Sparse Reduced-Rank Regression for Exploratory Visualisation of Paired Multivariate Data

Abstract

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High-throughput analysis of dendritic and axonal arbors reveals transcriptomic correlates of neuroanatomy

“…Having established that registered 2-d ADRs are as successful as a standardized, rich set of morphometric features in predicting transcriptomic identity and that ADRs can be generated in a fully automated manner without significant performance loss, we study layer-specific axon and dendrite innervation. We treat the search for genes that are predictive of laminar innervation strength as a sparse regression problem 30, 31 (Table 1, Supplementary Tables S1– S3). We find that the sets of laminae innervation-predicting genes within molecularly defined subclasses (Sst, Pvalb, Vip, Lamp5) and terminal, t-types (3 Sst, 2 Pvalb, 2 Lamp5 types) are highly reproducible (Supplementary Table S3) and almost mutually exclusive(Figure 3f).…”

Circuit-selective cell-autonomous regulation of inhibition in pyramidal neurons by Ste20-like kinase

“…To determine how the transcriptomic profile of shSLK neurons relates to the changes in electrophysiological parameters, we applied a sparse reduced-rank regression (RRR) approach to predict the three electrophysiological properties we found to be altered in shSLK neurons. This approach uses a low-dimensional representation of the expression of selected genes, 26 and allows to visualize relationships between electrophysiological features and gene expression. We used cross-validation to tune the hyperparameters ( Figures S10 A–S10C) and obtained a model that selected 113 candidate genes best explaining the variability of the electrophysiological data ( Table S3 ).…”

Machine learning-based personalized composite score dissects risk and protective factors for cognitive and motor function in elderly

“…RRR is a computationally efficient method which increases statistical power in settings where the number of dimensions is large compared to the number of examples. In such m ≫ j settings RRR is nowadays a state-of-the-art method in fields with high dimensional data such as genetics and imaging 21,22 . Given j observations of m predictors and n outcome measures, standard multivariate regression requires fitting m · n coefficients Y = XC + E , with Y being the response matrix of size j × n, X being the j × m predictor matrix, C the m × n coefficient matrix and E being the error term matrix of size j × n .…”

“…RRR is a computationally efficient method which increases statistical power in settings where the number of dimensions is large compared to the number of examples. In such 𝑚 ≫ 𝑗 settings RRR is nowadays a state-of-the-art method in fields with high dimensional data such as genetics and imaging 21,22 This decomposition allows for interpretations of 𝐴 and 𝐵. 𝐴 is a mapping from the predictor matrix 𝑋 to a latent representation of dimension 𝑘. 𝐵 is a mapping from the latent scores to the responses 𝑌.…”