Detecting rumors on social media is a very critical task with significant implications to the economy, public health, etc. Previous works generally capture effective features from texts and the propagation structure. However, the uncertainty caused by unreliable relations in the propagation structure is common and inevitable due to wily rumor producers and the limited collection of spread data. Most approaches neglect it and may seriously limit the learning of features. Towards this issue, this paper makes the first attempt to explore propagation uncertainty for rumor detection. Specifically, we propose a novel Edge-enhanced Bayesian Graph Convolutional Network (EBGCN) to capture robust structural features. The model adaptively rethinks the reliability of latent relations by adopting a Bayesian approach. Besides, we design a new edge-wise consistency training framework to optimize the model by enforcing consistency on relations. Experiments on three public benchmark datasets demonstrate that the proposed model achieves better performance than baseline methods on both rumor detection and early rumor detection tasks.

Statistical signal processing applications usually require the estimation of some parameters of interest given a set of observed data. These estimates are typically obtained either by solving a multi-variate optimization problem, as in the maximum likelihood (ML) or maximum a posteriori (MAP) estimators, or by performing a multi-dimensional integration, as in the minimum mean squared error (MMSE) estimators. Unfortunately, analytical expressions for these estimators cannot be found in most real-world applications, and the Monte Carlo (MC) methodology is one feasible approach. MC methods proceed by drawing random samples, either from the desired distribution or from a simpler one, and using them to compute consistent estimators. The most important families of MC algorithms are Markov chain MC (MCMC) and importance sampling (IS). On the one hand, MCMC methods draw samples from a proposal density, building then an ergodic Markov chain whose stationary distribution is the desired distribution by accepting or rejecting those candidate samples as the new state of the chain. On the other hand, IS techniques draw samples from a simple proposal density, and then assign them suitable weights that measure their quality in some appropriate way. In this paper, we perform a thorough review of MC methods for the estimation of static parameters in signal processing applications. A historical note on the development of MC schemes is also provided, followed by the basic MC method and a brief description of the rejection sampling (RS) algorithm, as well as three sections describing many of the most relevant MCMC and IS algorithms, and their combined use.

Bayesian networks are a class of models that are widely used for risk assessment of complex operational systems. There are now multiple approaches, as well as implemented software, that guide their construction via data learning or expert elicitation. However, a constructed Bayesian network needs to be validated before it can be used for practical risk assessment. Here, we illustrate the usage of the bnmonitor R package: the first comprehensive software for the validation of a Bayesian network. An applied data analysis using bnmonitor is carried out over a medical dataset to illustrate the use of its wide array of functions.

We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the variables of interest (i.e., the parameters of the model to invert), whereas we employ a maximum likelihood approach for the estimation of the noise power. The whole technique is implemented by means of an iterative procedure, alternating sampling and optimization steps. Moreover, the noise power is also used as a tempered parameter for the posterior distribution of the the variables of interest. Therefore, a sequence of tempered posterior densities is generated, where the tempered parameter is automatically selected according to the actual estimation of the noise power. A complete Bayesian study over the model parameters and the scale parameter can be also performed. Numerical experiments show the benefits of the proposed approach.

Recent studies have shown that it is possible to combine machine learning methods with data assimilation to reconstruct a dynamical system using only sparse and noisy observations of that system. The same approach can be used to correct the error of a knowledge-based model. The resulting surrogate model is hybrid, with a statistical part supplementing a physical part. In practice, the correction can be added as an integrated term (i.e. in the model resolvent) or directly inside the tendencies of the physical model. The resolvent correction is easy to implement. The tendency correction is more technical, in particular it requires the adjoint of the physical model, but also more flexible. We use the two-scale Lorenz model to compare the two methods. The accuracy in long-range forecast experiments is somewhat similar between the surrogate models using the resolvent correction and the tendency correction. By contrast, the surrogate models using the tendency correction significantly outperform the surrogate models using the resolvent correction in data assimilation experiments. Finally, we show that the tendency correction opens the possibility to make online model error correction, i.e. improving the model progressively as new observations become available. The resulting algorithm can be seen as a new formulation of weak-constraint 4D-Var. We compare online and offline learning using the same framework with the two-scale Lorenz system, and show that with online learning, it is possible to extract all the information from sparse and noisy observations.

