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High-dimensional regression with potential prior information on variable importance
Abstract: There are a variety of settings where vague prior information may be available on the importance of predictors in high-dimensional regression settings. Examples include the ordering on the variables offered by their empirical variances (which is typically discarded through standardisation), the lag of predictors when fitting autoregressive models in time series settings, or the level of missingness of the variables. Whilst such orderings may not match the true importance of variables, we argue that there is little to be lost, and potentially much to be gained, by using them. We propose a simple scheme involving fitting a sequence of models indicated by the ordering. We show that the computational cost for fitting all models when ridge regression is used is no more than for a single fit of ridge regression, and describe a strategy for Lasso regression that makes use of previous fits to greatly speed up fitting the entire sequence of models. We propose to select a final estimator by cross-validation and provide a general result on the quality of the best performing estimator on a test set selected from among a number M of competing estimators in a high-dimensional linear regression setting. Our result requires no sparsity assumptions and shows that only a logM price is incurred compared to the unknown best estimator. We demonstrate the effectiveness of our approach when applied to missing or corrupted data, and in time series settings. An R package is available on github
Epigenetic Regulation of Vascular Smooth Muscle Cells by Histone H3 Lysine 9 Dimethylation Attenuates Target Gene-Induction by Inflammatory Signaling.
OBJECTIVE: Vascular inflammation underlies cardiovascular disease. Vascular smooth muscle cells (VSMCs) upregulate selective genes, including MMPs (matrix metalloproteinases) and proinflammatory cytokines upon local inflammation, which directly contribute to vascular disease and adverse clinical outcome. Identification of factors controlling VSMC responses to inflammation is therefore of considerable therapeutic importance. Here, we determine the role of Histone H3 lysine 9 di-methylation (H3K9me2), a repressive epigenetic mark that is reduced in atherosclerotic lesions, in regulating the VSMC inflammatory response. Approach and Results: We used VSMC-lineage tracing to reveal reduced H3K9me2 levels in VSMCs of arteries after injury and in atherosclerotic lesions compared with control vessels. Intriguingly, chromatin immunoprecipitation showed H3K9me2 enrichment at a subset of inflammation-responsive gene promoters, including MMP3, MMP9, MMP12, and IL6, in mouse and human VSMCs. Inhibition of G9A/GLP (G9A-like protein), the primary enzymes responsible for H3K9me2, significantly potentiated inflammation-induced gene induction in vitro and in vivo without altering NFκB (nuclear factor kappa-light-chain-enhancer of activated B cell) and MAPK (mitogen-activated protein kinase) signaling. Rather, reduced G9A/GLP activity enhanced inflammation-induced binding of transcription factors NFκB-p65 and cJUN to H3K9me2 target gene promoters MMP3 and IL6. Taken together, these results suggest that promoter-associated H3K9me2 directly attenuates the induction of target genes in response to inflammation in human VSMCs. CONCLUSIONS: This study implicates H3K9me2 in regulating the proinflammatory VSMC phenotype. Our findings suggest that reduced H3K9me2 in disease enhance binding of NFκB and AP-1 (activator protein-1) transcription factors at specific inflammation-responsive genes to augment proinflammatory stimuli in VSMC. Therefore, H3K9me2-regulation could be targeted clinically to limit expression of MMPs and IL6, which are induced in vascular disease.British Heart Foundatio