Probabilistic Predictions with Federated Learning

Probabilistic predictions with machine learning are important in many applications. These are commonly done with Bayesian learning algorithms. However, Bayesian learning methods are computationally expensive in comparison with non-Bayesian methods. Furthermore, the data used to train these algorithms are often distributed over a large group of end devices. Federated learning can be applied in this setting in a communication-efficient and privacy-preserving manner but does not include predictive uncertainty. To represent predictive uncertainty in federated learning, our suggestion is to introduce uncertainty in the aggregation step of the algorithm by treating the set of local weights as a posterior distribution for the weights of the global model. We compare our approach to state-of-the-art Bayesian and non-Bayesian probabilistic learning algorithms. By applying proper scoring rules to evaluate the predictive distributions, we show that our approach can achieve similar performance as the benchmark would achieve in a non-distributed setting.     

From a Point Cloud to a Simulation Model—Bayesian Segmentation and Entropy Based Uncertainty Estimation for 3D Modelling

The 3D modelling of indoor environments and the generation of process simulations play an important role in factory and assembly planning. In brownfield planning cases, existing data are often outdated and incomplete especially for older plants, which were mostly planned in 2D. Thus, current environment models cannot be generated directly on the basis of existing data and a holistic approach on how to build such a factory model in a highly automated fashion is mostly non-existent. Major steps in generating an environment model of a production plant include data collection, data pre-processing and object identification as well as pose estimation. In this work, we elaborate on a methodical modelling approach, which starts with the digitalization of large-scale indoor environments and ends with the generation of a static environment or simulation model. The object identification step is realized using a Bayesian neural network capable of point cloud segmentation. We elaborate on the impact of the uncertainty information estimated by a Bayesian segmentation framework on the accuracy of the generated environment model. The steps of data collection and point cloud segmentation as well as the resulting model accuracy are evaluated on a real-world data set collected at the assembly line of a large-scale automotive production plant. The Bayesian segmentation network clearly surpasses the performance of the frequentist baseline and allows us to considerably increase the accuracy of the model placement in a simulation scene.     

“Exact” and Approximate Methods for Bayesian Inference: Stochastic Volatility Case Study

We conduct a case study in which we empirically illustrate the performance of different classes of Bayesian inference methods to estimate stochastic volatility models. In particular, we consider how different particle filtering methods affect the variance of the estimated likelihood. We review and compare particle Markov Chain Monte Carlo (MCMC), RMHMC, fixed-form variational Bayes, and integrated nested Laplace approximation to estimate the posterior distribution of the parameters. Additionally, we conduct the review from the point of view of whether these methods are (1) easily adaptable to different model specifications; (2) adaptable to higher dimensions of the model in a straightforward way; (3) feasible in the multivariate case. We show that when using the stochastic volatility model for methods comparison, various data-generating processes have to be considered to make a fair assessment of the methods. Finally, we present a challenging specification of the multivariate stochastic volatility model, which is rarely used to illustrate the methods but constitutes an important practical application.     

Bayesian inference on isospin splitting of nucleon effective mass from giant resonances in ~(208)Pb

From a Bayesian analysis of the electric dipole polarizability,the constrained energy of isovector giant dipole resonance,the peak energy of isocalar giant quadrupole resonance,and the constrained energy of isocalar giant monopole resonance in ~(208)Pb,we extract the iso scalar and isovector effective masses in nuclear matter at saturation density p_0 as m_(s,0)~*/m=0.87_(-0.04)~(+0.04) and m_(v,0)~*/m=0.78_(-0.05)~(+0.06),respectively,at 90% confidence level.The constraints obtained on m_(s,0)~* and m_(v,0)~* lead to a positive iso spin splitting of nucleon effective mass in asymmetric nuclear matter of iso spin asymmetry δ at p_0 as m_(n-p)~*/m=(0.20_(-0.14)~(+0.15))δ.In addition,the symmetry energy at the subsaturation density p~*=0.05 fm~(-3) is determined to be E_(sym)(p~*)=16.7±1.3 MeV at 90% confidence level.     

贝叶斯公式的几个应用

介绍了贝叶斯公式的一些应用实例及分析,以使在教学中能帮助学生更深入地理解该公式.     

Bayesian inference for Pr (Y

《Applied Mathematical Modelling》2014,38(5-6):1698-1709

中国经济随机前沿模型效率的贝叶斯统计推断

基于扩展的随机生产前沿模型,研究了区域生产效率的差异和其影响因素的作用效果,应用贝叶斯统计方法对中国各省份2010-2017的年度数据(不包含港澳台地区,下同)进行了实证研究.研究发现:生产效率总体呈逐渐下降的趋势,地区间生产效率有一定的差异,高等教育规模对生产效率具有显著的直接影响.人力资本能有效促进东部和中部地区的经济增长,西部地区主要依靠资本促进经济增长.环境污染对中部地区的经济增长具有一定的负向作用.     

Improvements to message computation in lazy propagation

Even though existing algorithms for belief update in Bayesian networks (BNs) have exponential time and space complexity, belief update in many real-world BNs is feasible. However, in some cases the efficiency of belief update may be insufficient. In such cases minor improvements in efficiency may be important or even necessary to make a task tractable. This paper introduces two improvements to the message computation in Lazy propagation (LP): (1) we introduce myopic methods for sorting the operations involved in a variable elimination using arc-reversal and (2) extend LP with the any-space property. The performance impacts of the methods are assessed empirically.     

Comparative analysis of multiobjective evolutionary algorithms for random and correlated instances of multiobjective d-dimensional knapsack problems

This study analyzes multiobjective d-dimensional knapsack problems (MOd-KP) within a comparative analysis of three multiobjective evolutionary algorithms (MOEAs): the ε-nondominated sorted genetic algorithm II (ε-NSGAII), the strength Pareto evolutionary algorithm 2 (SPEA2) and the ε-nondominated hierarchical Bayesian optimization algorithm (ε-hBOA). This study contributes new insights into the challenges posed by correlated instances of the MOd-KP that better capture the decision interdependencies often present in real world applications. A statistical performance analysis of the algorithms uses the unary ε-indicator, the hypervolume indicator and success rate plots to demonstrate their relative effectiveness, efficiency, and reliability for the MOd-KP instances analyzed. Our results indicate that the ε-hBOA achieves superior performance relative to ε-NSGAII and SPEA2 with increasing number of objectives, number of decisions, and correlative linkages between the two. Performance of the ε-hBOA suggests that probabilistic model building evolutionary algorithms have significant promise for expanding the size and scope of challenging multiobjective problems that can be explored.