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Cheap robust learning of data anomalies with analytically solvable entropic outlier sparsification.

ABSTRACT: Entropic outlier sparsification (EOS) is proposed as a cheap and robust computational strategy for learning in the presence of data anomalies and outliers. EOS dwells on the derived analytic solution of the (weighted) expected loss minimization problem subject to Shannon entropy regularization. An identified closed-form solution is proven to impose additional costs that depend linearly on statistics size and are independent of data dimension. Obtained analytic results also explain why the mixtures of spherically symmetric Gaussians-used heuristically in many popular data analysis algorithms-represent an optimal and least-biased choice for the nonparametric probability distributions when working with squared Euclidean distances. The performance of EOS is compared to a range of commonly used tools on synthetic problems and on partially mislabeled supervised classification problems from biomedicine. Applying EOS for coinference of data anomalies during learning is shown to allow reaching an accuracy of [Formula: see text] when predicting patient mortality after heart failure, statistically significantly outperforming predictive performance of common learning tools for the same data.

SUBMITTER: Horenko I

PROVIDER: S-EPMC8917346 | biostudies-literature | 2022 Mar

REPOSITORIES: biostudies-literature

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Publications

Cheap robust learning of data anomalies with analytically solvable entropic outlier sparsification.

Horenko Illia I

Proceedings of the National Academy of Sciences of the United States of America 20220301 9

Entropic outlier sparsification (EOS) is proposed as a cheap and robust computational strategy for learning in the presence of data anomalies and outliers. EOS dwells on the derived analytic solution of the (weighted) expected loss minimization problem subject to Shannon entropy regularization. An identified closed-form solution is proven to impose additional costs that depend linearly on statistics size and are independent of data dimension. Obtained analytic results also explain why the mixtur ...[more]

PMID: 35197293

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Project description:BackgroundHigh throughput RNA sequencing is a powerful approach to study gene expression. Due to the complex multiple-steps protocols in data acquisition, extreme deviation of a sample from samples of the same treatment group may occur due to technical variation or true biological differences. The high-dimensionality of the data with few biological replicates make it challenging to accurately detect those samples, and this issue is not well studied in the literature currently. Robust statistics is a family of theories and techniques aim to detect the outliers by first fitting the majority of the data and then flagging data points that deviate from it. Robust statistics have been widely used in multivariate data analysis for outlier detection in chemometrics and engineering. Here we apply robust statistics on RNA-seq data analysis.ResultsWe report the use of two robust principal component analysis (rPCA) methods, PcaHubert and PcaGrid, to detect outlier samples in multiple simulated and real biological RNA-seq data sets with positive control outlier samples. PcaGrid achieved 100% sensitivity and 100% specificity in all the tests using positive control outliers with varying degrees of divergence. We applied rPCA methods and classical principal component analysis (cPCA) on an RNA-Seq data set profiling gene expression of the external granule layer in the cerebellum of control and conditional SnoN knockout mice. Both rPCA methods detected the same two outlier samples but cPCA failed to detect any. We performed differentially expressed gene detection before and after outlier removal as well as with and without batch effect modeling. We validated gene expression changes using quantitative reverse transcription PCR and used the result as reference to compare the performance of eight different data analysis strategies. Removing outliers without batch effect modeling performed the best in term of detecting biologically relevant differentially expressed genes.ConclusionsrPCA implemented in the PcaGrid function is an accurate and objective method to detect outlier samples. It is well suited for high-dimensional data with small sample sizes like RNA-seq data. Outlier removal can significantly improve the performance of differential gene detection and downstream functional analysis.

Dataset Information

Cheap robust learning of data anomalies with analytically solvable entropic outlier sparsification.

Publications

Cheap robust learning of data anomalies with analytically solvable entropic outlier sparsification.

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