LapDDPM is a conditional Graph Diffusion Probabilistic Model that generates high‑fidelity, biologically plausible single‑cell RNA sequencing data. It incorporates graph‑based inductive biases and a spectral adversarial perturbation mechanism to enforce robustness against structural noise, effectively acting as a Distributionally Robust Optimization framework. The model extends to spatial transcriptomics and multi‑modal data, and experimental results on datasets such as PBMC3K, Dentate Gyrus, HLCA, Visium, and 10x Multiome show it outperforms state‑of‑the‑art baselines in distribution matching, manifold preservation, and downstream utility.
By Lorenzo Bini, Stephane Marchand-Maillet
arXiv:2608. 11269v1 Announce Type: cross Abstract: Omics datasets, particularly single-cell RNA sequencing data, are high-dimensional, sparse, noisy, and dominated by zero values, making faithful low-dimensional representation challenging.
By Fenosoa Randrianjatovo, Maya Saleh, Simon Girard, Amadou Barry
arXiv:2407. 01718v2 Announce Type: replace-cross Abstract: Embedding high-dimensional data into a low-dimensional space is an indispensable component of data analysis.
By Boris Landa, Yuval Kluger, Rong Ma
arXiv:2608. 04827v1 Announce Type: cross Abstract: We introduce the Intrinsic Hybrid Latent Diffusion Model (ILDM), a generative framework that integrates probabilistic dimensionality reduction with geometry-aware diffusion on unknown manifolds.
By Yizhu Wang, Mu Niu, Xiaochen Yang
The paper introduces the Sparse Landmark Embedding (SLE) kernel, a new framework that removes the need for conditionally negative definite (CND) distance measures in kernel methods and Gaussian Processes. By embedding each input into a sparse feature vector using compactly supported bump functions centered at all training points, any standard positive semi-definite (PSD) kernel can be applied in this embedding space, guaranteeing PSD for arbitrary distance measures. The authors provide theoretical guarantees on PSD, sparsity, stability, and universal approximation, and show through experiments with geodesic and Wasserstein distances that the SLE kernel matches or surpasses domain-specific baselines in predictive accuracy and uncertainty quantification.
By Marcus M. Noack, Maher B. Alghalayini, Mark D. Risser
arXiv:2506. 22228v2 Announce Type: replace-cross Abstract: Single-cell sequencing is revolutionizing biology by enabling detailed investigations of cell-state transitions.
By Rong Ma, Xi Li, Jingyuan Hu, Bin Yu