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DOE OSTI2017

Examining robustness of model selection with half-normal and LASSO plots for unreplicated factorial designs

When there are constraints on resources, an unreplicated factorial or fractional factorial design can allow efficient exploration of numerous factor and interaction effects. A half-normal plot is a common graphical tool used to compare the relative magnitude of effects and to identify important effects from these experiments when no estimate of error from the experiment is available. An alternative is to use a least absolute shrinkage and selection operation plot to examine the pattern of model selection terms from an experiment. We examine how both the half-normal and least absolute shrinkage and selection operation plots are impacted by the absence of individual observations or an outlier, and the robustness of conclusions obtained from these 2 techniques for identifying important effects from factorial experiments. As a result, the methods are illustrated with 2 examples from the literature.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Influence plots for LASSO

With many predictors in regression, fitting the full model can induce multicollinearity problems. Least Absolute Shrinkage and Selection Operation (LASSO) is useful when the effects of many explanatory variables are sparse in a high-dimensional dataset. Influential points can have a disproportionate impact on the estimated values of model parameters. Here, this paper describes a new influence plot that can be used to increase understanding of the contributions of individual observations and the robustness of results. This can serve as a complement to other regression diagnostics techniques in the LASSO regression setting. Using this influence plot, we can find influential points and their impact on shrinkage of model parameters and model selection. Lastly, we provide two examples to illustrate the methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Assessing robustness of factor ranking for supersaturated designs

Supersaturated designs can potentially be a beneficial tool for efficiently exploring a large number of factors with a moderately sized design. However, because more factors are being considered than there are runs, the stability of the identified factors depends heavily on effect sparsity and the lack of highly influential observations. A helpful tool for the analysis of supersaturated designs is least absolute shrinkage and selection operation (LASSO), which is useful when the effects of many explanatory variables are sparse in a high-dimensional dataset. To understand the impact of individual observations on the selected factors, the LASSO influence plot was created. This work describes an application of this plot and its variants that can be used to identify influential points, increase understanding of the impact of individual observations on model parameters, and the robustness of results in analyses with supersaturated designs. These graphical methods can serve as a complement to other regression diagnostics techniques in the LASSO regression setting.

3-D LASSO influence plots↗

DOE OSTI2017

Signatures of Mechanically Interlocked Topology of Lasso Peptides by Ion Mobility–Mass Spectrometry: Lessons from a Collection of Representatives

Lasso peptides are characterized by a mechanically interlocked structure, where the C-terminal tail of the peptide is threaded and trapped within an N-terminal macrolactam ring. Their compact and stable structures have a significant impact on their biological and physical properties and make them highly interesting for drug development. Ion mobility - mass spectrometry (IM-MS) has shown to be effective to discriminate the lasso topology from their corresponding branched-cyclic topoisomers in which the C-terminal tail is unthreaded. In fact, previous comparison of the IM-MS data of the two topologies has yielded three trends that allow differentiation of the lasso fold from the branched-cyclic structure: (1) the low abundance of highly charged ions, (2) the low change in collision cross sections (CCS) with increasing charge state and (3) a narrow ion mobility peak width. In this study, a three-dimensional plot was generated using three indicators based on these three trends: (1) mean charge divided by mass (ζ), (2) relative range of CCS covered by all protonated molecules (ΔΩ/Ω) and (3) mean ion mobility peak width (δΩ). The data were first collected on a set of twenty one lasso peptides and eight branched-cyclic peptides. The indicators were obtained also for eight variants of the well-known lasso peptide MccJ25 obtained by site-directed mutagenesis and further extended to five linear peptides, two macrocyclic peptides and one disulfide constrained peptide. In all cases, a clear clustering was observed between constrained and unconstrained structures, thus providing a new strategy to discriminate mechanically interlocked topologies. .

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2018

Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions

Here, compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quantification analysis of expensive and high-dimensional physical models. We perform numerical investigations employing several compressive sensing solvers that target the unconstrained LASSO formulation, with a focus on linear systems that arise in the construction of polynomial chaos expansions. With core solvers l1_ls, SpaRSA, CGIST, FPC_AS, and ADMM, we develop techniques to mitigate overfitting through an automated selection of regularization constant based on cross-validation, and a heuristic strategy to guide the stop-sampling decision. Practical recommendations on parameter settings for these techniques are provided and discussed. The overall method is applied to a series of numerical examples of increasing complexity, including large eddy simulations of supersonic turbulent jet-in-crossflow involving a 24-dimensional input. Through empirical phase-transition diagrams and convergence plots, we illustrate sparse recovery performance under structures induced by polynomial chaos, accuracy, and computational trade-offs between polynomial bases of different degrees, and practicability of conducting compressive sensing for a realistic, high-dimensional physical application. Across test cases studied in this paper, we find ADMM to have demonstrated empirical advantages through consistent lower errors and faster computational times.

97 MATHEMATICS AND COMPUTING↗