ProBoost, a new boosting algorithm for probabilistic classifiers, is proposed in this work. This algorithm uses the epistemic uncertainty of each training sample to determine the most challenging/uncertain ones; the relevance of these samples is then increased for the next weak learner, producing a sequence that progressively focuses on the samples found to have the highest uncertainty. In the end, the weak learners' outputs are combined into a weighted ensemble of classifiers. Three methods are proposed to manipulate the training set: undersampling, oversampling, and weighting the training samples according to the uncertainty estimated by the weak learners. Furthermore, two approaches are studied regarding the ensemble combination. The weak learner herein considered is a standard convolutional neural network, and the probabilistic models underlying the uncertainty estimation use either variational inference or Monte Carlo dropout. The experimental evaluation carried out on MNIST benchmark datasets shows that ProBoost yields a significant performance improvement. The results are further highlighted by assessing the relative achievable improvement, a metric proposed in this work, which shows that a model with only four weak learners leads to an improvement exceeding 12% in this metric (for either accuracy, sensitivity, or specificity), in comparison to the model learned without ProBoost.

In the context of modern environmental and societal concerns, there is an increasing demand for methods able to identify management strategies for civil engineering systems, minimizing structural failure risks while optimally planning inspection and maintenance (I&M) processes. Most available methods simplify the I&M decision problem to the component level due to the computational complexity associated with global optimization methodologies under joint system-level state descriptions. In this paper, we propose an efficient algorithmic framework for inference and decision-making under uncertainty for engineering systems exposed to deteriorating environments, providing optimal management strategies directly at the system level. In our approach, the decision problem is formulated as a factored partially observable Markov decision process, whose dynamics are encoded in Bayesian network conditional structures. The methodology can handle environments under equal or general, unequal deterioration correlations among components, through Gaussian hierarchical structures and dynamic Bayesian networks. In terms of policy optimization, we adopt a deep decentralized multi-agent actor-critic (DDMAC) reinforcement learning approach, in which the policies are approximated by actor neural networks guided by a critic network. By including deterioration dependence in the simulated environment, and by formulating the cost model at the system level, DDMAC policies intrinsically consider the underlying system-effects. This is demonstrated through numerical experiments conducted for both a 9-out-of-10 system and a steel frame under fatigue deterioration. Results demonstrate that DDMAC policies offer substantial benefits when compared to state-of-the-art heuristic approaches. The inherent consideration of system-effects by DDMAC strategies is also interpreted based on the learned policies.

Surprising events trigger measurable brain activity and influence human behavior by affecting learning, memory, and decision-making. Currently there is, however, no consensus on the definition of surprise. Here we identify 18 mathematical definitions of surprise in a unifying framework. We first propose a technical classification of these definitions into three groups based on their dependence on an agent's belief, show how they relate to each other, and prove under what conditions they are indistinguishable. Going beyond this technical analysis, we propose a taxonomy of surprise definitions and classify them into four conceptual categories based on the quantity they measure: (i) 'prediction surprise' measures a mismatch between a prediction and an observation; (ii) 'change-point detection surprise' measures the probability of a change in the environment; (iii) 'confidence-corrected surprise' explicitly accounts for the effect of confidence; and (iv) 'information gain surprise' measures the belief-update upon a new observation. The taxonomy poses the foundation for principled studies of the functional roles and physiological signatures of surprise in the brain.

In this article, we describe a {\tt R} package for sampling from an empirical likelihood-based posterior using a Hamiltonian Monte Carlo method. Empirical likelihood-based methodologies have been used in Bayesian modeling of many problems of interest in recent times. This semiparametric procedure can easily combine the flexibility of a non-parametric distribution estimator together with the interpretability of a parametric model. The model is specified by estimating equations-based constraints. Drawing an inference from a Bayesian empirical likelihood (BayesEL) posterior is challenging. The likelihood is computed numerically, so no closed expression of the posterior exists. Moreover, for any sample of finite size, the support of the likelihood is non-convex, which hinders the fast mixing of many Markov Chain Monte Carlo (MCMC) procedures. It has been recently shown that using the properties of the gradient of log empirical likelihood, one can devise an efficient Hamiltonian Monte Carlo (HMC) algorithm to sample from a BayesEL posterior. The package requires the user to specify only the estimating equations, the prior, and their respective gradients. An MCMC sample drawn from the BayesEL posterior of the parameters, with various details required by the user is obtained.

We consider the identification of large-scale linear and stable dynamic systems whose outputs may be the result of many correlated inputs. Hence, severe ill-conditioning may affect the estimation problem. This is a scenario often arising when modeling complex physical systems given by the interconnection of many sub-units where feedback and algebraic loops can be encountered. We develop a strategy based on Bayesian regularization where any impulse response is modeled as the realization of a zero-mean Gaussian process. The stable spline covariance is used to include information on smooth exponential decay of the impulse responses. We then design a new Markov chain Monte Carlo scheme that deals with collinearity and is able to efficiently reconstruct the posterior of the impulse responses. It is based on a variation of Gibbs sampling which updates possibly overlapping blocks of the parameter space on the basis of the level of collinearity affecting the different inputs. Numerical experiments are included to test the goodness of the approach where hundreds of impulse responses form the system and inputs correlation may be very high.

