We consider the problem of projecting a vector onto the so-called k-capped simplex, which is a hyper-cube cut by a hyperplane. For an n-dimensional input vector with bounded elements, we found that a simple algorithm based on Newton's method is able to solve the projection problem to high precision with a complexity roughly about O(n), which has a much lower computational cost compared with the existing sorting-based methods proposed in the literature. We provide a theory for partial explanation and justification of the method. We demonstrate that the proposed algorithm can produce a solution of the projection problem with high precision on large scale datasets, and the algorithm is able to significantly outperform the state-of-the-art methods in terms of runtime (about 6-8 times faster than a commercial software with respect to CPU time for input vector with 1 million variables or more). We further illustrate the effectiveness of the proposed algorithm on solving sparse regression in a bioinformatics problem. Empirical results on the GWAS dataset (with 1,500,000 single-nucleotide polymorphisms) show that, when using the proposed method to accelerate the Projected Quasi-Newton (PQN) method, the accelerated PQN algorithm is able to handle huge-scale regression problem and it is more efficient (about 3-6 times faster) than the current state-of-the-art methods.

A plant's phenome is defined by its physical and biochemical characteristics, and is the result of the interaction of its genome and its environment.

Weconsidertwoscenarios where causal effects are estimable.

Genomic Selection (GS) uses whole-genome information to predict crop phenotypes and accelerate breeding. Traditional GS methods, however, struggle with prediction accuracy for complex traits and large datasets. We propose DPCformer, a deep learning model integrating convolutional neural networks with a self-attention mechanism to model complex genotype-phenotype relationships. We applied DPCformer to 13 traits across five crops (maize, cotton, tomato, rice, chickpea). Our approach uses an 8-dimensional one-hot encoding for SNP data, ordered by chromosome, and employs the PMF algorithm for feature selection. Evaluations show DPCformer outperforms existing methods. In maize datasets, accuracy for traits like days to tasseling and plant height improved by up to 2.92%. For cotton, accuracy gains for fiber traits reached 8.37%. On small-sample tomato data, the Pearson Correlation Coefficient for a key trait increased by up to 57.35%. In chickpea, the yield correlation was boosted by 16.62%. DPCformer demonstrates superior accuracy, robustness in small-sample scenarios, and enhanced interpretability, providing a powerful tool for precision breeding and addressing global food security challenges.

Lung cancer (LC) is the third most common cancer and the leading cause of cancer deaths in the US. Although smoking is the primary risk factor, the occurrence of LC in never-smokers and familial aggregation studies highlight a genetic component. Genetic biomarkers identified through genome-wide association studies (GWAS) are promising tools for assessing LC risk. We introduce HEMERA (Human-Explainable Transformer Model for Estimating Lung Cancer Risk using GWAS Data), a new framework that applies explainable transformer-based deep learning to GWAS data of single nucleotide polymorphisms (SNPs) for predicting LC risk. Unlike prior approaches, HEMERA directly processes raw genotype data without clinical covariates, introducing additive positional encodings, neural genotype embeddings, and refined variant filtering. A post hoc explainability module based on Layer-wise Integrated Gradients enables attribution of model predictions to specific SNPs, aligning strongly with known LC risk loci. Trained on data from 27,254 Million Veteran Program participants, HEMERA achieved >99% AUC (area under receiver characteristics) score. These findings support transparent, hypothesis-generating models for personalized LC risk assessment and early intervention.

Single nucleotide polymorphism (SNP) datasets are fundamental to genetic studies but pose significant privacy risks when shared. The correlation of SNPs with each other makes strong adversarial attacks such as masked-value reconstruction, kin, and membership inference attacks possible. Existing privacy-preserving approaches either apply differential privacy to statistical summaries of these datasets or offer complex methods that require post-processing and the usage of a publicly available dataset to suppress or selectively share SNPs. In this study, we introduce an innovative framework for generating synthetic SNP sequence datasets using samples derived from time-inhomogeneous hidden Markov models (TIHMMs). To preserve the privacy of the training data, we ensure that each SNP sequence contributes only a bounded influence during training, enabling strong differential privacy guarantees. Crucially, by operating on full SNP sequences and bounding their gradient contributions, our method directly addresses the privacy risks introduced by their inherent correlations. Through experiments conducted on the real-world 1000 Genomes dataset, we demonstrate the efficacy of our method using privacy budgets of $\varepsilon \in [1, 10]$ at $δ=10^{-4}$. Notably, by allowing the transition models of the HMM to be dependent on the location in the sequence, we significantly enhance performance, enabling the synthetic datasets to closely replicate the statistical properties of non-private datasets. This framework facilitates the private sharing of genomic data while offering researchers exceptional flexibility and utility.

Neural Processes combine the strengths of neural networks and Gaussian processes to achieve both flexible learning and fast prediction in stochastic processes.