Physical Sciences and Mathematics Commons^™

Using Bayesian Networks To Provide Educational Implications: Mobile Learning And Ethnomathematics To Improve Sustainability In Mathematics Education, Jason D. Johnson, Linda Smail, Darryl Corey, Adeeb M. Jarrah

All Works

There are many Western apps that help students strengthen their mathematics skills through learning and game apps. A research project was designed to create an IOS Math App to provide Grade 6 Emirati students with the opportunity to explore mathematics, then, using Bayesian Networks, to examine the educational implications. The learning app was developed using ethnomathematics modules based on the Emirati culture. Students were required to navigate through several modules to examine various mathematical concepts in algebra and geometry. The survey was written for Grade 6 English language learners. Based on the Bayesian Networks, the findings suggested that if students …

Bayesian Convolutional Neural Network With Prediction Smoothing And Adversarial Class Thresholds, Noah M. Miller

Theses and Dissertations

Using convolutional neural networks (CNNs) for image classification for each frame in a video is a very common technique. Unfortunately, CNNs are very brittle and have a tendency to be over confident in their predictions. This can lead to what we will refer to as “flickering,” which is when the predictions between frames jump back and forth between classes. In this paper, new methods are proposed to combat these shortcomings. This paper utilizes a Bayesian CNN which allows for a distribution of outputs on each data point instead of just a point estimate. These distributions are then smoothed over multiple …

Multilevel Hierarchical Decomposition Of Finite Element White Noise With Application To Multilevel Markov Chain Monte Carlo, Hillary R. Fairbanks, Umberto E. Villa, Panayot S. Vassilevski

Mathematics and Statistics Faculty Publications and Presentations

In this work we develop a new hierarchical multilevel approach to generate Gaussian random field realizations in an algorithmically scalable manner that is well suited to incorporating into multilevel Markov chain Monte Carlo (MCMC) algorithms. This approach builds off of other partial differential equation (PDE) approaches for generating Gaussian random field realizations; in particular, a single field realization may be formed by solving a reaction-diffusion PDE with a spatial white noise source function as the right-hand side. While these approaches have been explored to accelerate forward uncertainty quantification tasks, e.g., multilevel Monte Carlo, the previous constructions are not directly applicable …

Estimating Posterior Quantity Of Interest Expectations In A Multilevel Scalable Framework, Hillary R. Fairbanks, Sarah Osborn, Panayot S. Vassilevski

Mathematics and Statistics Faculty Publications and Presentations

Scalable approaches for uncertainty quantification are necessary for characterizing prediction confidence in large‐scale subsurface flow simulations with uncertain permeability. To this end we explore a multilevel Monte Carlo approach for estimating posterior moments of a particular quantity of interest, where we employ an element‐agglomerated algebraic multigrid (AMG) technique to generate the hierarchy of coarse spaces with guaranteed approximation properties for both the generation of spatially correlated random fields and the forward simulation of Darcy's law to model subsurface flow. In both these components (sampling and forward solves), we exploit solvers that rely on state‐of‐the‐art scalable AMG. To showcase the applicability …

Analysis With Dynamic Bayesian Networks Compared To Simulation, Aaron J. Salazar

Theses and Dissertations

This research compares simulations to Dynamic Bayesian Networks in analyzing situations. The research applies models that have known output mean and variance. Queueing systems have theoretical values of the steady-state mean and variance for the number of entities in the system. Monte Carlo simulation development is broken down into two separate approaches: discrete-event simulation and time-oriented simulation. The discrete-event simulation uses pseudo-random numbers to schedule and trigger future events (i.e. customer arrivals and services) and is based on the generated objects.The time-oriented simulation utilizes fixed-width time intervals and updates the system state according to a stochastic process for the set …

Heart Attack Mortality Prediction: An Application Of Machine Learning Methods, Issam Salman

