Scalable estimation strategies based on stochastic approximations: classical results and new insights

Toulis Panos; Airoldi Edoardo M.

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Scalable estimation strategies based on stochastic approximations: classical results and new insights

机译：基于随机近似的可扩展估计策略：经典结果和新见解

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Estimation with large amounts of data can be facilitated by stochastic gradient methods, in which model parameters are updated sequentially using small batches of data at each step. Here, we review early work and modern results that illustrate the statistical properties of these methods, including convergence rates, stability, and asymptotic bias and variance. We then overview modern applications where these methods are useful, ranging from an online version of the EM algorithm to deep learning. In light of these results, we argue that stochastic gradient methods are poised to become benchmark principled estimation procedures for large datasets, especially those in the family of stable proximal methods, such as implicit stochastic gradient descent.

机译：随机梯度方法可以促进对大量数据的估计，在随机梯度方法中，在每个步骤中使用小批数据顺序更新模型参数。在这里，我们回顾了早期工作和现代结果，这些结果说明了这些方法的统计特性，包括收敛速度，稳定性以及渐近偏差和方差。然后，我们概述了在这些方法有用的现代应用程序，从EM算法的在线版本到深度学习。根据这些结果，我们认为随机梯度方法有望成为大型数据集（尤其是稳定近端方法系列中的那些）的基准原则估计程序，例如隐式随机梯度下降。

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来源
《Statistics and computing》 |2015年第4期|781-795|共15页
作者
Toulis Panos; Airoldi Edoardo M.;
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作者单位

Harvard Univ, Dept Stat, Cambridge, MA 02138 USA;

Harvard Univ, Dept Stat, Cambridge, MA 02138 USA;

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原文格式 PDF
正文语种 eng
中图分类
关键词
Maximum likelihood; Recursive estimation; Implicit stochastic gradient descent methods; Optimal learning rate; Asymptotic analysis; Big data;

机译：最大似然;递归估计;隐式随机梯度下降法;最优学习率;渐近分析;大数据;

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1. Algorithm of Adaptive Estimation of Random Processes Based on Dynamic Stochastic Approximations [J] . Yu.S. RASSHCHEPLYAEV, S.P. PIROGOV Journal of automation and information sciences . 2002,第9a12期

机译：基于动态随机逼近的随机过程自适应估计算法
2. Strategies for measurement-based quantum computation with cluster states transformed by stochastic local operations and classical communication [J] . Adam G. D Souza, David L. Feder Physical Review, A. Atomic, molecular, and optical physics . 2011,第4aPta1期

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3. An Online Sample-Based Method for Mode Estimation Using ODE Analysis of Stochastic Approximation Algorithms [J] . Chandramouli Kamanchi, Raghuram Bharadwaj Diddigi, Prabuchandran K. J., IEEE Control Systems Letters . 2019,第3期

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4. A stochastic approximation based state estimation algorithm for Stochastic Hybrid Systems [C] . Liu, Weiyi American Control Conference;ACC . 2012

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5. Stochastic Optimization Based on White-Box Deterministic Approximations: Models, Algorithms and Application to Service Networks [D] . Krishnamoorthy, Mohan. 2018

机译：基于白盒确定性近似的随机优化：模型，算法及其在服务网络中的应用
6. Scalable estimation strategies based on stochastic approximations: Classical results and new insights [O] . Edoardo M. Airoldi, Panos Toulis -1

机译：基于随机近似的可扩展估计策略：经典结果和新见解
7. This article presents a new numerical model describing the behaviour of a thermally thick wood sample exposed to high solar heat flux (above 1 MW/m2). A preliminary study based on dimensionless numbers is used to classify the problem and support model building assumptions. Then, a model based on mass, momentum and energy balance equations is proposed. These equations are coupled with liquid-vapour drying model and pseudo species biomass degradation model. By comparing to a former experimental study, preliminary results have shown that these equations are not enough to accurately predict biomass behaviour under high solar heat flux. Indeed, a char layer acting as radiative shield forms on the sample exposed surface. In addition to this classical set of equations, it is mandatory to take into account radiation penetration into the medium. Furthermore, as biomass contains water, medium deformation consecutively to char steam gasification must also be implemented. Finally, with the addition of these two strategies, the model is able to properly capture the degradation of biomass when exposed to high radiative heat flux over a range of sample initial moisture content. Additional insights of biomass behaviour under high solar heat flux were also derived. Drying, pyrolysis and gasification fronts are present at the same time inside of the sample. The coexistence of these three thermochemical fronts leads to char gasification by the steam produced from drying of the sample, which it is the main phenomenon behind medium ablation. [O] . Pozzobon, Victor, Salvador, Sylvain, Bézian, Jean Jacques 2018

机译：本文提供了一个新的数值模型，该模型描述了暴露于高太阳热通量（高于1 / MW / m2）的热厚木材样品的行为。基于无量纲数的初步研究用于对问题进行分类并支持模型构建假设。然后，提出了一种基于质量，动量和能量平衡方程的模型。这些方程式与液体蒸汽干燥模型和假物种生物质降解模型耦合。通过与以前的实验研究进行比较，初步结果表明，这些方程不足以准确预测高太阳热通量下的生物量行为。的确，在样品暴露的表面上形成了充当辐射屏蔽层的炭层。除了这套经典的方程式之外，还必须考虑到辐射向介质的渗透。此外，由于生物质中含有水，因此还必须在炭蒸气汽化后进行连续的介质变形。最后，通过添加这两种策略，该模型能够在一定范围的样品初始水分含量下暴露于高辐射热通量的情况下，正确捕获生物质的降解。还得出了在高太阳热通量下生物量行为的其他见解。样品内部同时存在干燥，热解和气化前沿。这三个热化学前沿的共存会导致样品干燥产生的蒸汽产生焦炭气化，这是介质烧蚀的主要现象。

Scalable estimation strategies based on stochastic approximations: classical results and new insights

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