Deep Sufficient Representation Learning via Mutual Information

We propose a mutual information-based sufficient representation learning (MSRL) approach, which uses the variational formulation of the mutual information and leverages the approximation power of deep neural networks. MSRL learns a sufficient representation with the maximum mutual information with the response and a user-selected distribution. It can easily handle multi-dimensional continuous or categorical response variables. MSRL is shown to be consistent in the sense that the conditional probability density function of the response variable given the learned representation converges to the conditional probability density function of the response variable given the predictor. Non-asymptotic error bounds for MSRL are also established under suitable conditions. To establish the error bounds, we derive a generalized Dudley's inequality for an order-two U-process indexed by deep neural networks, which may be of independent interest. We discuss how to determine the intrinsic dimension of the underlying data distribution. Moreover, we evaluate the performance of MSRL via extensive numerical experiments and real data analysis and demonstrate that MSRL outperforms some existing nonlinear sufficient dimension reduction methods.Comment: 43 pages, 6 figures and 5 table

SUVH1, a Su(var)3-9 family member, promotes the expression of genes targeted by DNA methylation.

Transposable elements are found throughout the genomes of all organisms. Repressive marks such as DNA methylation and histone H3 lysine 9 (H3K9) methylation silence these elements and maintain genome integrity. However, how silencing mechanisms are themselves regulated to avoid the silencing of genes remains unclear. Here, an anti-silencing factor was identified using a forward genetic screen on a reporter line that harbors a LUCIFERASE (LUC) gene driven by a promoter that undergoes DNA methylation. SUVH1, a Su(var)3-9 homolog, was identified as a factor promoting the expression of the LUC gene. Treatment with a cytosine methylation inhibitor completely suppressed the LUC expression defects of suvh1, indicating that SUVH1 is dispensable for LUC expression in the absence of DNA methylation. SUVH1 also promotes the expression of several endogenous genes with promoter DNA methylation. However, the suvh1 mutation did not alter DNA methylation levels at the LUC transgene or on a genome-wide scale; thus, SUVH1 functions downstream of DNA methylation. Histone H3 lysine 4 (H3K4) trimethylation was reduced in suvh1; in contrast, H3K9 methylation levels remained unchanged. This work has uncovered a novel, anti-silencing function for a member of the Su(var)3-9 family that has previously been associated with silencing through H3K9 methylation