Transcriptomics and the “curse of dimensionality”: Monte Carlo simulations of ml-models as a tool for analyzing multidimensional data in tasks of searching markers of biological processes

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Abstract

High-throughput transcriptomic research methods provide the assessment of a vast number of factors, valuable for researchers. At the same time the “curse of dimensionality” issues arise, which lead to increasing requirements on data processing and analysis methods. In this study, we propose a new algorithm that combines Monte Carlo methods and machine learning. This algorithm will enable feature space reduction by highlighting genes most likely associated with the investigated diseases. Our approach allows not only to generate a set of “interesting” genes but also to assign weight to each gene, indicating its “importance”. This measure can be used in subsequent statistical analysis, visualization, and interpretation of results. Algorithm performance was demonstrated on open transcriptomic data of patients with HCM (GSE36961 and GSE1145). The analysis revealed genes MYH6, FCN3, RASD1, and SERPINA3, which is in good agreement with the available literature.

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About the authors

G. J. Osmak

Сhazov National Medical Research Center for Cardiology; Pirogov Russian National Research Medical University

Author for correspondence.
Email: german.osmak@gmail.com
Russian Federation, Moscow; Moscow

M. V. Pisklova

Сhazov National Medical Research Center for Cardiology; Pirogov Russian National Research Medical University

Email: german.osmak@gmail.com
Russian Federation, Moscow; Moscow

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Supplementary files

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2. Fig. 1. Research scheme.

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3. Fig. 2. Results of Monte Carlo simulations for training classifiers. a — Convergence of the algorithm by the size of the set of the most significant genes; red dashes along the abscissa axis show the moments of change in the composition of this set. b — Dynamics of growth depending on the iteration of the algorithm of the number of selected genes (green line); weights of genes included in more than half of the models (red line); iteration at which the set of the most significant genes was changed (red vertical dashes along the abscissa axis). c — Histogram of the distribution of the ROC-AUC measure for ML classifiers in 3000 Monte Carlo simulations. d — Histogram of the distribution of the estimated weight of genes included in at least one model.

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4. Fig. 3. Testing hypotheses about the association of selected genes on the independent GSE1145 dataset. a — Gene expression comparison graph (Volcano plot), the size of the dots denotes their WeightML. b — Summary table of statistics; only significant (by p-value) results are shown. p-valMW — p-value according to the Mann–Whitney criterion; FDRBH — Benjamini–Hochberg multiple comparison correction; FDRwBH — weighted Benjamini–Hochberg multiple comparison correction; WeightML — gene weight, reflecting its significance for classification models based on the results of Monte Carlo simulations; log2FC — logarithm of the ratio of means.

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