Non-Bayesian social learning theory provides a framework that models distributed inference for a group of agents interacting over a social network. In this framework, each agent iteratively forms and communicates beliefs about an unknown state of the world with their neighbors using a learning rule. Existing approaches assume agents have access to precise statistical models (in the form of likelihoods) for the state of the world. However in many situations, such models must be learned from finite data. We propose a social learning rule that takes into account uncertainty in the statistical models using second-order probabilities. Therefore, beliefs derived from uncertain models are sensitive to the amount of past evidence collected for each hypothesis. We characterize how well the hypotheses can be tested on a social network, as consistent or not with the state of the world. We explicitly show the dependency of the generated beliefs with respect to the amount of prior evidence. Moreover, as the amount of prior evidence goes to infinity, learning occurs and is consistent with traditional social learning theory.
One of the main challenges of deep learning tools is their inability to capture model uncertainty. While Bayesian deep learning can be used to tackle the problem, Bayesian neural networks often require more time and computational power to train than deterministic networks. Our work explores whether fully Bayesian networks are needed to successfully capture model uncertainty. We vary the number and position of Bayesian layers in a network and compare their performance on active learning with the MNIST dataset. We found that we can fully capture the model uncertainty by using only a few Bayesian…
Sapienza University of Rome（罗马第一大学）；IDSIA（意大利瑞士人工智能研究所）
A reliable modeling of uncertain evidence in Bayesian networks based on a set-valued quantification is proposed. Both soft and virtual evidences are considered. We show that evidence propagation in this setup can be reduced to standard updating in an augmented credal network, equivalent to a set of consistent Bayesian networks. A characterization of the computational complexity for this task is derived together with an efficient exact procedure for a subclass of instances. In the case of multiple uncertain evidences over the same variable, the proposed procedure can provide a set-valued versio…
University of Electronic Science and Technology of China（电子科技大学）
In a crowdsourcing contest, a principal holding a task posts it to a crowd. People in the crowd then compete with each other to win the rewards. Although in real life, a crowd is usually networked and people influence each other via social ties, existing crowdsourcing contest theories do not aim to answer how interpersonal relationships influence people's incentives and behaviors and thereby affect the crowdsourcing performance. In this work, we novelly take people's social ties as a key factor in the modeling and designing of agents' incentives in crowdsourcing contests. We establish two cont…
University of Duisburg-Essen（杜伊斯堡-埃森大学）；University of Leicester（莱斯特大学）
This paper exploits extended Bayesian networks for uncertainty reasoning on Petri nets, where firing of transitions is probabilistic. In particular, Bayesian networks are used as symbolic representations of probability distributions, modelling the observer's knowledge about the tokens in the net. The observer can study the net by monitoring successful and failed steps. An update mechanism for Bayesian nets is enabled by relaxing some of their restrictions, leading to modular Bayesian nets that can conveniently be represented and modified. As for every symbolic representation, the question is h…
University of Cambridge（剑桥大学）；Microsoft Research（微软研究院）；Alan Turing Institute（艾伦·图灵研究所）
We describe a limitation in the expressiveness of the predictive uncertainty estimate given by mean-field variational inference (MFVI), a popular approximate inference method for Bayesian neural networks. In particular, MFVI fails to give calibrated uncertainty estimates in between separated regions of observations. This can lead to catastrophically overconfident predictions when testing on out-of-distribution data. Avoiding such overconfidence is critical for active learning, Bayesian optimisation and out-of-distribution robustness. We instead find that a classical technique, the linearised L…
