Image inpainting aims to restore missing regions by leveraging surrounding spatial context, where nearby pixels provide crucial structural cues and distant regions offer complementary semantic guidance. To jointly model these complementary dependencies, this paper proposes Hierarchical Sequential Context Modeling (HSCM), a novel inpainting framework that employs state-space models for multi-scale autoregressive sequence modeling. Unlike existing single-scale SSM-based approaches, HSCM explicitly separates pixel-level and semanticlevel modeling into two complementary branches. The Local Perception Unit preserves fine-grained textures, and the Global Compensation Unit propagates high-level semantics across patches to enhance overall coherence. The asynchronous hierarchical design first reconstructs local textures and then performs semantic compensation, achieving notable performance gains with minimal computational overhead. Leveraging its four-directional architecture, HSCM maintains linear computational growth with spatial resolution and effectively establishes a comprehensive global receptive field. Furthermore, a Cross-Gated Feedforward Network is proposed to alleviate patch boundary artifacts and enhance inter-channel feature consistency. Built upon a multi-scale encoder–decoder architecture, HSCM delivers state-of-the-art inpainting quality and robust generalization across diverse benchmarks, including CelebA-HQ, FFHQ, Paris Street View, and Places2.

As opaque black-box predictive models such as neural networks become more prevalent, the need to develop interpretations for these models is of great interest. The concept of $\textit{variable importance}$ is an interpretability measure that applies to any predictive model and assesses how much a variable or set of variables improves prediction performance. When the number of variables is large, estimating variable importance presents a significant challenge because re-training neural networks or other black-box algorithms requires significant additional computation. In this paper, we address this challenge for algorithms using gradient descent and gradient boosting (e.g. neural networks, gradient-boosted decision trees). By using the ideas of early stopping of gradient-based methods in combination with warm-start using the $\textit{dropout}$ method, we develop a scalable method to estimate variable importance for any algorithm that can be expressed as an $\textit{iterative kernel update equation}$. Importantly, we provide theoretical guarantees by using the theory for early stopping of kernel-based methods for neural networks with sufficient large width and gradient-boosting decision trees that use symmetric tree as a weaker learner. We also demonstrate the efficacy of our methods through simulations and a real data example which illustrates the computational benefit of early stopping rather than fully re-training the model as well as the increased accuracy of taking initial steps from the dropout solution.

The single-cell multiomics technologies provide an unprecedented opportunity to study the cellular heterogeneity from different layers of transcriptional regulation. However, the datasets generated from these technologies tend to have high levels of noise, making data analysis challenging. Here, we propose jointly semi-orthogonal nonnegative matrix factorization (JSNMF), which is a versatile toolkit for the integrative analysis of transcriptomic and epigenomic data profiled from the same cell. JSNMF enables data visualization and clustering of the cells and also facilitates downstream analysis, including the characterization of markers and functional pathway enrichment analysis. The core of JSNMF is an unsupervised method based on JSNMF, where it assumes different latent variables for the two molecular modalities, and integrates the information of transcriptomic and epigenomic data with consensus graph fusion, which better tackles the distinct characteristics and levels of noise across different molecular modalities in single-cell multiomics data. We applied JSNMF to single-cell multiomics datasets from different tissues and different technologies. The results demonstrate the superior performance of JSNMF in clustering and data visualization of the cells. JSNMF also allows joint analysis of multiple single-cell multiomics experiments and single-cell multiomics data with more than two modalities profiled on the same cell. JSNMF also provides rich biological insight on the markers, cell-type-specific region-gene associations and the functions of the identified cell subpopulation.

MOTIVATION: The advancement in technologies and the growth of available single-cell datasets motivate integrative analysis of multiple single-cell genomic datasets. Integrative analysis of multimodal single-cell datasets combines complementary information offered by single-omic datasets and can offer deeper insights on complex biological process. Clustering methods that identify the unknown cell types are among the first few steps in the analysis of single-cell datasets, and they are important for downstream analysis built upon the identified cell types. RESULTS: We propose scAMACE for the integrative analysis and clustering of single-cell data on chromatin accessibility, gene expression and methylation. We demonstrate that cell types are better identified and characterized through analyzing the three data types jointly. We develop an efficient Expectation-Maximization algorithm to perform statistical inference, and evaluate our methods on both simulation study and real data applications. We also provide the GPU implementation of scAMACE, making it scalable to large datasets. AVAILABILITY AND IMPLEMENTATION: The software and datasets are available at https://github.com/cuhklinlab/scAMACE_py (python implementation) and https://github.com/cuhklinlab/scAMACE (R implementation). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: Combination therapies have been widely used to treat cancers. However, it is cost and time consuming to experimentally screen synergistic drug pairs due to the enormous number of possible drug combinations. Thus, computational methods have become an important way to predict and prioritize synergistic drug pairs. RESULTS: We proposed a Deep Tensor Factorization (DTF) model, which integrated a tensor factorization method and a deep neural network (DNN), to predict drug synergy. The former extracts latent features from drug synergy information while the latter constructs a binary classifier to predict the drug synergy status. Compared to the tensor-based method, the DTF model performed better in predicting drug synergy. The area under precision-recall curve (PR AUC) was 0.58 for DTF and 0.24 for the tensor method. We also compared the DTF model with DeepSynergy and logistic regression models, and found that the DTF outperformed the logistic regression model and achieved similar performance as DeepSynergy using several performance metrics for classification task. Applying the DTF model to predict missing entries in our drug-cell-line tensor, we identified novel synergistic drug combinations for 10 cell lines from the 5 cancer types. A literature survey showed that some of these predicted drug synergies have been identified in vivo or in vitro. Thus, the DTF model could be a valuable in silico tool for prioritizing novel synergistic drug combinations. AVAILABILITY AND IMPLEMENTATION: Source code and data are available at https://github.com/ZexuanSun/DTF-Drug-Synergy. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.