Fourth chapter: Using a Naive-Bayes approach we construct a simple spam email filter.

Artificial Intelligence is one of the fastest growing technologies of the 21st century and accompanies us in our daily lives when interacting with technical applications. However, reliance on such technical systems is crucial for their widespread applicability and acceptance. The societal tools to express reliance are usually formalized by lawful regulations, i.e., standards, norms, accreditations, and certificates. Therefore, the T\"UV AUSTRIA Group in cooperation with the Institute for Machine Learning at the Johannes Kepler University Linz, proposes a certification process and an audit catalog for Machine Learning applications. We are convinced that our approach can serve as the foundation for the certification of applications that use Machine Learning and Deep Learning, the techniques that drive the current revolution in Artificial Intelligence. While certain high-risk areas, such as fully autonomous robots in workspaces shared with humans, are still some time away from certification, we aim to cover low-risk applications with our certification procedure. Our holistic approach attempts to analyze Machine Learning applications from multiple perspectives to evaluate and verify the aspects of secure software development, functional requirements, data quality, data protection, and ethics. Inspired by existing work, we introduce four criticality levels to map the criticality of a Machine Learning application regarding the impact of its decisions on people, environment, and organizations. Currently, the audit catalog can be applied to low-risk applications within the scope of supervised learning as commonly encountered in industry. Guided by field experience, scientific developments, and market demands, the audit catalog will be extended and modified accordingly.

This paper surveys state-of-the-art methods and models dedicated to time series analysis and modeling, with the final aim of prediction. This review aims to offer a structured and comprehensive view of the full process flow, and encompasses time series decomposition, stationary tests, modeling and forecasting. Besides, to meet didactic purposes, a unified presentation has been adopted throughout this survey, to present decomposition frameworks on the one hand and linear and nonlinear time series models on the other hand. First, we decrypt the relationships between stationarity and linearity, and further examine the main classes of methods used to test for weak stationarity. Next, the main frameworks for time series decomposition are presented in a unified way: depending on the time series, a more or less complex decomposition scheme seeks to obtain nonstationary effects (the deterministic components) and a remaining stochastic component. An appropriate modeling of the latter is a critical step to guarantee prediction accuracy. We then present three popular linear models, together with two more flexible variants of the latter. A step further in model complexity, and still in a unified way, we present five major nonlinear models used for time series. Amongst nonlinear models, artificial neural networks hold a place apart as deep learning has recently gained considerable attention. A whole section is therefore dedicated to time series forecasting relying on deep learning approaches. A final section provides a list of R and Python implementations for the methods, models and tests presented throughout this review. In this document, our intention is to bring sufficient in-depth knowledge, while covering a broad range of models and forecasting methods: this compilation spans from well-established conventional approaches to more recent adaptations of deep learning to time series forecasting.

Cluster assignment of large and complex images is a crucial but challenging task in pattern recognition and computer vision. In this study, we explore the possibility of employing fuzzy clustering in a deep neural network framework. Thus, we present a novel evolutionary unsupervised learning representation model with iterative optimization. It implements the deep adaptive fuzzy clustering (DAFC) strategy that learns a convolutional neural network classifier from given only unlabeled data samples. DAFC consists of a deep feature quality-verifying model and a fuzzy clustering model, where deep feature representation learning loss function and embedded fuzzy clustering with the weighted adaptive entropy is implemented. We joint fuzzy clustering to the deep reconstruction model, in which fuzzy membership is utilized to represent a clear structure of deep cluster assignments and jointly optimize for the deep representation learning and clustering. Also, the joint model evaluates current clustering performance by inspecting whether the re-sampled data from estimated bottleneck space have consistent clustering properties to progressively improve the deep clustering model. Comprehensive experiments on a variety of datasets show that the proposed method obtains a substantially better performance for both reconstruction and clustering quality when compared to the other state-of-the-art deep clustering methods, as demonstrated with the in-depth analysis in the extensive experiments.

These subprocesses are interrelated, with mapping considered to be the pivotal process (Gentner, 1983). Mapping may play a role in retrieval, as mapping a target analog to multiple potential source analogs stored in memory can help identify one or more that seems promising; and the correspondences computed by mapping support subsequent inference and schema induction. Thus, because of its centrality to analogical reasoning, the present paper focuses on the process of mapping between two analogs. We also consider the possible role that mapping may play in analog retrieval. Computational Approaches to Analogy Computational models of analogy have been developed in both artificial intelligence (AI) and cognitive science over more than half a century (for a recent review and critical analysis, see Mitchell, 2021). These models differ in many ways, both in terms of basic assumptions about the constraints that define a "good" analogy for humans, and in the detailed algorithms that accomplish analogical reasoning. For our present purposes, two broad approaches can be distinguished. The first approach, which can be termed representation matching, combines mental representations of structured knowledge about each analog with a matching process that computes some form of relational similarity, yielding a set of correspondences between the elements of the two analogs. The structured knowledge about an analog is typically assumed to approximate the content of propositions expressed in predicate calculus; e.g., the instantiated relation "hammer hits nail" might be coded as hit (hammer, nail).