Turkish Journal of Electrical Engineering and Computer Sciences

The heart is an important organ in the human body, and acute myocardial infarction (AMI) is the leading cause of death in most countries. Researchers are doing a lot of data analysis work to assist doctors in predicting the heart problem. An analysis of the data related to different health problems and its functions can help in predicting the wellness of this organ with a degree of certainty. Our research reported in this paper consists of two main parts. In the first part of the paper, we compare different predictive models of hospital mortality for patients with AMI. All results …

Junction Trees Constructions In Bayesian Networks, Linda Smail

All Works

© Published under licence by IOP Publishing Ltd. Junction trees are used as graphical structures over which propagation will be carried out through a very important property called the ruining intersection property. This paper examines an alternative method for constructing junction trees that are essential for the efficient computations of probabilities in Bayesian networks. The new proposed method converts a sequence of subsets of a Bayesian network into a junction tree, in other words, into a set of cliques that has the running intersection property. The obtained set of cliques and separators coincide with the junction trees obtained by the …

Using Bayesian Networks To Understand Relationships Among Math Anxiety, Genders, Personality Types, And Study Habits At A University In Jordan, Linda Smail

All Works

© 2017 Journal on Mathematics Education.All Rights Reserved. Mathematics is the foundation of all sciences, but most students have problems learning math. Although students' success in life related to their success in learning, many would not take a math course unless it is their university's core requirements. Multiple reasons exist for students' poor performance in mathematics, but one prevalent variable worth consideration is the personality type. This work seeks to uncover relationships, if any, between students' math anxiety and the students' learning type in learning math and preparing for exams and tests. We use Bayesian networks to link those different …

Bayesian Networks To Assess The Newborn Stool Microbiome, William E. Bennett Jr.

McKelvey School of Engineering Theses & Dissertations

In human stool, a large population of bacterial genes and transcripts from hundreds of genera coexist with host genes and transcripts. Assessments of the metagenome and transcriptome are particularly challenging, since there is a great deal of sequence overlap among related species and related genes. We sequenced the total RNA content from stool samples in a neonate using previously-described methods. We then performed stepwise alignment of different populations of RNA sequence reads to different indices, including ribosomal databases, the human genome, and all sequenced bacterial genomes. Each pool of RNA at each alignment step was subjected to compression to assess …

Shortest Path Based Decision Making Using Probabilistic Inference, Akshat Kumar

Research Collection School Of Computing and Information Systems

We present a new perspective on the classical shortest path routing (SPR) problem in graphs. We show that the SPR problem can be recast to that of probabilistic inference in a mixture of simple Bayesian networks. Maximizing the likelihood in this mixture becomes equivalent to solving the SPR problem. We develop the well known Expectation-Maximization (EM) algorithm for the SPR problem that maximizes the likelihood, and show that it does not get stuck in a locally optimal solution. Using the same probabilistic framework, we then address an NP-Hard network design problem where the goal is to repair a network of …

Development Of A Stakeholder-Driven Spatial Modeling Framework For Strategic Landscape Planning Using Bayesian Networks Across Two Urban-Rural Gradients In Maine, Usa, Spencer Meyer, Michelle Johnson, Robert Lilieholm, Christopher Cronan

Publications

Land use change results from frequent, independent actions by decision-makers working in isolation, often with a focus on a single land use. In order to develop integrated land use policies that encourage sustainable outcomes, scientists and practitioners must understand the specific drivers of land use change across mixed land use types and ownerships, and must consider the combined influences of biophysical, economic, and social factors that affect land use decisions. In this analysis of two large watersheds covering a total of 1.9 million hectares in Maine, USA, we co-developed with groups of stakeholders land use suitability models that integrated four …

Towards Real-Time, On-Board, Hardware-Supported Sensor And Software Health Management For Unmanned Aerial Systems, Johann Schumann, Kristin Y. Rozier, Thomas Reinbacher, Ole J. Mengshoel, Timmy Mbaya, Corey Ippolito

Ole J Mengshoel

Optimizing Parallel Belief Propagation In Junction Trees Using Regression, Lu Zheng, Ole J. Mengshoel

