To make advanced learning machines such as Deep Neural Networks (DNNs) more transparent in decision making, explainable AI (XAI) aims to provide interpretations of DNNs' predictions. These interpretations are usually given in the form of heatmaps, each one illustrating relevant patterns regarding the prediction for a given instance. Bayesian approaches such as Bayesian Neural Networks (BNNs) so far have a limited form of transparency (model transparency) already built-in through their prior weight distribution, but notably, they lack explanations of their predictions for given instances. In this work, we bring together these two perspectives of transparency into a holistic explanation framework for explaining BNNs. Within the Bayesian framework, the network weights follow a probability distribution. Hence, the standard (deterministic) prediction strategy of DNNs extends in BNNs to a predictive distribution, and thus the standard explanation extends to an explanation distribution. Exploiting this view, we uncover that BNNs implicitly employ multiple heterogeneous prediction strategies. While some of these are inherited from standard DNNs, others are revealed to us by considering the inherent uncertainty in BNNs. Our quantitative and qualitative experiments on toy/benchmark data and real-world data from pathology show that the proposed approach of explaining BNNs can lead to more effective and insightful explanations.

The novel coronavirus disease 2019 (COVID-19) presents unique and unknown problem complexities and modeling challenges, where an imperative task is to model both its process and data uncertainties, represented in implicit and high-proportional undocumented infections, asymptomatic contagion, social reinforcement of infections, and various quality issues in the reported data. These uncertainties become even more phenomenal in the overwhelming mutation-dominated resurgences with vaccinated but still susceptible populations. Here we introduce a novel hybrid approach to (1) characterizing and distinguishing Undocumented (U) and Documented (D) infections commonly seen during COVID-19 incubation periods and asymptomatic infections by expanding the foundational compartmental epidemic Susceptible-Infected-Recovered (SIR) model with two compartments, resulting in a new Susceptible-Undocumented infected-Documented infected-Recovered (SUDR) model; (2) characterizing the probabilistic density of infections by empowering SUDR to capture exogenous processes like clustering contagion interactions, superspreading and social reinforcement; and (3) approximating the density likelihood of COVID-19 prevalence over time by incorporating Bayesian inference into SUDR. Different from existing COVID-19 models, SUDR characterizes the undocumented infections during unknown transmission processes. To capture the uncertainties of temporal transmission and social reinforcement during the COVID-19 contagion, the transmission rate is modeled by a time-varying density function of undocumented infectious cases. We solve the modeling by sampling from the mean-field posterior distribution with reasonable priors, making SUDR suitable to handle the randomness, noise and sparsity of COVID-19 observations widely seen in the public COVID-19 case data.

As the world is rapidly moving towards digitization and money transactions are becoming cashless, the use of credit cards has rapidly increased. The fraud activities associated with it have also been increasing which leads to a huge loss to the financial institutions. Therefore, we need to analyze and detect the fraudulent transaction from the non-fraudulent ones. In this paper, we present a comprehensive review of various methods used to detect credit card fraud. These methodologies include Hidden Markov Model, Decision Trees, Logistic Regression, Support Vector Machines (SVM), Genetic algorithm, Neural Networks, Random Forests, Bayesian Belief Network. A comprehensive analysis of various techniques is presented. We conclude the paper with the pros and cons of the same as stated in the respective papers.

Conditional Neural Processes (CNP; Garnelo et al., 2018) are an attractive family of meta-learning models which produce well-calibrated predictions, enable fast inference at test time, and are trainable via a simple maximum likelihood procedure. A limitation of CNPs is their inability to model dependencies in the outputs. This significantly hurts predictive performance and renders it impossible to draw coherent function samples, which limits the applicability of CNPs in down-stream applications and decision making. NeuralProcesses (NPs; Garnelo et al., 2018) attempt to alleviate this issue by using latent variables, rely-ing on these to model output dependencies, but introduces difficulties stemming from approximate inference. One recent alternative (Bruinsma et al.,2021), which we refer to as the FullConvGNP, models dependencies in the predictions while still being trainable via exact maximum-likelihood.Unfortunately, the FullConvGNP relies on expensive 2D-dimensional convolutions, which limit its applicability to only one-dimensional data.In this work, we present an alternative way to model output dependencies which also lends it-self maximum likelihood training but, unlike the FullConvGNP, can be scaled to two- and three-dimensional data. The proposed models exhibit good performance in synthetic experiments

This paper addresses the problem of learning a sparse structure Bayesian network from high-dimensional discrete data. Compared to continuous Bayesian networks, learning a discrete Bayesian network is a challenging problem due to the large parameter space. Although many approaches have been developed for learning continuous Bayesian networks, few approaches have been proposed for the discrete ones. In this paper, we address learning Bayesian networks as an optimization problem and propose a score function that satisfies the sparsity and the DAG property simultaneously. Besides, we implement a block-wised stochastic coordinate descent algorithm to optimize the score function. Specifically, we use a variance reducing method in our optimization algorithm to make the algorithm work efficiently in high-dimensional data. The proposed approach is applied to synthetic data from well-known benchmark networks. The quality, scalability, and robustness of the constructed network are measured. Compared to some competitive approaches, the results reveal that our algorithm outperforms the others in evaluation metrics.

