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.

We present plingo, an extension of the ASP system clingo with various probabilistic reasoning modes. Plingo is centered upon LP^MLN, a probabilistic extension of ASP based on a weight scheme from Markov Logic. This choice is motivated by the fact that the core probabilistic reasoning modes can be mapped onto optimization problems and that LP^MLN may serve as a middle-ground formalism connecting to other probabilistic approaches. As a result, plingo offers three alternative frontends, for LP^MLN, P-log, and ProbLog. The corresponding input languages and reasoning modes are implemented by means of clingo's multi-shot and theory solving capabilities. The core of plingo amounts to a re-implementation of LP^MLN in terms of modern ASP technology, extended by an approximation technique based on a new method for answer set enumeration in the order of optimality. We evaluate plingo's performance empirically by comparing it to other probabilistic systems.

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.

Recent work has shown logical background knowledge can be used in learning systems to compensate for a lack of labeled training data. Many methods work by creating a loss function that encodes this knowledge. However, often the logic is discarded after training, even if it is still useful at test time. Instead, we ensure neural network predictions satisfy the knowledge by refining the predictions with an extra computation step. We introduce differentiable refinement functions that find a corrected prediction close to the original prediction. We study how to effectively and efficiently compute these refinement functions. Using a new algorithm called Iterative Local Refinement (ILR), we combine refinement functions to find refined predictions for logical formulas of any complexity. ILR finds refinements on complex SAT formulas in significantly fewer iterations and frequently finds solutions where gradient descent can not. Finally, ILR produces competitive results in the MNIST addition task.

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.

Stochastic planning can be reduced to probabilistic inference in large discrete graphical models, but hardness of inference requires approximation schemes to be used. In this paper we argue that such applications can be disentangled along two dimensions. The first is the direction of information flow in the idealized exact optimization objective, i.e., forward vs backward inference. The second is the type of approximation used to compute this objective, e.g., Belief Propagation (BP) vs mean field variational inference (MFVI). This new categorization allows us to unify a large amount of isolated efforts in prior work explaining their connections and differences as well as potential improvements. An extensive experimental evaluation over large stochastic planning problems shows the advantage of forward BP over several algorithms based on MFVI. An analysis of practical limitations of MFVI motivates a novel algorithm, collapsed state variational inference (CSVI), which provides a tighter approximation and achieves comparable planning performance with forward BP.

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.

Why is ordinary language vague? We argue that in contexts in which a cooperative speaker is not perfectly informed about the world, the use of vague expressions can offer an optimal tradeoff between truthfulness (Gricean Quality) and informativeness (Gricean Quantity). Focusing on expressions of approximation such as "around", which are semantically vague, we show that they allow the speaker to convey indirect probabilistic information, in a way that can give the listener a more accurate representation of the information available to the speaker than any more precise expression would (intervals of the form "between"). That is, vague sentences can be more informative than their precise counterparts. We give a probabilistic treatment of the interpretation of "around", and offer a model for the interpretation and use of "around"-statements within the Rational Speech Act (RSA) framework. In our account the shape of the speaker's distribution matters in ways not predicted by the Lexical Uncertainty model standardly used in the RSA framework for vague predicates. We use our approach to draw further lessons concerning the semantic flexibility of vague expressions and their irreducibility to more precise meanings.

We are assisting at a growing interest in the development of learning architectures with application to digital communication systems. Herein, we consider the detection/decoding problem. We aim at developing an optimal neural architecture for such a task. The definition of the optimal criterion is a fundamental step. We propose to use the mutual information (MI) of the channel input-output signal pair, which yields to the minimization of the a-posteriori information of the transmitted codeword given the communication channel output observation. The computation of the a-posteriori information is a formidable task, and for the majority of channels it is unknown. Therefore, it has to be learned. For such an objective, we propose a novel neural estimator based on a discriminative formulation. This leads to the derivation of the mutual information neural decoder (MIND). The developed neural architecture is capable not only to solve the decoding problem in unknown channels, but also to return an estimate of the average MI achieved with the coding scheme, as well as the decoding error probability. Several numerical results are reported and compared with maximum a-posteriori and maximum likelihood decoding strategies.