Recently, there are unprecedented data growth originating from different online platforms which contribute to big data in terms of volume, velocity, variety and veracity (4Vs). Given this nature of big data which is unstructured, performing analytics to extract meaningful information is currently a great challenge to big data analytics. Collecting and analyzing unstructured textual data allows decision makers to study the escalation of comments/posts on our social media platforms. Hence, there is need for automatic big data analysis to overcome the noise and the non-reliability of these unstructured dataset from the digital media platforms. However, current machine learning algorithms used are performance driven focusing on the classification/prediction accuracy based on known properties learned from the training samples. With the learning task in a large dataset, most machine learning models are known to require high computational cost which eventually leads to computational complexity. In this work, two supervised machine learning algorithms are combined with text mining techniques to produce a hybrid model which consists of Na\"ive Bayes and support vector machines (SVM). This is to increase the efficiency and accuracy of the results obtained and also to reduce the computational cost and complexity. The system also provides an open platform where a group of persons with a common interest can share their comments/messages and these comments classified automatically as legal or illegal. This improves the quality of conversation among users. The hybrid model was developed using WEKA tools and Java programming language. The result shows that the hybrid model gave 96.76% accuracy as against the 61.45% and 69.21% of the Na\"ive Bayes and SVM models respectively.

How to estimate heterogeneity, e.g. the effect of some variable differing across observations, is a key question in political science. Methods for doing so make simplifying assumptions about the underlying nature of the heterogeneity to draw reliable inferences. This paper allows a common way of simplifying complex phenomenon (placing observations with similar effects into discrete groups) to be integrated into regression analysis. The framework allows researchers to (i) use their prior knowledge to guide which groups are permissible and (ii) appropriately quantify uncertainty. The paper does this by extending work on "structured sparsity" from a traditional penalized likelihood approach to a Bayesian one by deriving new theoretical results and inferential techniques. It shows that this method outperforms state-of-the-art methods for estimating heterogeneous effects when the underlying heterogeneity is grouped and more effectively identifies groups of observations with different effects in observational data.

We study the type of distributions that Restricted Boltzmann Machines (RBMs) with different activation functions can express by investigating the effect of the activation function of the hidden nodes on the marginal distribution they impose on observed binary nodes. We report an exact expression for these marginals in the form of a model of interacting binary variables with the explicit form of the interactions depending on the hidden node activation function. We study the properties of these interactions in detail and evaluate how the accuracy with which the RBM approximates distributions over binary variables depends on the hidden node activation function and on the number of hidden nodes. When the inferred RBM parameters are weak, an intuitive pattern is found for the expression of the interaction terms which reduces substantially the differences across activation functions. We show that the weak parameter approximation is a good approximation for different RBMs trained on the MNIST dataset. Interestingly, in these cases, the mapping reveals that the inferred models are essentially low order interaction models.

The potential of digital twin technology is immense, specifically in the infrastructure, aerospace, and automotive sector. However, practical implementation of this technology is not at an expected speed, specifically because of lack of application-specific details. In this paper, we propose a novel digital twin framework for stochastic nonlinear multi-degree of freedom (MDOF) dynamical systems. The approach proposed in this paper strategically decouples the problem into two time-scales -- (a) a fast time-scale governing the system dynamics and (b) a slow time-scale governing the degradation in the system. The proposed digital twin has four components - (a) a physics-based nominal model (low-fidelity), (b) a Bayesian filtering algorithm a (c) a supervised machine learning algorithm and (d) a high-fidelity model for predicting future responses. The physics-based nominal model combined with Bayesian filtering is used combined parameter state estimation and the supervised machine learning algorithm is used for learning the temporal evolution of the parameters. While the proposed framework can be used with any choice of Bayesian filtering and machine learning algorithm, we propose to use unscented Kalman filter and Gaussian process. Performance of the proposed approach is illustrated using two examples. Results obtained indicate the applicability and excellent performance of the proposed digital twin framework.

We develop a formalism for constructing stochastic upper bounds on the expected full sample risk for supervised classification tasks via the Hilbert coresets approach within a transductive framework. We explicitly compute tight and meaningful bounds for complex datasets and complex hypothesis classes such as state-of-the-art deep neural network architectures. The bounds we develop exhibit nice properties: i) the bounds are non-uniform in the hypothesis space H, ii) in many practical examples, the bounds become effectively deterministic by appropriate choice of prior and training data-dependent posterior distributions on the hypothesis space, and iii) the bounds become significantly better with increase in the size of the training set. We also lay out some ideas to explore for future research. Generalization bounds for learning provide a theoretical guarantee on the performance of a learning algorithm on unseen data. The goal of such bounds is to provide control of the error on unseen data with pre-specified confidence. In certain situations, such bounds may also help in designing new learning algorithms.