Ole J Mengshoel

Exploring Multiple Dimensions Of Parallelism In Junction Tree Message Passing, Lu Zheng, Ole J. Mengshoel

Ole J Mengshoel

Latent Topic Analysis For Predicting Group Purchasing Behavior On The Social Web, Feng-Tso Sun, Martin Griss, Ole J. Mengshoel, Yi-Ting Yeh

Ole J Mengshoel

Software Health Management With Bayesian Networks, Johann Schumann, Timmy Mbaya, Ole J. Mengshoel, Knot Pipatsrisawat, Ashok Srivastava, Arthur Choi, Adnan Darwiche

Ole J Mengshoel

Software And System Health Management For Autonomous Robotics Missions, Johann Schumann, Timmy Mbaya, Ole J. Mengshoel

Ole J Mengshoel

Advanced autonomous robotics space missions rely heavily on the flawless interaction of complex hardware, multiple sensors, and a mission-critical software system. This software system consists of an operating system, device drivers, controllers, and executives; recently highly complex AI-based autonomy software have also been introduced. Prior to launch, this software has to undergo rigorous verification and validation (V&V). Nevertheless, dormant software bugs, failing sensors, unexpected hardware-software interactions, and unanticipated environmental conditions—likely on a space exploration mission—can cause major software faults that can endanger the entire mission.

Our Integrated Software Health Management (ISWHM) system continuously monitors the hardware sensors and the software …

Reactive Bayesian Network Computation Using Feedback Control: An Empirical Study, Ole J. Mengshoel, Abe Ishihara, Erik Reed

Ole J Mengshoel

Accelerating Bayesian Network Parameter Learning Using Hadoop And Mapreduce, Aniruddha Basak, Irina Brinster, Xianheng Ma, Ole J. Mengshoel

Ole J Mengshoel

Age-Layered Expectation Maximization For Parameter Learning In Bayesian Networks, Avneesh Saluja, Priya Sundararajan, Ole J. Mengshoel

Ole J Mengshoel

Bayesian Software Health Management For Aircraft Guidance, Navigation, And Control, Johann M. Schumann, Timmy Mbaya, Ole J. Mengshoel

Ole J Mengshoel

Modern aircraft — both piloted fly-by-wire commercial aircraft as well as UAVs — more and more depend on highly complex safety critical software systems with many sensors and computer-controlled actuators. Despite careful design and V&V of the software, severe incidents have happened due to malfunctioning software.

In this paper, we discuss the use of Bayesian networks to monitor the health of the on-board software and sensor system, and to perform advanced on-board diagnostic reasoning. We focus on the development of reliable and robust health models for combined software and sensor systems, with application to guidance, navigation, and control (GN&C). Our …

Integrating Probabilistic Reasoning And Statistical Quality Control Techniques For Fault Diagnosis In Hybrid Domains, Brian Ricks, Craig Harrison, Ole J. Mengshoel

Ole J Mengshoel

Integrated Software And Sensor Health Management For Small Spacecraft, Johann Schumann, Ole J. Mengshoel, Timmy Mbaya

Ole J Mengshoel

Despite their size, small spacecraft have highly complex architectures with many sensors and computer-controlled actuators. At the same time, size, weight, and budget constraints often dictate that small spacecraft are designed as single-string systems, which means that there are no or few redundant systems. Thus, all components, including software, must operate as reliably. Faults, if present, must be detected as early as possible to enable (usually limited) forms of mitigation. Telemetry bandwidth for such spacecraft is usually very limited. Therefore, fault detection and diagnosis must be performed on-board. Further restrictions include low computational power and small memory.

