Score-based algorithms that learn Bayesian Network (BN) structures provide solutions ranging from different levels of approximate learning to exact learning. Approximate solutions exist because exact learning is generally not applicable to networks of moderate or higher complexity. In general, approximate solutions tend to sacrifice accuracy for speed, where the aim is to minimise the loss in accuracy and maximise the gain in speed. While some approximate algorithms are optimised to handle thousands of variables, these algorithms may still be unable to learn such high dimensional structures. Some of the most efficient score-based algorithms cast the structure learning problem as a combinatorial optimisation of candidate parent sets. This paper explores a strategy towards pruning the size of candidate parent sets, aimed at high dimensionality problems. The results illustrate how different levels of pruning affect the learning speed relative to the loss in accuracy in terms of model fitting, and show that aggressive pruning may be required to produce approximate solutions for high complexity problems.

Bayesian Network, also known as Bayes network is a probabilistic directed acyclic graphical model, which can be used for time series prediction, anomaly detection, diagnostics and more. In machine learning, the Bayesian inference is known for its robust set of tools for modelling any random variable, including the business performance indicators, the value of a regression parameter, among others. This method is also known as one of the best approaches to modelling uncertainty. In this article, we list down the top eight open-source tools for Bayesian Networks. Bayesian inference Using Gibbs Sampling or BUGS is a software package for the Bayesian analysis of statistical models by utilising the Markov chain Monte Carlo techniques.

"Critical thinking is an active and ongoing process. It requires that we all think like Bayesians, updating our knowledge as new information comes in." ― Daniel J. Levitin, A Field Guide to Lies: Critical Thinking in the Information Age Before we delve into the intuition behind using the Bayesian approach of estimation, we need to understand a few concepts. Inferential statistics is when you infer something about a whole population based on a sample of that population, as opposed to descriptive statistics which describes something about the whole population. When it comes to inferential statistics, there are two main philosophies: frequentist inference and Bayesian inference. The frequentist approach is known to be the more traditional approach to statistical inference, and thus studied more in most statistics courses (especially introductory courses). However, many would argue that the Bayesian approach is much closer to the way humans naturally perceive probability.

Civil and maritime engineering systems, among others, from bridges to offshore platforms and wind turbines, must be efficiently managed as they are exposed to deterioration mechanisms throughout their operational life, such as fatigue or corrosion. Identifying optimal inspection and maintenance policies demands the solution of a complex sequential decision-making problem under uncertainty, with the main objective of efficiently controlling the risk associated with structural failures. Addressing this complexity, risk-based inspection planning methodologies, supported often by dynamic Bayesian networks, evaluate a set of pre-defined heuristic decision rules to reasonably simplify the decision problem. However, the resulting policies may be compromised by the limited space considered in the definition of the decision rules. Avoiding this limitation, Partially Observable Markov Decision Processes (POMDPs) provide a principled mathematical methodology for stochastic optimal control under uncertain action outcomes and observations, in which the optimal actions are prescribed as a function of the entire, dynamically updated, state probability distribution. In this paper, we combine dynamic Bayesian networks with POMDPs in a joint framework for optimal inspection and maintenance planning, and we provide the formulation for developing both infinite and finite horizon POMDPs in a structural reliability context. The proposed methodology is implemented and tested for the case of a structural component subject to fatigue deterioration, demonstrating the capability of state-of-the-art point-based POMDP solvers for solving the underlying planning optimization problem. Within the numerical experiments, POMDP and heuristic-based policies are thoroughly compared, and results showcase that POMDPs achieve substantially lower costs as compared to their counterparts, even for traditional problem settings.

We present a general approach to deriving bounds on the generalization error of randomized learning algorithms. Our approach can be used to obtain bounds on the average generalization error as well as bounds on its tail probabilities, both for the case in which a new hypothesis is randomly generated every time the algorithm is used - as often assumed in the probably approximately correct (PAC)-Bayesian literature - and in the single-draw case, where the hypothesis is extracted only once. For this last scenario, we present a novel bound that is explicit in the central moments of the information density. The bound reveals that the higher the order of the information density moment that can be controlled, the milder the dependence of the generalization bound on the desired confidence level. Furthermore, we use tools from binary hypothesis testing to derive a second bound, which is explicit in the tail of the information density. This bound confirms that a fast decay of the tail of the information density yields a more favorable dependence of the generalization bound on the confidence level.

