Bayesian Networks (BNs) have become increasingly popular over the last few decades as a tool for reasoning under uncertainty in fields as diverse as medicine, biology, epidemiology, economics and the social sciences. This is especially true in real-world areas where we seek to answer complex questions based on hypothetical evidence to determine actions for intervention. However, determining the graphical structure of a BN remains a major challenge, especially when modelling a problem under causal assumptions. Solutions to this problem include the automated discovery of BN graphs from data, constructing them based on expert knowledge, or a combination of the two. This paper provides a comprehensive review of combinatoric algorithms proposed for learning BN structure from data, describing 61 algorithms including prototypical, well-established and state-of-the-art approaches. The basic approach of each algorithm is described in consistent terms, and the similarities and differences between them highlighted. Methods of evaluating algorithms and their comparative performance are discussed including the consistency of claims made in the literature. Approaches for dealing with data noise in real-world datasets and incorporating expert knowledge into the learning process are also covered.

Deep generative models trained by maximum likelihood remain very popular methods for reasoning about data probabilistically. However, it has been observed that they can assign higher likelihoods to out-of-distribution (OOD) data than in-distribution data, thus calling into question the meaning of these likelihood values. In this work we provide a novel perspective on this phenomenon, decomposing the average likelihood into a KL divergence term and an entropy term. We argue that the latter can explain the curious OOD behaviour mentioned above, suppressing likelihood values on datasets with higher entropy. Although our idea is simple, we have not seen it explored yet in the literature. This analysis provides further explanation for the success of OOD detection methods based on likelihood ratios, as the problematic entropy term cancels out in expectation. Finally, we discuss how this observation relates to recent success in OOD detection with manifold-supported models, for which the above decomposition does not hold.

Identification of nonlinear dynamic systems remains a significant challenge across engineering. This work suggests an approach based on Bayesian filtering to extract and identify the contribution of an unknown nonlinear term in the system which can be seen as an alternative viewpoint on restoring force surface type approaches. To achieve this identification, the contribution which is the nonlinear restoring force is modelled, initially, as a Gaussian process in time. That Gaussian process is converted into a state-space model and combined with the linear dynamic component of the system. Then, by inference of the filtering and smoothing distributions, the internal states of the system and the nonlinear restoring force can be extracted. In possession of these states a nonlinear model can be constructed. The approach is demonstrated to be effective in both a simulated case study and on an experimental benchmark dataset.

In many fields of science and engineering, models with different fidelities are available. Physical experiments or detailed simulations that accurately capture the behavior of the system are regarded as high-fidelity models with low model uncertainty, however, they are expensive to run. On the other hand, simplified physical experiments or numerical models are seen as low-fidelity models that are cheaper to evaluate. Although low-fidelity models are often not suitable for direct use in reliability analysis due to their low accuracy, they can offer information about the trend of the high-fidelity model thus providing the opportunity to explore the design space at a low cost. This study presents a new approach called adaptive multi-fidelity Gaussian process for reliability analysis (AMGPRA). Contrary to selecting training points and information sources in two separate stages as done in state-of-the-art mfEGRA method, the proposed approach finds the optimal training point and information source simultaneously using the novel collective learning function (CLF). CLF is able to assess the global impact of a candidate training point from an information source and it accommodates any learning function that satisfies a certain profile. In this context, CLF provides a new direction for quantifying the impact of new training points and can be easily extended with new learning functions to adapt to different reliability problems. The performance of the proposed method is demonstrated by three mathematical examples and one engineering problem concerning the wind reliability of transmission towers. It is shown that the proposed method achieves similar or higher accuracy with reduced computational costs compared to state-of-the-art single and multi-fidelity methods. A key application of AMGPRA is high-fidelity fragility modeling using complex and costly physics-based computational models.

Causal effect estimation for dynamic treatment regimes (DTRs) contributes to sequential decision making. However, censoring and time-dependent confounding under DTRs are challenging as the amount of observational data declines over time due to a reducing sample size but the feature dimension increases over time. Long-term follow-up compounds these challenges. Another challenge is the highly complex relationships between confounders, treatments, and outcomes, which causes the traditional and commonly used linear methods to fail. We combine outcome regression models with treatment models for high dimensional features using uncensored subjects that are small in sample size and we fit deep Bayesian models for outcome regression models to reveal the complex relationships between confounders, treatments, and outcomes. Also, the developed deep Bayesian models can model uncertainty and output the prediction variance which is essential for the safety-aware applications, such as self-driving cars and medical treatment design. The experimental results on medical simulations of HIV treatment show the ability of the proposed method to obtain stable and accurate dynamic causal effect estimation from observational data, especially with long-term follow-up. Our technique provides practical guidance for sequential decision making, and policy-making.