In this paper, …

Belief Propagation By Message Passing In Junction Trees: Computing Each Message Faster Using Gpu Parallelization, Lu Zheng, Ole J. Mengshoel, Jike Chong

Ole J Mengshoel

Compiling Bayesian networks (BNs) to junction trees and performing belief propagation over them is among the most prominent approaches to computing posteriors in BNs. However, belief propagation over junction tree is known to be computationally intensive in the general case. Its complexity may increase dramatically with the connectivity and state space cardinality of Bayesian network nodes. In this paper, we address this computational challenge using GPU parallelization. We develop data structures and algorithms that extend existing junction tree techniques, and specifically develop a novel approach to computing each belief propagation message in parallel. We implement our approach on an NVIDIA …

Verification And Validation Of System Health Management Models Using Parametric Testing, Erik Reed, Johann Schumann, Ole J. Mengshoel

Ole J Mengshoel

System Health Management (SHM) systems have found their way into many safety-critical aerospace and industrial applications. A SHM system processes readings from sensors throughout the system and uses a Health Management (HM) model to detect and identify potential faults (diagnosis) and to predict possible failures in the near future (prognosis). It is essential that a SHM system, which monitors a safety-critical component, must be at least as reliable and safe as the component itself—false alarms or missed adverse events can potentially result in catastrophic failures. The SHM system including the HM model, a piece of software, must therefore undergo rigorous …

Initialization And Restart In Stochastic Local Search: Computing A Most Probable Explanation In Bayesian Networks, Ole J. Mengshoel, David C. Wilkins, Dan Roth

Ole J Mengshoel

For hard computational problems, stochastic local search has proven to be a competitive approach to finding optimal or approximately optimal problem solutions. Two key research questions for stochastic local search algorithms are: Which algorithms are effective for initialization? When should the search process be restarted? In the present work, we investigate these research questions in the context of approximate computation of most probable explanations (MPEs) in Bayesian networks (BNs). We introduce a novel approach, based on the Viterbi algorithm, to explanation initialization in BNs. While the Viterbi algorithm works on sequences and trees, our approach works on BNs with arbitrary …

Towards Software Health Management With Bayesian Networks, Johann Schumann, Ole J. Mengshoel, Ashok Srivastava, Adnan Darwiche

Ole J Mengshoel

More and more systems (e.g., aircraft, machinery, cars) rely heavily on software, which performs safety-critical operations. Assuring software safety though traditional V&V has become a tremendous, if not impossible task, given the growing size and complexity of the software. We propose that iSWHM (Integrated SoftWare Health Management) can increase safety and reliability of high-assurance software systems. iSWHM uses advanced techniques from the area of system health management in order to continuously monitor the behavior of the software during operation, quickly detect anomalies and perform automatic and reliable root-cause analysis, while not replacing traditional V&V. Information provided by the iSWHM system …

Generalized Crowding For Genetic Algorithms, Ole J. Mengshoel, Severino F. Galan

Ole J Mengshoel

Understanding The Scalability Of Bayesian Network Inference Using Clique Tree Growth Curves, Ole J. Mengshoel

Ole J Mengshoel

One of the main approaches to performing computation in Bayesian networks (BNs) is clique tree clustering and propagation. The clique tree approach consists of propagation in a clique tree compiled from a BN, and while it was introduced in the 1980s, there is still a lack of understanding of how clique tree computation time depends on variations in BN size and structure. In this article, we improve this understanding by developing an approach to characterizing clique tree growth as a function of parameters that can be computed in polynomial time from BNs, specifically: (i) the ratio of the number of …

Portfolios In Stochastic Local Search: Efficiently Computing Most Probable Explanations In Bayesian Networks, Ole J. Mengshoel, D Roth, D Wilkins

Ole J Mengshoel

Portfolio methods support the combination of different algorithms and heuristics, including stochastic local search (SLS) heuristics, and have been identified as a promising approach to solve computationally hard problems. While successful in experiments, theoretical foundations and analytical results for portfolio-based SLS heuristics are less developed. This article aims to improve the understanding of the role of portfolios of heuristics in SLS. We emphasize the problem of computing most probable explanations (MPEs) in Bayesian networks (BNs). Algorithmically, we discuss a portfolio-based SLS algorithm for MPE computation, Stochastic Greedy Search (SGS). SGS supports the integration of different initialization operators (or initialization heuristics) …