We consider a regret minimization task under the average-reward criterion in an unknown Factored Markov Decision Process (FMDP). More specifically, we consider an FMDP where the state-action space $\mathcal X$ and the state-space $\mathcal S$ admit the respective factored forms of $\mathcal X = \otimes_{i=1}^n \mathcal X_i$ and $\mathcal S=\otimes_{i=1}^m \mathcal S_i$, and the transition and reward functions are factored over $\mathcal X$ and $\mathcal S$. Assuming known factorization structure, we introduce a novel regret minimization strategy inspired by the popular UCRL2 strategy, called DBN-UCRL, which relies on Bernstein-type confidence sets defined for individual elements of the transition function. We show that for a generic factorization structure, DBN-UCRL achieves a regret bound, whose leading term strictly improves over existing regret bounds in terms of the dependencies on the size of $\mathcal S_i$'s and the involved diameter-related terms. We further show that when the factorization structure corresponds to the Cartesian product of some base MDPs, the regret of DBN-UCRL is upper bounded by the sum of regret of the base MDPs. We demonstrate, through numerical experiments on standard environments, that DBN-UCRL enjoys a substantially improved regret empirically over existing algorithms.

Online customer reviews have become important for managers and executives in the hospitality and catering industry who wish to obtain a comprehensive understanding of their customers' demands and expectations. We propose a Regularized Text Logistic (RTL) regression model to perform text analytics and sentiment classification on unstructured text data, which automatically identifies a set of statistically significant and operationally insightful word features, and achieves satisfactory predictive classification accuracy. We apply the RTL model to two online review datasets, Restaurant and Hotel, from TripAdvisor. Our results demonstrate satisfactory classification performance compared with alternative classifiers with a highest true positive rate of 94.9%. Moreover, RTL identifies a small set of word features, corresponding to 3% for Restaurant and 20% for Hotel, which boosts working efficiency by allowing managers to drill down into a much smaller set of important customer reviews. We also develop the consistency, sparsity and oracle property of the estimator.

Replica exchange Monte Carlo (reMC), also known as parallel tempering, is an important technique for accelerating the convergence of the conventional Markov Chain Monte Carlo (MCMC) algorithms. However, such a method requires the evaluation of the energy function based on the full dataset and is not scalable to big data. The na\"ive implementation of reMC in mini-batch settings introduces large biases, which cannot be directly extended to the stochastic gradient MCMC (SGMCMC), the standard sampling method for simulating from deep neural networks (DNNs). In this paper, we propose an adaptive replica exchange SGMCMC (reSGMCMC) to automatically correct the bias and study the corresponding properties. The analysis implies an acceleration-accuracy trade-off in the numerical discretization of a Markov jump process in a stochastic environment. Empirically, we test the algorithm through extensive experiments on various setups and obtain the state-of-the-art results on CIFAR10, CIFAR100, and SVHN in both supervised learning and semi-supervised learning tasks.

Abstract--In this paper, several Collaborative Filtering (CF) approaches with latent variable methods were studied using user-item interactions to capture important hidden variations of the sparse customer purchasing behaviors. The latent factors are used to generalize the purchasing pattern of the customers and to provide product recommendations. CF with Neural Collaborative Filtering (NCF) was shown to produce the highest Normalized Discounted Cumulative Gain (NDCG) performance on the real-world proprietary dataset provided by a large parts supply company. Different hyperparameters were tested using Bayesian Optimization (BO) for applicability in the CF framework. External data sources like click-data and metrics like Clickthrough Rate (CTR) were reviewed for potential extensions to the work presented. The work shown in this paper provides techniques the Company can use to provide product recommendations to enhance revenues, attract new customers, and gain advantages over competitors. With today's ever-increasing ease of access to the internet more advertisements, attract new clients, and retain existing and information, we have reached a point of information clients [6].

Agent-based methods allow for defining simple rules that generate complex group behaviors. The governing rules of such models are typically set a priori and parameters are tuned from observed behavior trajectories. Instead of making simplifying assumptions across all anticipated scenarios, inverse reinforcement learning provides inference on the short-term (local) rules governing long term behavior policies by using properties of a Markov decision process. We use the computationally efficient linearly-solvable Markov decision process to learn the local rules governing collective movement for a simulation of the self propelled-particle (SPP) model and a data application for a captive guppy population. The estimation of the behavioral decision costs is done in a Bayesian framework with basis function smoothing. We recover the true costs in the SPP simulation and find the guppies value collective movement more than targeted movement toward shelter.