Probabilistic numerical methods (PNMs) solve numerical problems via probabilistic inference. They have been developed for linear algebra, optimization, integration and differential equation simulation. PNMs naturally incorporate prior information about a problem and quantify uncertainty due to finite computational resources as well as stochastic input. In this paper, we present ProbNum: a Python library providing state-of-the-art probabilistic numerical solvers. ProbNum enables custom composition of PNMs for specific problem classes via a modular design as well as wrappers for off-the-shelf use. Tutorials, documentation, developer guides and benchmarks are available online at www.probnum.org.
Linear systems are the bedrock of virtually all numerical computation. Machine learning poses specific challenges for the solution of such systems due to their scale, characteristic structure, stochasticity and the central role of uncertainty in the field. Unifying earlier work we propose a class of probabilistic linear solvers which jointly infer the matrix, its inverse and the solution from matrix-vector product observations. This class emerges from a fundamental set of desiderata which constrains the space of possible algorithms and recovers the method of conjugate gradients under certain conditions. We demonstrate how to incorporate prior spectral information in order to calibrate uncertainty and experimentally showcase the potential of such solvers for machine learning.34th Conference on Neural Information Processing Systems (NeurIPS 2020),
Ce complément met sommairement à jour la bibliographie d’Alexandre Koyré, apportant une quarantaine de références actuellement non répertoriées (textes, rééditions et traductions) et illustrant l’intérêt toujours pérenne de l’œuvre de cet historien des idées.
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This complement updates Alexander Koyré’s bibliography : about forty unknown references (newly discovered texts, reeditions and translations) are illustrating the constant interest for the work of the historian of ideas.
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