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Accelerating Monte Carlo methods for Bayesian inference in dynamical models

機(jī)譯：動力學(xué)模型中貝葉斯推理的加速蒙特卡洛方法

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摘要

Making decisions and predictions from noisy observations are two important and challenging problems in many areas of society. Some examples of applications are recommendation systems for online shopping and streaming services, connecting genes with certain diseases and modelling climate change. In this thesis, we make use of Bayesian statistics to construct probabilistic models given prior information and historical data, which can be used for decision support and predictions. The main obstacle with this approach is that it often results in mathematical problems lacking analytical solutions. To cope with this, we make use of statistical simulation algorithms known as Monte Carlo methods to approximate the intractable solution. These methods enjoy well-understood statistical properties but are often computational prohibitive to employ. The main contribution of this thesis is the exploration of different strategies for accelerating inference methods based on sequential Monte Carlo (SMC) and Markov chain Monte Carlo (MCMC). That is, strategies for reducing the computational effort while keeping or improving the accuracy. A major part of the thesis is devoted to proposing such strategies for the MCMC method known as the particle Metropolis-Hastings (PMH) algorithm. We investigate two strategies: (i) introducing estimates of the gradient and Hessian of the target to better tailor the algorithm to the problem and (ii) introducing a positive correlation between the point-wise estimates of the target. Furthermore, we propose an algorithm based on the combination of SMC and Gaussian process optimisation, which can provide reasonable estimates of the posterior but with a significant decrease in computational effort compared with PMH. Moreover, we explore the use of sparseness priors for approximate inference in over-parametrised mixed effects models and autoregressive processes. This can potentially be a practical strategy for inference in the big data era. Finally, we propose a general method for increasing the accuracy of the parameter estimates in non-linear state space models by applying a designed input signal.
機(jī)譯：從嘈雜的觀察中做出決策和預(yù)測是社會許多領(lǐng)域中兩個(gè)重要且具有挑戰(zhàn)性的問題。應(yīng)用程序的一些示例是用于在線購物和流媒體服務(wù)的推薦系統(tǒng)，該系統(tǒng)將基因與某些疾病聯(lián)系起來并模擬氣候變化。在本文中，我們利用貝葉斯統(tǒng)計(jì)數(shù)據(jù)來構(gòu)造具有先驗(yàn)信息和歷史數(shù)據(jù)的概率模型，這些模型可用于決策支持和預(yù)測。這種方法的主要障礙是，它常常導(dǎo)致數(shù)學(xué)問題缺乏解析解。為了解決這個(gè)問題，我們利用稱為蒙特卡洛方法的統(tǒng)計(jì)模擬算法來近似難解。這些方法具有很好理解的統(tǒng)計(jì)屬性，但通常在計(jì)算上難以使用。本文的主要貢獻(xiàn)是探索了基于順序蒙特卡洛（SMC）和馬爾可夫鏈蒙特卡洛（MCMC）的各種加速推理方法的策略。即，在保持或提高精度的同時(shí)減少計(jì)算量的策略。本文的主要部分致力于為MCMC方法提出這樣的策略，這種方法被稱為粒子都市-停頓（PMH）算法。我們研究了兩種策略：（i）引入目標(biāo)的梯度和Hessian估計(jì)，以更好地針對該問題調(diào)整算法，以及（ii）在目標(biāo)的逐點(diǎn)估計(jì)之間引入正相關(guān)。此外，我們提出了一種基于SMC和高斯過程優(yōu)化相結(jié)合的算法，該算法可以提供合理的后驗(yàn)估計(jì)，但與PMH相比，計(jì)算量大為減少。此外，我們探索了稀疏先驗(yàn)在過度參數(shù)化混合效應(yīng)模型和自回歸過程中的近似推斷。在大數(shù)據(jù)時(shí)代，這可能是一種可行的推理策略。最后，我們提出了一種通用方法，通過應(yīng)用設(shè)計(jì)的輸入信號來提高非線性狀態(tài)空間模型中參數(shù)估計(jì)的準(zhǔn)確性。

著錄項(xiàng)

  • 作者

    Dahlin, Johan;

  • 作者單位
  • 年度 2016
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  • 原文格式 PDF
  • 正文語種 eng
  • 中圖分類

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