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On the convergence of two sequential Monte Carlo methods for maximum a posteriori sequence estimation and stochastic global optimization

機(jī)譯：關(guān)于最大后驗(yàn)序列估計(jì)和隨機(jī)全局優(yōu)化的兩個(gè)順序蒙特卡洛方法的收斂性

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This paper addresses the problem of maximum a posteriori (MAP) sequence estimation in general state-space models. We consider two algorithms based on the sequential Monte Carlo (SMC) methodology (also known as particle filtering). We prove that they produce approximations of the MAP estimator and that they converge almost surely. We also derive a lower bound for the number of particles that are needed to achieve a given approximation accuracy. In the last part of the paper, we investigate the application of particle filtering and MAP estimation to the global optimization of a class of (possibly non-convex and possibly non-differentiable) cost functions. In particular, we show how to convert the cost-minimization problem into one of MAP sequence estimation for a state-space model that is "matched" to the cost of interest. We provide examples that illustrate the application of the methodology as well as numerical results.
機(jī)譯：本文解決了一般狀態(tài)空間模型中最大后驗(yàn)（MAP）序列估計(jì)的問(wèn)題。我們考慮兩種基于順序蒙特卡洛（SMC）方法（也稱為粒子濾波）的算法。我們證明它們產(chǎn)生MAP估計(jì)量的近似值，并且?guī)缀蹩梢钥隙ǖ厥諗?。我們還得出了達(dá)到給定近似精度所需的粒子數(shù)量的下限。在本文的最后一部分，我們研究了粒子濾波和MAP估計(jì)在一類（可能是非凸且可能是不可微分的）成本函數(shù)的全局優(yōu)化中的應(yīng)用。特別是，我們展示了如何將成本最小化問(wèn)題轉(zhuǎn)換為與所需成本“匹配”的狀態(tài)空間模型的MAP序列估計(jì)之一。我們提供的示例說(shuō)明了該方法的應(yīng)用以及數(shù)值結(jié)果。

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