Bayesian Kernel Methods for Non-Gaussian Distributions: Binary and Multi- class Classification Problems

Project Objective: The objective of this project is to develop a Bayesian kernel model built around non- Gaussian prior distributions to address binary and multi-class classification problems.Recent advances in data mining have integrated kernel functions with Bayesian probabilistic analysis of Gaussian distributions. These machine learning approaches can incorporate prior information with new data to calculate probabilistic rather than deterministic values for unknown parameters. This paper analyzes extensively a specific Bayesian kernel model that uses a kernel function to calculate a posterior beta distribution that is conjugate to the prior beta distribution. Numerical testing of the beta kernel model on several benchmark data sets reveal that this model’s accuracy is comparable with those of the support vector machine and relevance vector machine, and the model runs more quickly than the other algorithms. When one class occurs much more frequently than the other class, the beta kernel model often outperforms other strategies to handle imbalanced data sets. If data arrive sequentially over time, the beta kernel model easily and quickly updates the probability distribution, and this model is more accurate than an incremental support vector machine algorithm for online learning when fewer than 50 data points are available.U.S. Army Research OfficeSponsor/Monitor's Report Number(s): 61414-MA-II.3W911NF-12-1-040

Improved Acquisition for System Sustainment: Availability-Based Importance Framework for Maintenance, Repair, and Overhaul Acquisition

Naval Postgraduate School Acquisition Research Progra

Improved Acquisition for System Sustainment: Multiobjective Tradeoff Analysis for Condition-Based Decision-Making

Naval Postgraduate School Acquisition Research Progra

Availability-Based Importance Framework for Supplier Selection

Naval Postgraduate School Acquisition Research Progra

Availability-Based Importance Framework For Supplier Selection

Naval Postgraduate School Acquisition Research Progra

Static and Dynamic Resource Allocation Models for Recovery of Interdependent Systems: Application to the Deepwater Horizon Oil Spill

Annals of Operations Research. In press. Author's accepted manuscript||The article of record may be found at http://dx.doi.org/10.1007/s10479-014-1696-1Determining where and when to invest resources during and after a disruption can challenge policy makers and homeland security officials. Two decision models, one static and one dynamic, are proposed to determine the optimal resource allocation to facilitate the recovery of impacted industries after a disruption where the objective is to minimize the production losses due to the disruption. This paper presents conditions for optimality for each model as a function of model parameters as well as an algorithm to solve for the optimal conditions in both models. Both models are applied to the Deepwater Horizon oil spill, which adversely impacted several industries in the Gulf region, such as fishing, tourism, real estate, and oil and gas. Results demonstrate the importance of allocating enough resources to stop the oil spill and clean up the oil, which reduces the economic loss across all industries. These models can be applied to different homeland security and disaster response situations to help governments and organizations decide among different resource allocation strategies during and after a disruption.This work was funded in part by the National Science Foundation, Division of Civil, Mechanical, and Manufacturing Innovation, under award 0927299

A Bayesian beta kernel model for binary classification and online learning problems

Statistical Analysis and Data Mining, 7(6), 434-449. Author's accepted manuscriptThe article of record may be found at http://dx.doi.org/10.1002/sam.11241Recent advances in data mining have integrated kernel functions with Bayesian probabilistic analysis of Gaussian distributions. These machine learning approaches can incorporate prior information with new data to calculate probabilistic rather than deterministic values for unknown parameters. This paper extensively analyzes a speci c Bayesian kernel model that uses a kernel function to calculate a posterior beta distribution that is conjugate to the prior beta distribution. Numerical testing of the beta kernel model on several benchmark data sets reveals that this model's accuracy is comparable with those of the support vector machine, relevance vector machine, naive Bayes, and logistic regression, and the model runs more quickly than other algorithms. When one class occurs much more frequently than the other class, the beta kernel model often outperforms other strategies to handle imbalanced data sets, including undersampling, over-sampling, and the Synthetic Minority Over-Sampling Technique. If data arrive sequentially over time, the beta kernel model easily and quickly updates the probability distribution, and this model is more accurate than an incremental support vector machine algorithm for online learning.This work was funded in part by the U.S. Army Research, Development and Engineering Command, Army Research Office, Mathematical Science Division, under proposal no. 61414-MA-II

An Approach for Modeling Supplier Resilience

Naval Postgraduate School Acquisition Research Progra

Improved Acquisition for System Sustainment: Resilient Supplier Evaluation and Selection with Bayesian Networks

Naval Postgraduate School Acquisition Research Progra

Modeling a Severe Supply Chain Disruption and Post-Disaster Decision Making with Application to the Japanese Earthquake and Tsunami

IIE Transactions, 46(12), 1243-1260. Author's accepted manuscript||The article of record may be found at http://dx.doi.org/10.1080/0740817X.2013.876241Modern supply chains are increasingly vulnerable to disruptions, and a disruption in one part of the world can cause supply diffi culties for companies around the globe. This paper develops a model of severe supply chain disruptions in which several suppliers su ffer from disabled production facilities and firms that purchase goods from those suppliers may consequently suff er a supply shortage. Suppliers and firms can choose disruption management strategies to maintain operations. A supplier with a disabled facility may choose to move production to an alternate facility, and a rm encountering a supply shortage may be able to use inventory or buy supplies from an alternate supplier. The supplier's and rm's optimal decisions are expressed in terms of model parameters such as the cost of each strategy, the chances of losing business, and the probability of facilities reopening. The model is applied to a simulation based on the 2011 Japanese earthquake and tsunami, which closed several facilities of key suppliers in the automobile industry and caused supply difficulties for both Japanese and U.S. automakers