University of Michigan（密歇根大学）；DEVCOM Army Research Laboratory（DEVCOM陆军研究实验室）；BI Norwegian Business School（BI挪威商学院）；University of Brescia（布雷西亚大学）
In second-order uncertain Bayesian networks, the conditional probabilities are only known within distributions, i.e., probabilities over probabilities. The delta-method has been applied to extend exact first-order inference methods to propagate both means and variances through sum-product networks derived from Bayesian networks, thereby characterizing epistemic uncertainty, or the uncertainty in the model itself. Alternatively, second-order belief propagation has been demonstrated for polytrees but not for general directed acyclic graph structures. In this work, we extend Loopy Belief Propagat…
Pohang University of Science and Technology (POSTECH)（浦项科技大学）
We develop a novel deep learning method for uncertainty quantification in stochastic partial differential equations based on Bayesian neural network (BNN) and Hamiltonian Monte Carlo (HMC). A BNN efficiently learns the posterior distribution of the parameters in deep neural networks by performing Bayesian inference on the network parameters. The posterior distribution is efficiently sampled using HMC to quantify uncertainties in the system. Several numerical examples are shown for both forward and inverse problems in high dimension to demonstrate the effectiveness of the proposed method for un…
Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks
University of Oxford（牛津大学）
无向图模型在统计学、物理学和机器视觉等领域有着广泛的应用。然而，无向模型的贝叶斯参数估计是极具挑战性的，因为后验的评估通常涉及到一个棘手的归一化常数的计算。这个问题已经得到了很大的关注，但很少集中在重要的实际情况下，数据包括噪音或不完整的观察潜在的隐藏结构。本文专门针对这个问题，比较两种替代方法。在这些方法的第一种中，粒子马尔可夫链蒙特卡罗（Andrieu等人，2010）用于有效地探索参数空间，结合交换算法（Murray et al.，2006），以避免计算棘手的归一化常数（证明这种组合的目标是正确的分布，可以在在线补充附录中找到）。该方法与近似贝叶斯计算（Pritchard等人，1999年）。应用估计伊辛模型和指数随机图的参数从噪声数据。由于使用MCMC从潜在图形模型进行模拟，本文中使用的每个算法都以接近真实后验为目标，而不是能够在一般情况下准确地做到这一点。补充附录还说明了由此得出的近似值的性质。
University of Tübingen（图宾根大学）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
High-quality calibrated uncertainty estimates are crucial for numerous real-world applications, especially for deep learning-based deployed ML systems. While Bayesian deep learning techniques allow uncertainty estimation, training them with large-scale datasets is an expensive process that does not always yield models competitive with non-Bayesian counterparts. Moreover, many of the high-performing deep learning models that are already trained and deployed are non-Bayesian in nature and do not provide uncertainty estimates. To address these issues, we propose BayesCap that learns a Bayesian id…
Univ. of Michigan（密歇根大学）；US Army DEVCOM ARL（美国陆军作战能力发展司令部陆军研究实验室）；Univ. of Brescia（布雷西亚大学）
When the historical data are limited, the conditional probabilities associated with the nodes of Bayesian networks are uncertain and can be empirically estimated. Second order estimation methods provide a framework for both estimating the probabilities and quantifying the uncertainty in these estimates. We refer to these cases as uncer tain or second-order Bayesian networks. When such data are complete, i.e., all variable values are observed for each instantiation, the conditional probabilities are known to be Dirichlet-distributed. This paper improves the current state-of-the-art approaches f…
Probabilistic predictions from neural networks which account for predictive uncertainty during classification is crucial in many real-world and high-impact decision making settings. However, in practice most datasets are trained on non-probabilistic neural networks which by default do not capture this inherent uncertainty. This well-known problem has led to the development of post-hoc calibration procedures, such as Platt scaling (logistic), isotonic and beta calibration, which transforms the scores into well calibrated empirical probabilities. A plausible alternative to the calibration approa…
Uncertainty estimation is an indispensable capability for AI-enabled, safety-critical applications, e.g. autonomous vehicles or medical diagnosis. Bayesian neural networks (BNNs) use Bayesian statistics to provide both classification predictions and uncertainty estimation, but they suffer from high computational overhead associated with random number generation and repeated sample iterations. Furthermore, BNNs are not immediately amenable to acceleration through compute-in-memory architectures due to the frequent memory writes necessary after each RNG operation. To address these challenges, we…
