We address the common yet often-overlooked selection bias in interventional studies, where subjects are selectively enrolled into experiments. For instance, participants in a drug trial are usually patients of the relevant disease; A/B tests on mobile applications target existing users only, and gene perturbation studies typically focus on specific cell types, such as cancer cells. Ignoring this bias leads to incorrect causal discovery results. Even when recognized, the existing paradigm for interventional causal discovery still fails to address it. This is because subtle differences in _when_ and _where_ interventions happen can lead to significantly different statistical patterns. We capture this dynamic by introducing a graphical model that explicitly accounts for both the observed world (where interventions are applied) and the counterfactual world (where selection occurs while interventions have not been applied). We characterize the Markov property of the model, and propose a provably sound algorithm to identify causal relations as well as selection mechanisms up to the equivalence class, from data with soft interventions and unknown targets. Through synthetic and real-world experiments, we demonstrate that our algorithm effectively identifies true causal relations despite the presence of selection bias.

Advances in single-cell sequencing have enabled high-resolution profiling of diverse molecular modalities, while integrating unpaired multi-omics single-cell data remains challenging. Existing approaches either rely on pair information or prior correspondences, or require computing a global pairwise coupling matrix, limiting their scalability and flexibility. In this paper, we introduce a scalable and flexible generative framework called single-cell Multi-omics Regularized Disentangled Representations (scMRDR) for unpaired multi-omics integration. Specifically, we disentangle each cell’s latent representations into modality-shared and modality-specific components using a well-designed $\beta$-VAE architecture, which are augmented with isometric regularization to preserve intra-omics biological heterogeneity, adversarial objective to encourage cross-modal alignment, and masked reconstruction loss strategy to address the issue of missing features across modalities. Our method achieves excellent performance on benchmark datasets in terms of batch correction, modality alignment, and biological signal preservation. Crucially, it scales effectively to large-scale datasets and supports integration of more than two omics, offering a powerful and flexible solution for large-scale multi-omics data integration and downstream biological discovery.

Bayesian methods are widely used in the GWAS meta-analysis. But the considerable consumption in both computing time and memory space poses great challenges for large-scale meta-analyses. In this research, we propose an algorithm named SMetABF to rapidly obtain the optimal ABF in the GWAS meta-analysis, where shotgun stochastic search (SSS) is introduced to improve the Bayesian GWAS meta-analysis framework, MetABF. Simulation studies confirm that SMetABF performs well in both speed and accuracy, compared to exhaustive methods and MCMC. SMetABF is applied to real GWAS datasets to find several essential loci related to Parkinson's disease (PD) and the results support the underlying relationship between PD and other autoimmune disorders. Developed as an R package and a web tool, SMetABF will become a useful tool to integrate different studies and identify more variants associated with complex traits.

With the development of genome-wide association studies, how to gain information from a large scale of data has become an issue of common concern, since traditional methods are not fully developed to solve problems such as identifying loci-to-loci interactions (also known as epistasis). Previous epistatic studies mainly focused on local information with a single outcome (phenotype), while in this paper, we developed a two-stage global search algorithm, Greedy Equivalence Search with Local Modification (GESLM), to implement a global search of directed acyclic graph in order to identify genome-wide epistatic interactions with multiple outcome variables (phenotypes) in a case-control design. GESLM integrates the advantages of score-based methods and constraint-based methods to learn the phenotype-related Bayesian network and is powerful and robust to find the interaction structures that display both genetic associations with phenotypes and gene interactions. We compared GESLM with some common phenotype-related loci detecting methods in simulation studies. The results showed that our method improved the accuracy and efficiency compared with others, especially in an unbalanced case-control study. Besides, its application on the UK Biobank dataset suggested that our algorithm has great performance when handling genome-wide association data with more than one phenotype.