Identifying key driver genes governing biological processes such as development and disease progression remains a challenge. While existing methods can reconstruct cellular trajectories or infer static gene regulatory networks (GRNs), they often fail to quantify time-resolved regulatory effects within specific temporal windows. Here, we present Time-varying Network Driver Estimation (TNDE), a computational framework quantifying dynamic gene driver effects from single-cell snapshot data under a linear Markov assumption. TNDE leverages a shared graph attention encoder to preserve the local topological structure of the data. Furthermore, by incorporating partial optimal transport, TNDE accounts for unmatched cells arising from proliferation or apoptosis, thereby enabling trajectory alignment in non-equilibrium processes. Benchmarking on simulated datasets demonstrates that TNDE outperforms existing baseline methods across diverse complex regulatory scenarios. Applied to mouse erythropoiesis data, TNDE identifies stage-specific driver genes, the functional relevance of which is corroborated by biological validation. TNDE offers an effective quantitative tool for dissecting dynamic regulatory mechanisms underlying complex biological processes.

Causal discovery in multi-omic datasets is crucial for understanding the bigger picture of gene regulatory mechanisms, but remains challenging due to high dimensionality, differentiation of direct from indirect relationships, and hidden confounders. We introduce GENESIS (GEne Network inference from Expression SIgnals and SNPs), a constraint-based algorithm that leverages the natural causal precedence of genotypes to infer ancestral relationships in transcriptomic data. Unlike traditional causal discovery methods that start with a fully connected graph, GENESIS initialises an empty ancestrality matrix and iteratively populates it with direct, indirect or non-causal relationships using a series of provably sound marginal and conditional independence tests. By integrating genotypes as fixed causal anchors, GENESIS provides a principled ``head start'' to classical causal discovery algorithms, restricting the search space to biologically plausible edges. We test GENESIS on synthetic and real-world genomic datasets. This framework offers a powerful avenue for uncovering causal pathways in complex traits, with promising applications to functional genomics, drug discovery, and precision medicine.

Causal structure learning (CSL) refers to the task of learning causal relationships from data. Advances in CSL now allow learning of causal graphs in diverse application domains, which has the potential to facilitate data-driven causal decision-making. Real-world CSL performance depends on a number of $\textit{context-specific}$ factors, including context-specific data distributions and non-linear dependencies, that are important in practical use-cases. However, our understanding of how to assess and select CSL methods in specific contexts remains limited. To address this gap, we present $\textit{CausalRegNet}$, a multiplicative effect structural causal model that allows for generating observational and interventional data incorporating context-specific properties, with a focus on the setting of gene perturbation experiments. Using real-world gene perturbation data, we show that CausalRegNet generates accurate distributions and scales far better than current simulation frameworks. We illustrate the use of CausalRegNet in assessing CSL methods in the context of interventional experiments in biology.

Ordinary differential equation (ODE) is an important tool to study the dynamics of a system of biological and physical processes. A central question in ODE modeling is to infer the significance of individual regulatory effect of one signal variable on another. However, building confidence band for ODE with unknown regulatory relations is challenging, and it remains largely an open question. In this article, we construct post-regularization confidence band for individual regulatory function in ODE with unknown functionals and noisy data observations. Our proposal is the first of its kind, and is built on two novel ingredients. The first is a new localized kernel learning approach that combines reproducing kernel learning with local Taylor approximation, and the second is a new de-biasing method that tackles infinite-dimensional functionals and additional measurement errors. We show that the constructed confidence band has the desired asymptotic coverage probability, and the recovered regulatory network approaches the truth with probability tending to one. We establish the theoretical properties when the number of variables in the system can be either smaller or larger than the number of sampling time points, and we study the regime-switching phenomenon. We demonstrate the efficacy of the proposed method through both simulations and illustrations with two data applications.

The Genotype-Tissue Expression (GTEx) project was established to characterize genetic effects on the transcriptome across human tissues and to link these regulatory mechanisms to trait and disease associations. Here, we present analyses of the version 8 data, examining 15,201 RNA-sequencing samples from 49 tissues of 838 postmortem donors. We comprehensively characterize genetic associations for gene expression and splicing in cis and trans, showing that regulatory associations are found for almost all genes, and describe the underlying molecular mechanisms and their contribution to allelic heterogeneity and pleiotropy of complex traits. Leveraging the large diversity of tissues, we provide insights into the tissue specificity of genetic effects and show that cell type composition is a key factor in understanding gene regulatory mechanisms in human tissues.

We developed a novel statistical method to identify structural differences between networks characterized by structural equation models. We propose to reparameterize the model to separate the differential structures from common structures, and then design an algorithm with calibration and construction stages to identify these differential structures. The calibration stage serves to obtain consistent prediction by building the L2 regularized regression of each endogenous variables against pre-screened exogenous variables, correcting for potential endogeneity issue. The construction stage consistently selects and estimates both common and differential effects by undertaking L1 regularized regression of each endogenous variable against the predicts of other endogenous variables as well as its anchoring exogenous variables. Our method allows easy parallel computation at each stage. Theoretical results are obtained to establish nonasymptotic error bounds of predictions and estimates at both stages, as well as the consistency of identified common and differential effects. Our studies on synthetic data demonstrated that our proposed method performed much better than independently constructing the networks. A real data set is analyzed to illustrate the applicability of our method.