Markov chain Monte Carlo (MCMC) methods are frequently employed to sample from the posterior distribution of the parameters of interest. Such difficulties have restricted the use of Bayesian empirical likelihood (BayesEL) based methods in many applications. In this article, we propose a two-step Metropolis Hastings algorithm to sample from the BayesEL posteriors. Our proposal is specified hierarchically, where the estimating equations determining the empirical likelihood are used to propose values of a set of parameters depending on the proposed values of the remaining parameters. Furthermore, we discuss Bayesian model selection using empirical likelihood and extend our two-step Metropolis Hastings algorithm to a reversible jump Markov chain Monte Carlo procedure to sample from the resulting posterior. Finally, several applications of our proposed methods are presented. In recent years, empirical likelihood (Owen, 1988; Qin & Lawless, 1994) based procedures have been frequently used under Bayesian framework. Such procedures specify a statistical model through unbiased estimating equations, without requiring a declaration of the data distribution. The likelihood is estimated from the empirical distribution function computed under constraints imposed by these estimating equations. The estimated likelihood is then used to define a posterior. The validity of empirical and similar likelihoods for Bayesian inference has been a topic of extensive discussion (Monahan & Boos, 1992; Lazar, 2003; Fang & Mukerjee, 2006; Corcoran, 1998). Alternative likelihoods like Bayesian exponential tilted empirical likelihood (BETEL) (Schennach, 2005) have been proposed and justified using basic probabilistic arguments.

An ensemble of classifiers combines several single classifiers to deliver a final prediction or classification decision. An increasingly provoking question is whether such systems can outperform the single best classifier. If so, what form of an ensemble of classifiers (also known as multiple classifier learning systems or multiple classifiers) yields the most significant benefits in the size or diversity of the ensemble itself? Given that the tests used to detect autism traits are time-consuming and costly, developing a system that will provide the best outcome and measurement of autism spectrum disorder (ASD) has never been critical. In this paper, several single and later multiple classifiers learning systems are evaluated in terms of their ability to predict and identify factors that influence or contribute to ASD for early screening purposes. A dataset of behavioural data and robot-enhanced therapy of 3,000 sessions and 300 hours, recorded from 61 children are utilised for this task. Simulation results show the superior predictive performance of multiple classifier learning systems (especially those with three classifiers per ensemble) compared to individual classifiers, with bagging and boosting achieving excellent results. It also appears that social communication gestures remain the critical contributing factor to the ASD problem among children.

Unsupervised image transfer enables intra- and inter-modality image translation in applications where a large amount of paired training data is not abundant. To ensure a structure-preserving mapping from the input to the target domain, existing methods for unpaired image transfer are commonly based on cycle-consistency, causing additional computational resources and instability due to the learning of an inverse mapping. This paper presents a novel method for uni-directional domain mapping that does not rely on any paired training data. A proper transfer is achieved by using a GAN architecture and a novel generator loss based on patch invariance. To be more specific, the generator outputs are evaluated and compared at different scales, also leading to an increased focus on high-frequency details as well as an implicit data augmentation. This novel patch loss also offers the possibility to accurately predict aleatoric uncertainty by modeling an input-dependent scale map for the patch residuals. The proposed method is comprehensively evaluated on three well-established medical databases. As compared to four state-of-the-art methods, we observe significantly higher accuracy on these datasets, indicating great potential of the proposed method for unpaired image transfer with uncertainty taken into account. Implementation of the proposed framework is released here: \url{https://github.com/anger-man/unsupervised-image-transfer-and-uq}.

In layman's terms, machine learning is to allow computers to learn automatically from data to obtain certain knowledge. As a discipline, machine learning usually refers to a type of problem and the method to solve this type of problem, that is, how to find the law from the observation data, and use the learned law to predict the unknown or unobservable data. In the early engineering field, machine learning is often called pattern recognition, but pattern recognition is more biased towards specific application tasks, such as optical character recognition, speech recognition, and face recognition. The characteristic of these tasks is that for us humans, these tasks are easy to complete, but we do not know how we do it, so it is difficult to manually design a computer program to complete these tasks. A feasible method is to design an algorithm that allows the computer to learn the rules from the labeled samples and use it to complete various recognition tasks. With the increasing application of machine learning technology, the concept of machine learning is now gradually replacing pattern recognition, becoming the general term for this type of problem and its solutions. Taking handwritten digit recognition as an example, we need to allow the computer to automatically recognize handwritten digits. Handwritten digit recognition is a classic machine learning task, which is simple for humans, but very difficult for computers. It is difficult for us to summarize the handwriting characteristics of each digit, or the rules for distinguishing different digits, so designing a set of recognition algorithms is an almost impossible task. In real life, many problems are similar to those of handwritten number recognition, such as object recognition and speech recognition. For this kind of problem, we don't know how to design a computer program to solve it. Even if it can be realized by some heuristic rules, the process is extremely complicated. Therefore, people began to try another way of thinking, that is, let the computer see a large number of samples, and learn some experience from them, and then use these experiences to identify new samples. To recognize handwritten digits, first manually annotate a large number of handwritten digital images (that is, each image is manually marked with what number it is), these images are used as training data, and then a set of models are automatically generated through the learning algorithm, and rely on it. This method of learning through data is called the method of machine learning. First, we use a life example to introduce some basic concepts in machine learning: samples, features, labels, models, learning algorithms, etc. Suppose we want to buy mangoes in the market, but we have no previous experience in selecting mangoes, how can we obtain this knowledge through learning? First, we randomly select some mangoes from the market and list the characteristics of each mango.

Structural causal models (SCMs) provide a principled approach to identifying causation from observational and experimental data in disciplines ranging from economics to medicine. However, SCMs, which is typically represented as graphical models, cannot rely only on data, rather require support of domain knowledge. A key challenge in this context is the absence of a methodological framework for encoding priors (background knowledge) into causal models in a systematic manner. We propose an abstraction called causal knowledge hierarchy (CKH) for encoding priors into causal models. Our approach is based on the foundation of "levels of evidence" in medicine, with a focus on confidence in causal information. Using CKH, we present a methodological framework for encoding causal priors from various information sources and combining them to derive an SCM. We evaluate our approach on a simulated dataset and demonstrate overall performance compared to the ground truth causal model with sensitivity analysis.