Probabilistic numerics and uncertainty in computations.
Probabilistic numerics and uncertainty in computations.
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概率数值学和计算中的不确定性。
DOI：
10.1098/rspa.2015.0142
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发表时间：
2015-07-08
期刊：
影响因子：
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通讯作者：
Girolami M
中科院分区：
文献类型：
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作者：
Hennig P;Osborne MA;Girolami M
我们呼吁采用概率数值方法：用于数值任务的算法，包括线性代数、积分、优化和求解微分方程，这些算法会在计算中返回不确定性。这种由于时间或硬件有限的数值计算引起的精度损失而产生的不确定性对于当代科学和工业来说非常重要。在气候科学和天体物理学等应用中，根据大量复杂数据的计算做出决策的需要导致人们重新关注数值不确定性的管理。我们描述了几种开创性的经典数值方法如何自然地解释为概率推理。然后，我们表明概率视图提出了可以灵活调整以适应应用程序细节的新算法，同时提供改进的经验性能。我们提供了概率数值算法对天体测量和天文成像的实际科学问题的好处的具体说明，同时强调了这些新算法的未解决问题。最后，我们描述概率数值方法如何提供一个连贯的框架，用于识别结合数值算法（例如数值优化器和微分方程求解器）执行的计算中的不确定性，从而有可能允许诊断（和控制）计算中的误差源。
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 have 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 optimizers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.