The challenging task of learning structures of probabilistic graphical models is an important problem within modern AI research. Recent years have witnessed several major algorithmic advances in structure learning for Bayesian networks---arguably the most central class of graphical models---especially in what is known as the score-based setting. A successful generic approach to optimal Bayesian network structure learning (BNSL), based on integer programming (IP), is implemented in the GOBNILP system. Despite the recent algorithmic advances, current understanding of foundational aspects underlying the IP based approach to BNSL is still somewhat lacking. Understanding fundamental aspects of cutting planes and the related separation problem( is important not only from a purely theoretical perspective, but also since it holds out the promise of further improving the efficiency of state-of-the-art approaches to solving BNSL exactly. In this paper, we make several theoretical contributions towards these goals: (i) we study the computational complexity of the separation problem, proving that the problem is NP-hard; (ii) we formalise and analyse the relationship between three key polytopes underlying the IP-based approach to BNSL; (iii) we study the facets of the three polytopes both from the theoretical and practical perspective, providing, via exhaustive computation, a complete enumeration of facets for low-dimensional family-variable polytopes; and, furthermore, (iv) we establish a tight connection of the BNSL problem to the acyclic subgraph problem.

What is normal for a machine (or the System under observation) is environment-dependent and ever-changing in real life!

Finding meaning in increasingly larger and more complex datasets is a growing demand of the modern world. Machine learning and predictive analytics have become the most important approaches to uncover data gold mines. Machine learning uses complex algorithms to make improved predictions of outcomes based on historical patterns and the behaviour of data sets. Machine learning can deliver dynamic insights into trends, patterns, and relationships within data, immensely valuable to business growth and development. This book explores an extensive range of machine learning techniques uncovering hidden tricks and tips for several types of data using practical and real-world examples.

In this work, we study the use of logistic regression in manufacturing failures detection. As a data set for the analysis, we used the data from Kaggle competition Bosch Production Line Performance. We considered the use of machine learning, linear and Bayesian models. For machine learning approach, we analyzed XGBoost tree based classifier to obtain high scored classification. Using the generalized linear model for logistic regression makes it possible to analyze the influence of the factors under study. The Bayesian approach for logistic regression gives the statistical distribution for the parameters of the model. It can be useful in the probabilistic analysis, e.g. risk assessment.

Many people have found the table above to be useful for understanding two conceptual distinctions in the practice of data analysis. The article that discusses the table, and many other issues, is now in press. The in-press version can be found at OSF and at SSRN. Abstract: In the practice of data analysis, there is a conceptual distinction between hypothesis testing, on the one hand, and estimation with quantified uncertainty, on the other hand. Among frequentists in psychology a shift of emphasis from hypothesis testing to estimation has been dubbed "the New Statistics" (Cumming, 2014).

Directed graphs occur throughout statistical modeling of networks, and exchangeability is a natural assumption when the ordering of vertices does not matter. There is a deep structural theory for exchangeable undirected graphs, which extends to the directed case via measurable objects known as digraphons. Using digraphons, we first show how to construct models for exchangeable directed graphs, including special cases such as tournaments, linear orderings, directed acyclic graphs, and partial orderings. We then show how to construct priors on digraphons via the infinite relational digraphon model (di-IRM), a new Bayesian nonparametric block model for exchangeable directed graphs, and demonstrate inference on synthetic data.

The dataset used for training the model consists of public tweets which are already labelled -- positive or negative. There are lots of npm package that implement the Naive Bayes algorithm out there and most of them are very similar in the way they implement Bayes theorem. Some packages are a bundle of NLP algorithms. The package used in the demo is this. After initializing the bayes classifier in your node application, it is very easy to train the model and use it for real world applications.

Since 2006, deep learning (DL) has become a rapidly growing research direction, redefining state-of-the-art performances in a wide range of areas such as object recognition, image segmentation, speech recognition and machine translation. In modern manufacturing systems, data-driven machine health monitoring is gaining in popularity due to the widespread deployment of low-cost sensors and their connection to the Internet. Meanwhile, deep learning provides useful tools for processing and analyzing these big machinery data. The main purpose of this paper is to review and summarize the emerging research work of deep learning on machine health monitoring. After the brief introduction of deep learning techniques, the applications of deep learning in machine health monitoring systems are reviewed mainly from the following aspects: Auto-encoder (AE) and its variants, Restricted Boltzmann Machines and its variants including Deep Belief Network (DBN) and Deep Boltzmann Machines (DBM), Convolutional Neural Networks (CNN) and Recurrent Neural Networks (RNN). Finally, some new trends of DL-based machine health monitoring methods are discussed.

It emphasizes flexibility through the elegant use of object-oriented design patterns.

Many data-driven approaches exist to extract neural representations of functional magnetic resonance imaging (fMRI) data, but most of them lack a proper probabilistic formulation. We propose a group level scalable probabilistic sparse factor analysis (psFA) allowing spatially sparse maps, component pruning using automatic relevance determination (ARD) and subject specific heteroscedastic spatial noise modeling. For task-based and resting state fMRI, we show that the sparsity constraint gives rise to components similar to those obtained by group independent component analysis. The noise modeling shows that noise is reduced in areas typically associated with activation by the experimental design. The psFA model identifies sparse components and the probabilistic setting provides a natural way to handle parameter uncertainties. The variational Bayesian framework easily extends to more complex noise models than the presently considered.