High-dimensional genomic datasets contain complex patterns shaped by substantial biological noise, which pose major challenges for predictive modeling in genetics and breeding. Residual neural networks (ResNets) provide a powerful framework for capturing nonlinear genomic effects, but often overfit in settings where marker numbers greatly exceed sample sizes. As a solution, a range of regularization methods have been proposed. One promising approach relies on the proximal mapping technique, which is computationally efficient since it can be directly incorporated into the optimization algorithm. However, the performance of ResNets with various convex or non-convex proximal regularizers remains under-explored on high-dimensional data. In this study, we propose an extended stochastic adaptive proximal gradient ResNet method that can handle both convex and non-convex regularizers that range from $L_{0}$ to $L_{\infty }$ and give more analysis of the convergence guarantee for the convex and non-convex regularizers. Moreover, we evaluate the prediction performance in a supervised regression setting on four real high-dimensional genomic datasets from mice, pig, wheat, and loblolly pine. For comparison, we also implement and evaluate traditional sparse linear proximal methods with the same regularizers, as well as LightGBM. Experimental results demonstrate that an 18-layer ResNet with $L_{\frac{1}{2}}$ regularization outperforms other configurations on both mice and pig datasets. For the wheat and loblolly pine data, the 15-layer ResNet $L_{\frac{1}{2}}$ configuration achieves the lowest test mean squared errors and the highest distance correlation (dCor). These findings highlight the effectiveness of the regularized adaptive proximal gradient ResNet method and its potential for prediction tasks on high-dimensional genomic data.

Capacitated spatial clustering, a type of unsupervised machine learning method, is often used to tackle problems in compressing data, classification, logistic optimization and infrastructure optimization. Depending on the application at hand, a multitude of extensions to the clustering problem may be necessary. In this article, we propose a number of novel extensions to PACK, a recent capacitated partitional spatial clustering method which uses an optimization algorithm that is based on linear programming tasks. These extensions relate to the relocation and location preference of cluster centers, outliers, and non-spatial attributes, and they can be considered jointly. In the context of edge server placement, these improve the spatial location of servers while considering, for example, application placement on the servers in response to spatial application usage patterns. We demonstrate the usefulness of an extended version of PACK with an example with simulated data, as well as a real world example in edge server placement for a city region with various different setups. These setups are evaluated with summary statistics about spatial proximity and attribute similarity. As a result, the similarity of the clusters was improved by 53% at best while simultaneously the proximity degraded only by 18%. The extensions provide valuable means for including non-spatial information in the cluster analysis, and to attain better overall proximity and similarity.

MOTIVATION: Genome-wide association studies (GWAS) have been successful in identifying genomic loci associated with complex traits. Genetic fine-mapping aims to detect independent causal variants from the GWAS-identified loci, adjusting for linkage disequilibrium patterns. RESULTS: We present "FiniMOM" (fine-mapping using a product inverse-moment prior), a novel Bayesian fine-mapping method for summarized genetic associations. For causal effects, the method uses a nonlocal inverse-moment prior, which is a natural prior distribution to model non-null effects in finite samples. A beta-binomial prior is set for the number of causal variants, with a parameterization that can be used to control for potential misspecifications in the linkage disequilibrium reference. The results of simulations studies aimed to mimic a typical GWAS on circulating protein levels show improved credible set coverage and power of the proposed method over current state-of-the-art fine-mapping method SuSiE, especially in the case of multiple causal variants within a locus. AVAILABILITY AND IMPLEMENTATION: https://vkarhune.github.io/finimom/.