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Sparse reduced-rank regression for exploratory visualization of paired multivariate datasets

View ORCID ProfileDmitry Kobak, Yves Bernaerts, Marissa A. Weis, Federico Scala, Andreas Tolias, View ORCID ProfilePhilipp Berens
doi: https://doi.org/10.1101/302208
Dmitry Kobak
1Institute for Ophthalmic Research, University of Tübingen, Germany
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  • For correspondence: dmitry.kobak@uni-tuebingen.de
Yves Bernaerts
1Institute for Ophthalmic Research, University of Tübingen, Germany
2International Max Planck Research School for Intelligent Systems, Germany
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Marissa A. Weis
1Institute for Ophthalmic Research, University of Tübingen, Germany
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Federico Scala
3Department of Neuroscience, Baylor College of Medicine, Houston, Texas, USA
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Andreas Tolias
3Department of Neuroscience, Baylor College of Medicine, Houston, Texas, USA
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Philipp Berens
1Institute for Ophthalmic Research, University of Tübingen, Germany
4Department of Computer Science, University of Tübingen, Germany
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Abstract

In genomics, transcriptomics, and related biological fields (collectively known as omics), it is common to work with n ≪ p datasets with the dimensionality much larger than the sample size. In recent years, combinations of experimental techniques began to yield multiple sets of features for the same set of biological replicates. One example is Patch-seq, a method combining single-cell RNA sequencing with electrophysiological recordings from the same cells. Here we present a framework based on sparse reduced-rank regression for obtaining an interpretable visualization of the relationship between the transcriptomic and the electrophysiological data. We use an elastic net regularization penalty that yields sparse solutions and allows for an efficient computational implementation. Using several publicly available Patch-seq datasets, we show that sparse reduced-rank regression outperforms both sparse full-rank regression and non-sparse reduced-rank regression in terms of predictive performance, and can outperform existing methods for sparse partial least squares and sparse canonical correlation analysis in terms of out-of-sample correlations. We introduce a bibiplot visualization in order to display the dominant factors determining the relationship between transcriptomic and electrophysiological properties of neurons. We believe that sparse reduced-rank regression can provide a valuable tool for the exploration and visualization of paired multivariate datasets, including Patch-seq.

Competing Interest Statement

The authors have declared no competing interest.

Copyright 
The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY-NC-ND 4.0 International license.
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Posted April 14, 2020.
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Sparse reduced-rank regression for exploratory visualization of paired multivariate datasets
Dmitry Kobak, Yves Bernaerts, Marissa A. Weis, Federico Scala, Andreas Tolias, Philipp Berens
bioRxiv 302208; doi: https://doi.org/10.1101/302208
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Sparse reduced-rank regression for exploratory visualization of paired multivariate datasets
Dmitry Kobak, Yves Bernaerts, Marissa A. Weis, Federico Scala, Andreas Tolias, Philipp Berens
bioRxiv 302208; doi: https://doi.org/10.1101/302208

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