Score-based generative models (SGMs) aim at generating samples from a target distribution by approximating the reverse-time dynamics of a stochastic differential equation. Despite their strong empirical performance, classical samplers initialized from a Gaussian distribution require a long time horizon noising typically inducing a large number of discretization steps and high computational cost. In this work, we present a Kullback-Leibler convergence analysis of Variance Exploding diffusion samplers that highlights the critical role of the backward process initialization. Based on this result, we propose a theoretically grounded sampling strategy that learns the reverse-time initialization, directly minimizing the initialization error. The resulting procedure is independent of the specific score training procedure, network architecture, and discretization scheme. Experiments on toy distributions and benchmark datasets demonstrate competitive or improved generative quality while using significantly fewer sampling steps.

Data privacy is important in the AI era, and differential privacy (DP) is one of the golden solutions. However, DP is typically applicable only if data have a bounded underlying distribution. We address this limitation by leveraging second-moment information from a small amount of public data. We propose Public-moment-guided Truncation (PMT), which transforms private data using the public second-moment matrix and applies a principled truncation whose radius depends only on non-private quantities: data dimension and sample size. This transformation yields a well-conditioned second-moment matrix, enabling its inversion with a significantly strengthened ability to resist the DP noise. Furthermore, we demonstrate the applicability of PMT by using penalized and generalized linear regressions. Specifically, we design new loss functions and algorithms, ensuring that solutions in the transformed space can be mapped back to the original domain. We have established improvements in the models' DP estimation through theoretical error bounds, robustness guarantees, and convergence results, attributing the gains to the conditioning effect of PMT. Experiments on synthetic and real datasets confirm that PMT substantially improves the accuracy and stability of DP models.

Linear contextual bandits represent a fundamental class of models with numerous real-world applications, and it is critical to developing algorithms that can effectively manage noise with unknown variance, ensuring provable guarantees for both worst-case constant-variance noise and deterministic reward scenarios.

Independent Component Analysis (ICA) was introduced in the 1980's as a model