We consider the problem of detecting a community of densely connected vertices in a high-dimensional bipartite graph of size $n_1 \times n_2$. Under the null hypothesis, the observed graph is drawn from a bipartite Erdos-Renyi distribution with connection probability $p_0$. Under the alternative hypothesis, there exists an unknown bipartite subgraph of size $k_1 \times k_2$ in which edges appear with probability $p_1 = p_0 + \delta$ for some $\delta > 0$, while all other edges outside the subgraph appear with probability $p_0$. Specifically, we provide non-asymptotic upper and lower bounds on the smallest signal strength $\delta^*$ that is both necessary and sufficient to ensure the existence of a test with small enough type one and type two errors. We also derive novel minimax-optimal tests achieving these fundamental limits when the underlying graph is sufficiently dense. Our proposed tests involve a combination of hard-thresholded nonlinear statistics of the adjacency matrix, the analysis of which may be of independent interest. In contrast with previous work, our non-asymptotic upper and lower bounds match for any configuration of $n_1,n_2, k_1,k_2$.

Multi-task learning has emerged as a powerful machine learning paradigm for integrating data from multiple sources, leveraging similarities between tasks to improve overall model performance. However, the application of multi-task learning to real-world settings is hindered by data-sharing constraints, especially in healthcare settings. To address this challenge, we propose a flexible multi-task learning framework utilizing summary statistics from various sources. Additionally, we present an adaptive parameter selection approach based on a variant of Lepski's method, allowing for data-driven tuning parameter selection when only summary statistics are accessible. Our systematic non-asymptotic analysis characterizes the performance of the proposed methods under various regimes of the source datasets' sample complexity and overlap. We demonstrate our theoretical findings and the performance of the method through extensive simulations. This work offers a more flexible tool for training related models across various domains, with practical implications in genetic risk prediction and many other fields.

SUMMARY: Differential DNA methylation and chromatin accessibility are associated with disease development, particularly cancer. Methods that allow profiling of these epigenetic mechanisms in the same reaction and at the single-molecule or single-cell level continue to emerge. However, a challenge lies in jointly visualizing and analyzing the heterogeneous nature of the data and extracting regulatory insight. Here, we present methylscaper, a visualization framework for simultaneous analysis of DNA methylation and chromatin accessibility landscapes. Methylscaper implements a weighted principal component analysis that orders DNA molecules, each providing a record of the chromatin state of one epiallele, and reveals patterns of nucleosome positioning, transcription factor occupancy, and DNA methylation. We demonstrate methylscaper's utility on a long-read, single-molecule methyltransferase accessibility protocol for individual templates (MAPit-BGS) dataset and a single-cell nucleosome, methylation, and transcription sequencing (scNMT-seq) dataset. In comparison to other procedures, methylscaper is able to readily identify chromatin features that are biologically relevant to transcriptional status while scaling to larger datasets. AVAILABILITY AND IMPLEMENTATION: Methylscaper, is implemented in R (version > 4.1) and available on Bioconductor: https://bioconductor.org/packages/methylscaper/, GitHub: https://github.com/rhondabacher/methylscaper/, and Web: https://methylscaper.com. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.