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Estimating densities with non-linear support by using Fisher-Gaussian kernels.

ABSTRACT: Current tools for multivariate density estimation struggle when the density is concentrated near a non-linear subspace or manifold. Most approaches require the choice of a kernel, with the multivariate Gaussian kernel by far the most commonly used. Although heavy-tailed and skewed extensions have been proposed, such kernels cannot capture curvature in the support of the data. This leads to poor performance unless the sample size is very large relative to the dimension of the data. The paper proposes a novel generalization of the Gaussian distribution, which includes an additional curvature parameter. We refer to the proposed class as Fisher-Gaussian kernels, since they arise by sampling from a von Mises-Fisher density on the sphere and adding Gaussian noise. The Fisher-Gaussian density has an analytic form and is amenable to straightforward implementation within Bayesian mixture models by using Markov chain Monte Carlo sampling. We provide theory on large support and illustrate gains relative to competitors in simulated and real data applications.

SUBMITTER: Mukhopadhyay M

PROVIDER: S-EPMC9286319 | biostudies-literature | 2020 Dec

REPOSITORIES: biostudies-literature

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Estimating densities with non-linear support by using Fisher-Gaussian kernels.

Mukhopadhyay Minerva M Li Didong D Dunson David B DB

Journal of the Royal Statistical Society. Series B, Statistical methodology 20200809 5

Current tools for multivariate density estimation struggle when the density is concentrated near a non-linear subspace or manifold. Most approaches require the choice of a kernel, with the multivariate Gaussian kernel by far the most commonly used. Although heavy-tailed and skewed extensions have been proposed, such kernels cannot capture curvature in the support of the data. This leads to poor performance unless the sample size is very large relative to the dimension of the data. The paper prop ...[more]

PMID: 35845818

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Project description:BackgroundSupport vector machines (SVM) are a powerful tool to analyze data with a number of predictors approximately equal or larger than the number of observations. However, originally, application of SVM to analyze biomedical data was limited because SVM was not designed to evaluate importance of predictor variables. Creating predictor models based on only the most relevant variables is essential in biomedical research. Currently, substantial work has been done to allow assessment of variable importance in SVM models but this work has focused on SVM implemented with linear kernels. The power of SVM as a prediction model is associated with the flexibility generated by use of non-linear kernels. Moreover, SVM has been extended to model survival outcomes. This paper extends the Recursive Feature Elimination (RFE) algorithm by proposing three approaches to rank variables based on non-linear SVM and SVM for survival analysis.ResultsThe proposed algorithms allows visualization of each one the RFE iterations, and hence, identification of the most relevant predictors of the response variable. Using simulation studies based on time-to-event outcomes and three real datasets, we evaluate the three methods, based on pseudo-samples and kernel principal component analysis, and compare them with the original SVM-RFE algorithm for non-linear kernels. The three algorithms we proposed performed generally better than the gold standard RFE for non-linear kernels, when comparing the truly most relevant variables with the variable ranks produced by each algorithm in simulation studies. Generally, the RFE-pseudo-samples outperformed the other three methods, even when variables were assumed to be correlated in all tested scenarios.ConclusionsThe proposed approaches can be implemented with accuracy to select variables and assess direction and strength of associations in analysis of biomedical data using SVM for categorical or time-to-event responses. Conducting variable selection and interpreting direction and strength of associations between predictors and outcomes with the proposed approaches, particularly with the RFE-pseudo-samples approach can be implemented with accuracy when analyzing biomedical data. These approaches, perform better than the classical RFE of Guyon for realistic scenarios about the structure of biomedical data.

Project description:BACKGROUND: Accurate prediction of peptide immunogenicity and characterization of relation between peptide sequences and peptide immunogenicity will be greatly helpful for vaccine designs and understanding of the immune system. In contrast to the prediction of antigen processing and presentation pathway, the prediction of subsequent T-cell reactivity is a much harder topic. Previous studies of identifying T-cell receptor (TCR) recognition positions were based on small-scale analyses using only a few peptides and concluded different recognition positions such as positions 4, 6 and 8 of peptides with length 9. Large-scale analyses are necessary to better characterize the effect of peptide sequence variations on T-cell reactivity and design predictors of a peptide's T-cell reactivity (and thus immunogenicity). The identification and characterization of important positions influencing T-cell reactivity will provide insights into the underlying mechanism of immunogenicity. RESULTS: This work establishes a large dataset by collecting immunogenicity data from three major immunology databases. In order to consider the effect of MHC restriction, peptides are classified by their associated MHC alleles. Subsequently, a computational method (named POPISK) using support vector machine with a weighted degree string kernel is proposed to predict T-cell reactivity and identify important recognition positions. POPISK yields a mean 10-fold cross-validation accuracy of 68% in predicting T-cell reactivity of HLA-A2-binding peptides. POPISK is capable of predicting immunogenicity with scores that can also correctly predict the change in T-cell reactivity related to point mutations in epitopes reported in previous studies using crystal structures. Thorough analyses of the prediction results identify the important positions 4, 6, 8 and 9, and yield insights into the molecular basis for TCR recognition. Finally, we relate this finding to physicochemical properties and structural features of the MHC-peptide-TCR interaction. CONCLUSIONS: A computational method POPISK is proposed to predict immunogenicity with scores which are useful for predicting immunogenicity changes made by single-residue modifications. The web server of POPISK is freely available at http://iclab.life.nctu.edu.tw/POPISK.

Dataset Information

Estimating densities with non-linear support by using Fisher-Gaussian kernels.

Publications

Estimating densities with non-linear support by using Fisher-Gaussian kernels.

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