Multivariate stochastic modeling for transcriptional dynamics with cell-specific latent time using SDEvelo.

Recently, RNA velocity has driven a paradigmatic change in single-cell RNA sequencing (scRNA-seq) studies, allowing the reconstruction and prediction of directed trajectories in cell differentiation and state transitions. Most existing methods of dynamic modeling use ordinary differential equations (ODE) for individual genes without applying multivariate approaches. However, this modeling strategy inadequately captures the intrinsically stochastic nature of transcriptional dynamics governed by a cell-specific latent time across multiple genes, potentially leading to erroneous results.

Approximate Policy Iteration With Deep Minimax Average Bellman Error Minimization.

In this work, we investigate the utilization of deep approximate policy iteration (DAPI) in estimating the optimal action-value function Q within the context of reinforcement learning, employing rectified linear unit (ReLU) ResNet as the underlying framework. The iterative process of DAPI incorporates the minimax average Bellman error minimization principle. It employs ReLU ResNet to estimate the fixed point of the Bellman equation, which is aligned with the estimated greedy policy.

Newton-Raphson Meets Sparsity: Sparse Learning Via a Novel Penalty and a Fast Solver.

In machine learning and statistics, the penalized regression methods are the main tools for variable selection (or feature selection) in high-dimensional sparse data analysis. Due to the nonsmoothness of the associated thresholding operators of commonly used penalties such as the least absolute shrinkage and selection operator (LASSO), the smoothly clipped absolute deviation (SCAD), and the minimax concave penalty (MCP), the classical Newton-Raphson algorithm cannot be used. In this article, we propose a cubic Hermite interpolation penalty (CHIP) with a smoothing thresholding operator.