em Gestão de Informação (MagIC).The generation of synthetic data can be used for anonymization, regularization, oversampling, semi-supervised learning, self-supervised learning, and several other tasks. Such broad potential motivated the development of new algorithms, specialized in data generation for specific data formats and Machine Learning (ML) tasks. However, one of the most common data formats used in industrial applications, tabular data, is generally overlooked; Literature analyses are scarce, state-of-the-art methods are spread across domains or ML tasks and there is little to no distinction among the main types of mechanism underlying synthetic data generation algorithms. In this paper, we analyze tabular and latent space synthetic data generation algorithms. Specifically, we propose a unified taxonomy as an extension and generalization of previous taxonomies, review 70 generation algorithms across six ML problems, distinguish the main generation mechanisms identified into six categories, describe each type of generation mechanism, discuss metrics to evaluate the quality of synthetic data and provide recommendations for future research. We expect this study to assist researchers and practitioners identify relevant gaps in the literature and design better and more informed practices with synthetic data.publishersversionpublishe