Approximate Bayesian Computation is widely used in systems biology for inferring parameters in stochastic gene regulatory network models. Its performance hinges critically on the ability to summarize high-dimensional system responses such as time series into a few informative, low-dimensional summary statistics. The quality of those statistics acutely impacts the accuracy of the inference task. Existing methods to select the best subset out of a pool of candidate statistics do not scale well with large pools of several tens to hundreds of candidate statistics. Since high quality statistics are imperative for good performance, this becomes a serious bottleneck when performing inference on complex and high-dimensional problems. This paper proposes a convolutional neural network architecture for automatically learning informative summary statistics of temporal responses. We show that the proposed network can effectively circumvent the statistics selection problem of the preprocessing step for ABC inference. The proposed approach is demonstrated on two benchmark problem and one challenging inference problem learning parameters in a high-dimensional stochastic genetic oscillator. We also study the impact of experimental design on network performance by comparing different data richness and data acquisition strategies.
Some discussions of D. Fearnhead and D. Prangle's Read Paper "Constructing summary statistics for approximate Bayesian computation: semi-automatic approximate Bayesian computation"
Cardio/cerebrovascular diseases (CVD) have become one of the major health issue in our societies. But recent studies show that the present pathology tests to detect CVD are ineffectual as they do not consider different stages of platelet activation or the molecular dynamics involved in platelet interactions and are incapable to consider inter-individual variability. Here we propose a stochastic platelet deposition model and an inferential scheme to estimate the biologically meaningful model parameters using approximate Bayesian computation with a summary statistic that maximally discriminates …
Summary Statistics in Approximate Bayesian Computation
这篇文章将作为即将出版的由S。Sisson，Y. Fan和M.博蒙特由于最早的工作ABC，人们已经认识到，使用汇总统计是必不可少的，以产生有用的推理结果。这是因为ABC受到维数效应的诅咒，因此使用高维输入会导致输出中的大近似误差。因此，至关重要的是要找到低维摘要，这是信息的参数推断或模型选择任务在手。本章回顾了为选择此类摘要而提出的方法，扩展了Blum et al.（2013）先前的综述论文，并介绍了最新进展。对ABC维数灾难和充分性的相关理论结果也进行了讨论。
Kernel Approximate Bayesian Computation for Population Genetic Inferences
近似贝叶斯计算（ABC）是一种基于拒绝算法方法的贝叶斯推断的无似然方法，该方法应用了观察数据和模拟数据的汇总统计量之间的差异容限。虽然已经提出了对算法的几种改进，但是这些改进都没有避免以下两个近似源：1）缺乏足够的统计量：采样不是来自给定数据的真实后验密度，而是来自给定汇总统计量的近似后验密度;以及2）非零公差：仅在零公差的极限下实现从给定汇总统计量的后验密度采样。近似值的第一个来源可以通过添加汇总统计量来改进，但是汇总统计量数量的增加可能会引入由低接受率引起的额外方差。因此，许多研究人员试图开发技术来选择信息汇总统计量。本研究评估了基于核的ABC方法（Kazumizu et al. 2010，arXiv：1009.5736 and 2011，NIPS 24：1549-1557）在需要许多汇总统计量的复杂问题中的实用性。将核ABC应用于群体遗传推理。我们证明，在传统的ABC相比，内核ABC可以将大量的汇总统计，同时保持高性能的推理。
A thermodynamic approach to Approximate Bayesian Computation with multiple summary statistics
Swiss Federal Institute of Aquatic Science and Technology（瑞士联邦水科学与技术研究所）；Zurich University of Applied Sciences（苏黎世应用科学大学）；Swiss Data Science Center（瑞士数据中心）；ETH Zurich（苏黎世联邦理工学院）；Università della Svizzera italiana and University of Insubria（瑞士意大利语大学和不列颠尼亚大学）
In the modern age of social media and networks, graph representations of real-world phenomena have become an incredibly useful source to mine insights. Often, we are interested in understanding how entities in a graph are interconnected. The Graph Neural Network (GNN) has proven to be a very useful tool in a variety of graph learning tasks including node classification, link prediction, and edge classification. However, in most of these tasks, the graph data we are working with may be noisy and may contain spurious edges. That is, there is a lot of uncertainty associated with the underlying gr…
Distance-learning For Approximate Bayesian Computation To Model a Volcanic Eruption
近似贝叶斯计算（ABC）为我们提供了一种方法来推断模型的参数，其中的似然函数是不可用的，从一个观察。使用ABC，这取决于许多模拟所考虑的模型，我们开发了一个推理框架来学习参数的随机数值模拟火山喷发。此外，模型本身是并行使用消息传递接口（MPI）。因此，我们开发了一个嵌套并行MPI通信处理昂贵的数值模型与ABC算法。ABC通常依赖于数据的汇总统计，以衡量模型输出和观察的差异。但是，无法找到所考虑模型的信息性汇总统计量。因此，我们开发了一种基于深度度量学习的技术来学习模型输出之间的距离。我们使用这个框架来学习羽流特性（例如。初始羽流速度）的火山喷发火山碎屑沉积物收集的现场工作与2450 BP Pululagua（厄瓜多尔）火山喷发。
Uppsala University（乌普萨拉大学）；Department of Information Technology（信息技术系）；Division of Scientific Computing（科学计算部）；SE-751 05, Uppsala（乌普萨拉，SE-751 05）；Sweden（瑞典）
Approximate Bayesian computation is an established and popular method for likelihood-free inference with applications in many disciplines. The effectiveness of the method depends critically on the availability of well performing summary statistics. Summary statistic selection relies heavily on domain knowledge and carefully engineered features, and can be a laborious time consuming process. Since the method is sensitive to data dimensionality, the process of selecting summary statistics must balance the need to include informative statistics and the dimensionality of the feature vector. This p…