The ubiquitous availability of computing devices and the widespread use of the internet have generated a large amount of data continuously. Therefore, the amount of available information on any given topic is far beyond humans' processing capacity to properly process, causing what is known as information overload. To efficiently cope with large amounts of information and generate content with significant value to users, we require identifying, merging and summarising information. Data summaries can help gather related information and collect it into a shorter format that enables answering complicated questions, gaining new insight and discovering conceptual boundaries. This thesis focuses on three main challenges to alleviate information overload using novel summarisation techniques. It further intends to facilitate the analysis of documents to support personalised information extraction. This thesis separates the research issues into four areas, covering (i) feature engineering in document summarisation, (ii) traditional static and inflexible summaries, (iii) traditional generic summarisation approaches, and (iv) the need for reference summaries. We propose novel approaches to tackle these challenges, by: i)enabling automatic intelligent feature engineering, ii) enabling flexible and interactive summarisation, iii) utilising intelligent and personalised summarisation approaches. The experimental results prove the efficiency of the proposed approaches compared to other state-of-the-art models. We further propose solutions to the information overload problem in different domains through summarisation, covering network traffic data, health data and business process data.

Clustering has become a core technology in machine learning, largely due to its application in the field of unsupervised learning, clustering, classification, and density estimation. A frequentist approach exists to hand clustering based on mixture model which is known as the EM algorithm where the parameters of the mixture model are usually estimated into a maximum likelihood estimation framework. Bayesian approach for finite and infinite Gaussian mixture model generates point estimates for all variables as well as associated uncertainty in the form of the whole estimates' posterior distribution. The sole aim of this survey is to give a self-contained introduction to concepts and mathematical tools in Bayesian inference for finite and infinite Gaussian mixture model in order to seamlessly introduce their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning this field and given the paucity of scope to present this discussion, e.g., the separated analysis of the generation of Dirichlet samples by stick-breaking and Polya's Urn approaches. We refer the reader to literature in the field of the Dirichlet process mixture model for a much detailed introduction to the related fields. Some excellent examples include (Frigyik et al., 2010; Murphy, 2012; Gelman et al., 2014; Hoff, 2009). This survey is primarily a summary of purpose, significance of important background and techniques for Gaussian mixture model, e.g., Dirichlet prior, Chinese restaurant process, and most importantly the origin and complexity of the methods which shed light on their modern applications. The mathematical prerequisite is a first course in probability. Other than this modest background, the development is self-contained, with rigorous proofs provided throughout.

Let us talk about Bayesian Network. Bayesian Network is a probablistic model represent a set of random variables and their conditional dependencies. This model can be represented using DAG (Directed Acrylic Graph) where nodes can be observable quantities, latent variables (not observable, inferred only) and not known parameters or hypothesis. DAG can help to understand the model in a easy manner. Edges in DAG represents conditional dependencies between nodes.

We introduce a novel geometry-informed irreversible perturbation that accelerates convergence of the Langevin algorithm for Bayesian computation. It is well documented that there exist perturbations to the Langevin dynamics that preserve its invariant measure while accelerating its convergence. Irreversible perturbations and reversible perturbations (such as Riemannian manifold Langevin dynamics (RMLD)) have separately been shown to improve the performance of Langevin samplers. We consider these two perturbations simultaneously by presenting a novel form of irreversible perturbation for RMLD that is informed by the underlying geometry. Through numerical examples, we show that this new irreversible perturbation can improve performance of the estimator over reversible perturbations that do not take the geometry into account. Moreover we demonstrate that irreversible perturbations generally can be implemented in conjunction with the stochastic gradient version of the Langevin algorithm. Lastly, while continuous-time irreversible perturbations cannot impair the performance of a Langevin estimator, the situation can sometimes be more complicated when discretization is considered. To this end, we describe a discrete-time example in which irreversibility increases both the bias and variance of the resulting estimator.

Most data is automatically collected and only ever "seen" by algorithms. Yet, data compressors preserve perceptual fidelity rather than just the information needed by algorithms performing downstream tasks. In this paper, we characterize the bit-rate required to ensure high performance on all predictive tasks that are invariant under a set of transformations, such as data augmentations. Based on our theory, we design unsupervised objectives for training neural compressors. Using these objectives, we train a generic image compressor that achieves substantial rate savings (more than $1000\times$ on ImageNet) compared to JPEG on 8 datasets, without decreasing downstream classification performance.