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Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
The Support Vector Machine And Mixed Integer Linear Programming: Ramp Loss Svm With L1-Norm Regularization, Eric J. Hess, J. Paul Brooks
The Support Vector Machine And Mixed Integer Linear Programming: Ramp Loss Svm With L1-Norm Regularization, Eric J. Hess, J. Paul Brooks
Statistical Sciences and Operations Research Publications
The support vector machine (SVM) is a flexible classification method that accommodates a kernel trick to learn nonlinear decision rules. The traditional formulation as an optimization problem is a quadratic program. In efforts to reduce computational complexity, some have proposed using an L1-norm regularization to create a linear program (LP). In other efforts aimed at increasing the robustness to outliers, investigators have proposed using the ramp loss which results in what may be expressed as a quadratic integer programming problem (QIP). In this paper, we consider combining these ideas for ramp loss SVM with L1-norm regularization. The result is four …
Principal Component Analysis And Optimization: A Tutorial, Robert Reris, J. Paul Brooks
Principal Component Analysis And Optimization: A Tutorial, Robert Reris, J. Paul Brooks
Statistical Sciences and Operations Research Publications
No abstract provided.
Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, Cheng Ly
Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, Cheng Ly
Statistical Sciences and Operations Research Publications
Heterogeneity of neural attributes has recently gained a lot of attention and is increasing recognized as a crucial feature in neural processing. Despite its importance, this physiological feature has traditionally been neglected in theoretical studies of cortical neural networks. Thus, there is still a lot unknown about the consequences of cellular and circuit heterogeneity in spiking neural networks. In particular, combining network or synaptic heterogeneity and intrinsic heterogeneity has yet to be considered systematically despite the fact that both are known to exist and likely have significant roles in neural network dynamics. In a canonical recurrent spiking neural network model, …
Gap Detection For Genome-Scale Constraint-Based Models, J. Paul Brooks, William P. Burns, Stephen S. Fong, Chris M. Gowen, Seth B. Roberts
Gap Detection For Genome-Scale Constraint-Based Models, J. Paul Brooks, William P. Burns, Stephen S. Fong, Chris M. Gowen, Seth B. Roberts
Statistical Sciences and Operations Research Publications
Constraint-based metabolic models are currently the most comprehensive system-wide models of cellular metabolism. Several challenges arise when building an in silico constraint-based model of an organism that need to be addressed before flux balance analysis (FBA) can be applied for simulations. An algorithm called FBA-Gap is presented here that aids the construction of a working model based on plausible modifications to a given list of reactions that are known to occur in the organism. When applied to a working model, the algorithm gives a hypothesis concerning a minimal medium for sustaining the cell in culture. The utility of the algorithm …
Hypothesis Testing And Power Calculations For Taxonomic-Based Human Microbiome Data, P. S. Larossa, J. Paul Brooks, Elena Deych, Edward L. Boone, David J. Edwards, Qin Wang, Erica Sodergren, George Weinstock, William D. Shannon
Hypothesis Testing And Power Calculations For Taxonomic-Based Human Microbiome Data, P. S. Larossa, J. Paul Brooks, Elena Deych, Edward L. Boone, David J. Edwards, Qin Wang, Erica Sodergren, George Weinstock, William D. Shannon
Statistical Sciences and Operations Research Publications
This paper presents new biostatistical methods for the analysis of microbiome data based on a fully parametric approach using all the data. The Dirichlet-multinomial distribution allows the analyst to calculate power and sample sizes for experimental design, perform tests of hypotheses (e.g., compare microbiomes across groups), and to estimate parameters describing microbiome properties. The use of a fully parametric model for these data has the benefit over alternative non-parametric approaches such as bootstrapping and permutation testing, in that this model is able to retain more information contained in the data. This paper details the statistical approaches for several tests of …
Coverings And Matchings In R-Partite Hypergraphs, Douglas S. Altner, J. Paul Brooks
Coverings And Matchings In R-Partite Hypergraphs, Douglas S. Altner, J. Paul Brooks
Statistical Sciences and Operations Research Publications
Ryser's conjecture postulates that for r -partite hypergraphs, τ ≤ (r - 1)ν where τ is the covering number of the hypergraph and ν is the matching number. Although this conjecture has been open since the 1960s, researchers have resolved it for special cases such as for intersecting hypergraphs where r ≤ 5. In this article, we prove several results pertaining to matchings and coverings in r -partite intersecting hypergraphs. First, we prove that finding a minimum cardinality vertex cover for an r -partite intersecting hypergraph is NP-hard. Second, we note Ryser's conjecture for intersecting hypergraphs is easily resolved …
Outlier-Resistant L1 Orthogonal Regression Via The Reformulation-Linearization Technique, J. Paul Brooks, Edward L. Boone
Outlier-Resistant L1 Orthogonal Regression Via The Reformulation-Linearization Technique, J. Paul Brooks, Edward L. Boone
Statistical Sciences and Operations Research Publications
Assessing the linear relationship between a set of continuous predictors and a continuous response is a well-studied problem in statistics and data mining. L2-based methods such as ordinary least squares and orthogonal regression can be used to determine this relationship. However, both of these methods become impaired when influential values are present. This problem becomes compounded when outliers confound standard diagnostics. This work proposes an L1-norm orthogonal regression method (L1OR) formulated as a nonconvex optimization problem. Solution strategies for finding globally optimal solutions are presented. Simulation studies are conducted to assess the resistance of the method to outliers and the …
Analysis Of The Consistency Of A Mixed Integer Programming-Based Multi-Category Constrained Discriminant Model, J. Paul Brooks, Eva K. Lee
Analysis Of The Consistency Of A Mixed Integer Programming-Based Multi-Category Constrained Discriminant Model, J. Paul Brooks, Eva K. Lee
Statistical Sciences and Operations Research Publications
Classification is concerned with the development of rules for the allocation of observations to groups, and is a fundamental problem in machine learning. Much of previous work on classification models investigates two-group discrimination. Multi-category classification is less-often considered due to the tendency of generalizations of two-group models to produce misclassification rates that are higher than desirable. Indeed, producing “good” two-group classification rules is a challenging task for some applications, and producing good multi-category rules is generally more difficult. Additionally, even when the “optimal” classification rule is known, inter-group misclassification rates may be higher than tolerable for a given classification model. …
Is Screening Cargo Containers For Smuggled Nuclear Threats Worthwhile?, Jason R. W. Merrick, Laura A. Mclay
Is Screening Cargo Containers For Smuggled Nuclear Threats Worthwhile?, Jason R. W. Merrick, Laura A. Mclay
Statistical Sciences and Operations Research Publications
In recent years, Customs and Border Protection (CBP) has installed radiation sensors to screen cargo containers entering theUnited States. They are concerned that terrorists could use containers to smuggle radiological material into the country and carry out attacks with dirty bombs or a nuclear device. Recent studies have questioned the value of improving this screening system with new sensor technology. The cost of delays caused by frequent false alarms outweighs any reduction in the probability of an attack in an expected cost analysis. We extend existing methodology in three ways to demonstrate how additional factors affect the value of screening …