Inferring parameter distributions of complex industrial systems from noisy time series data requires methods to deal with the uncertainty of the underlying data and the used simulation model. Bayesian inference is well suited for these uncertain inverse problems. Standard methods used to identify uncertain parameters are Markov Chain Monte Carlo (MCMC) methods with explicit evaluation of a likelihood function. However, if the likelihood is very complex, such that its evaluation is computationally expensive, or even unknown in its explicit form, Approximate Bayesian Computation (ABC) methods pr…
Approximating the Likelihood in Approximate Bayesian Computation
本章将出现在即将出版的近似贝叶斯计算手册（2018）中。支撑近似贝叶斯计算（ABC）的概念和方法框架主要针对可能性具有挑战性或缺失的问题。ABC使用基于模拟的非参数估计汇总统计量的可能性，并假设从模型生成数据在计算上是便宜的。本章回顾了两种估计棘手的可能性的替代方法，目的是减少必要的模型模拟，以产生近似的后验。其中第一个是合成似然（SL）的贝叶斯版本，最初由Wood（2010）开发，它使用多变量正态近似来概括统计似然。使用ABC的参数近似而不是非参数近似，可以减少所需的模型模拟的数量。我们在本章中考虑的第二种似然近似方法是基于经验似然（EL），这是一种非参数技术，涉及在一组矩约束下最大化经验构建的似然。Mengersen et al（2013）修改了EL框架，以便它可以用于形成ABC可以应用的问题的近似后验，即具有棘手可能性的模型。然而，与ABC和贝叶斯SL（BSL）不同，贝叶斯EL（BCel）方法可以在某些情况下完全避免模型模拟。BSL和BCel方法说明了不同复杂性的模型。
Approximate Bayesian computation (ABC) has become an essential part of the Bayesian toolbox for addressing problems in which the likelihood is prohibitively expensive or entirely unknown, making it intractable. ABC defines a pseudo-posterior by comparing observed data with simulated data, traditionally based on some summary statistics, the elicitation of which is regarded as a key difficulty. Recently, using data discrepancy measures has been proposed in order to bypass the construction of summary statistics. Here we propose to use the importance-sampling ABC (IS-ABC) algorithm relying on the …
Bayesian neural networks (BNNs) can account for both aleatoric and epistemic uncertainty. However, in BNNs the priors are often specified over the weights which rarely reflects true prior knowledge in large and complex neural network architectures. We present a simple approach to incorporate prior knowledge in BNNs based on external summary information about the predicted classification probabilities for a given dataset. The available summary information is incorporated as augmented data and modeled with a Dirichlet process, and we derive the corresponding \emph{Summary Evidence Lower BOund}. …
Simulation-based Bayesian inference with ameliorative learned summary statistics -- Part I
Department of Electrical & Computer Engineering, College of Engineering, Physics, and Computing, The Catholic University of America（电气与计算机工程系，工程、物理与计算学院，天主教美国大学）
ABCMETAapp: R Shiny Application for Simulation-based Estimation of Mean and Standard Deviation for Meta-analysis via Approximate Bayesian Computation (ABC)
Swiss Data Science Center（瑞士数据科学中心）；Università Svizzera italiana（瑞士意大利语区大学）；University of Insubria（因苏布里亚大学）
For stochastic models with intractable likelihood functions, approximate Bayesian computation offers a way of approximating the true posterior through repeated comparisons of observations with simulated model outputs in terms of a small set of summary statistics. These statistics need to retain the information that is relevant for constraining the parameters but cancel out the noise. They can thus be seen as thermodynamic state variables, for general stochastic models. For many scientific applications, we need strictly more summary statistics than model parameters to reach a satisfactory appro…
In many instances, the application of approximate Bayesian methods is hampered by two practical features: 1) the requirement to project the data down to low-dimensional summary, including the choice of this projection, which ultimately yields inefficient inference; 2) a possible lack of robustness to deviations from the underlying model structure. Motivated by these efficiency and robustness concerns, we construct a new Bayesian method that can deliver efficient estimators when the underlying model is well-specified, and which is simultaneously robust to certain forms of model misspecification…
Uppsala University（乌普萨拉大学）；University of California-Santa Barbara（加州大学圣塔芭芭拉分校）；Umeå University（于默奥大学）
State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing step building upon deterministic neural networks, and do not take network prediction uncertainty into account. This work proposes a robust integrated approach that learns summary statistics using Bayesian neural networks, and directly estimates the posterior density using categorical distributions. An adaptive sampling scheme selects simulation locations to eff…