Probability distributions are central to Bayesian accounts of cognition, but behavioral assessments do not directly measure them. Posterior distributions are typically computed from collections of individual participant actions, yet are used to draw conclusions about the internal structure of participant beliefs. Also not explicitly measured are the prior distributions that distinguish Bayesian models from others by representing initial states of belief. Instead, priors are usually derived from experimenters' intuitions or model assumptions and applied equally to all participants. Here we present three experiments using "Plinko", a behavioral task in which participants estimate distributions of ball drops over all available outcomes and where distributions are explicitly measured before any observations. In Experiment 1, we show that participant priors cluster around prototypical probability distributions (Gaussian, bimodal, etc.), and that prior cluster membership may indicate learning ability. In Experiment 2, we highlight participants' ability to update to unannounced changes of presented distributions and how this ability is affected by environmental manipulation. Finally, in Experiment 3, we verify that individual participant priors are reliable representations and that learning is not impeded when faced with a physically implausible ball drop distribution that is dynamically defined according to individual participant input. This task will prove useful in more closely examining mechanisms of statistical learning and mental model updating without requiring many of the assumptions made by more traditional computational modeling methodologies.

Machine learning models always make a prediction, even when it is likely to be inaccurate. This behavior should be avoided in many decision support applications, where mistakes can have severe consequences. Albeit already studied in 1970, machine learning with a reject option recently gained interest. This machine learning subfield enables machine learning models to abstain from making a prediction when likely to make a mistake. This survey aims to provide an overview on machine learning with a reject option. We introduce the conditions leading to two types of rejection, ambiguity and novelty rejection. Moreover, we define the existing architectures for models with a reject option, describe the standard learning strategies to train such models and relate traditional machine learning techniques to rejection. Additionally, we review strategies to evaluate a model's predictive and rejective quality. Finally, we provide examples of relevant application domains and show how machine learning with rejection relates to other machine learning research areas.

Over the past three decades, the problem of learning directed graphical models from data has received enormous amount of attention since they provide a compact and flexible way to represent the joint distribution of the data, especially when the associated graph is a directed acyclic graph (DAG). A directed graph is called a DAG if it does not contain directed cycles. DAG models are popular in practice with applications in biology, genetics, machine learning and causal inference (Sachs et al., 2005; Zhang et al., 2013; Koller and Friedman, 2009; Spirtes et al., 2000). There exists an extensive literature on learning the graph structure from data under the assumption that the graph is a DAG. For a summary, see the survey of Drton and Maathuis (2017); Heinze-Deml et al. (2018). Existing approaches generally fall into two categories, constrain-based methods (Spirtes et al., 2000; Pearl, 2009) and score-based methods (Chickering, 2002). Constraint-based methods utilize conditional independence test to determine whether there exists an edge between two nodes and then orient the edges in the graph, such that the resulting graph is compatible with the conditional independencies seen in the data. Score-based methods formulate the structure learning task as optimizing a score function based on the unknown graph and the data. A polytree is a DAG which does not contain any cycles even if the directions of all edges are ignored.

Rough Set based Spanning Sets were recently proposed to deal with uncertainties arising in the problem in domain of natural language processing problems. This paper presents a novel span measure using upper approximations. The key contribution of this paper is to propose another uncertainty measure of span and spanning sets. Firstly, this paper proposes a new definition of computing span which use upper approximation instead of boundary regions. This is useful in situations where computing upper approximations are much more convenient that computing boundary region. Secondly, properties of novel span and relation with earlier span measure are discussed. Thirdly, the paper presents application areas where the proposed span measure can be utilized.

In this work, we propose a domain generalization (DG) approach to learn on several labeled source domains and transfer knowledge to a target domain that is inaccessible in training. Considering the inherent conditional and label shifts, we would expect the alignment of $p(x|y)$ and $p(y)$. However, the widely used domain invariant feature learning (IFL) methods relies on aligning the marginal concept shift w.r.t. $p(x)$, which rests on an unrealistic assumption that $p(y)$ is invariant across domains. We thereby propose a novel variational Bayesian inference framework to enforce the conditional distribution alignment w.r.t. $p(x|y)$ via the prior distribution matching in a latent space, which also takes the marginal label shift w.r.t. $p(y)$ into consideration with the posterior alignment. Extensive experiments on various benchmarks demonstrate that our framework is robust to the label shift and the cross-domain accuracy is significantly improved, thereby achieving superior performance over the conventional IFL counterparts.