In recent years, machine learning (ML) algorithms have been deployed in safety-critical and high-stake decision-making, where the fairness of algorithms is of paramount importance. Fairness in ML centers on detecting bias towards certain demographic populations induced by an ML classifier and proposes algorithmic solutions to mitigate the bias with respect to different fairness definitions. To this end, several fairness verifiers have been proposed that compute the bias in the prediction of an ML classifier -- essentially beyond a finite dataset -- given the probability distribution of input features. In the context of verifying linear classifiers, existing fairness verifiers are limited by accuracy due to imprecise modelling of correlations among features and scalability due to restrictive formulations of the classifiers as SSAT or SMT formulas or by sampling. In this paper, we propose an efficient fairness verifier, called FVGM, that encodes the correlations among features as a Bayesian network. In contrast to existing verifiers, FVGM proposes a stochastic subset-sum based approach for verifying linear classifiers. Experimentally, we show that FVGM leads to an accurate and scalable assessment for more diverse families of fairness-enhancing algorithms, fairness attacks, and group/causal fairness metrics than the state-of-the-art. We also demonstrate that FVGM facilitates the computation of fairness influence functions as a stepping stone to detect the source of bias induced by subsets of features.

Intelligent robots are redefining a multitude of critical domains but are still far from being fully capable of assisting human peers in day-to-day tasks. An important requirement of collaboration is for each teammate to maintain and respect an understanding of the others' expectations of itself. Lack of which may lead to serious issues such as loose coordination between teammates, reduced situation awareness, and ultimately teaming failures. Hence, it is important for robots to behave explicably by meeting the human's expectations. One of the challenges here is that the expectations of the human are often hidden and can change dynamically as the human interacts with the robot. However, existing approaches to generating explicable plans often assume that the human's expectations are known and static. In this paper, we propose the idea of active explicable planning to relax this assumption. We apply a Bayesian approach to model and predict dynamic human belief and expectations to make explicable planning more anticipatory. We hypothesize that active explicable plans can be more efficient and explicable at the same time, when compared to explicable plans generated by the existing methods. In our experimental evaluation, we verify that our approach generates more efficient explicable plans while successfully capturing the dynamic belief change of the human teammate.

Data augmentation (DA) algorithms are widely used for Bayesian inference due to their simplicity. In massive data settings, however, DA algorithms are prohibitively slow because they pass through the full data in any iteration, imposing serious restrictions on their usage despite the advantages. Addressing this problem, we develop a framework for extending any DA that exploits asynchronous and distributed computing. The extended DA algorithm is indexed by a parameter $r \in (0, 1)$ and is called Asynchronous and Distributed (AD) DA with the original DA as its parent. Any ADDA starts by dividing the full data into $k$ smaller disjoint subsets and storing them on $k$ processes, which could be machines or processors. Every iteration of ADDA augments only an $r$-fraction of the $k$ data subsets with some positive probability and leaves the remaining $(1-r)$-fraction of the augmented data unchanged. The parameter draws are obtained using the $r$-fraction of new and $(1-r)$-fraction of old augmented data. For many choices of $k$ and $r$, the fractional updates of ADDA lead to a significant speed-up over the parent DA in massive data settings, and it reduces to the distributed version of its parent DA when $r=1$. We show that the ADDA Markov chain is Harris ergodic with the desired stationary distribution under mild conditions on the parent DA algorithm. We demonstrate the numerical advantages of the ADDA in three representative examples corresponding to different kinds of massive data settings encountered in applications. In all these examples, our DA generalization is significantly faster than its parent DA algorithm for all the choices of $k$ and $r$. We also establish geometric ergodicity of the ADDA Markov chain for all three examples, which in turn yields asymptotically valid standard errors for estimates of desired posterior quantities.

There is a strong link between the general concept of intelligence and the ability to collect and use information. The theory of Bayes-adaptive exploration offers an attractive optimality framework for training machines to perform complex information gathering tasks. However, the computational complexity of the resulting optimal control problem has limited the diffusion of the theory to mainstream deep AI research. In this paper we exploit the inherent mathematical structure of Bayes-adaptive problems in order to dramatically simplify the problem by making the reward structure denser while simultaneously decoupling the learning of exploitation and exploration policies. The key to this simplification comes from the novel concept of cross-value (i.e. the value of being in an environment while acting optimally according to another), which we use to quantify the value of currently available information. This results in a new denser reward structure that "cashes in" all future rewards that can be predicted from the current information state. In a set of experiments we show that the approach makes it possible to learn challenging information gathering tasks without the use of shaping and heuristic bonuses in situations where the standard RL algorithms fail.

In this article, we will discuss the mathematical intuition behind Naive Bayes Classifiers, and we'll also see how to implement this on Python. This model is easy to build and is mostly used for large datasets. It is a probabilistic machine learning model that is used for classification problems. The core of the classifier depends on the Bayes theorem with an assumption of independence among predictors. That means changing the value of a feature doesn't change the value of another feature.