In the context of machine unlearning, the primary challenge lies in effectively removing traces of private data from trained models while maintaining model performance and security against privacy attacks like membership inference attacks. Traditional gradient-based unlearning methods often rely on extensive historical gradients, which becomes impractical with high unlearning ratios and may reduce the effectiveness of unlearning. Addressing these limitations, we introduce Mini-Unlearning, a novel approach that capitalizes on a critical observation: unlearned parameters correlate with retrained parameters through contraction mapping. Our method, Mini-Unlearning, utilizes a minimal subset of historical gradients and leverages this contraction mapping to facilitate scalable, efficient unlearning. This lightweight, scalable method significantly enhances model accuracy and strengthens resistance to membership inference attacks. Our experiments demonstrate that Mini-Unlearning not only works under higher unlearning ratios but also outperforms existing techniques in both accuracy and security, offering a promising solution for applications requiring robust unlearning capabilities.

Missing Not at Random (MNAR) and nonnormal data are challenging to handle. Traditional missing data analytical techniques such as full information maximum likelihood estimation (FIML) may fail with nonnormal data as they are built on normal distribution assumptions. Two-Stage Robust Estimation (TSRE) does manage nonnormal data, but both FIML and TSRE are less explored in longitudinal studies under MNAR conditions with nonnormal distributions. Unlike traditional statistical approaches, machine learning approaches do not require distributional assumptions about the data. More importantly, they have shown promise for MNAR data; however, their application in longitudinal studies, addressing both Missing at Random (MAR) and MNAR scenarios, is also underexplored. This study utilizes Monte Carlo simulations to assess and compare the effectiveness of six analytical techniques for missing data within the growth curve modeling framework. These techniques include traditional approaches like FIML and TSRE, machine learning approaches by single imputation (K-Nearest Neighbors and missForest), and machine learning approaches by multiple imputation (micecart and miceForest). We investigate the influence of sample size, missing data rate, missing data mechanism, and data distribution on the accuracy and efficiency of model estimation. Our findings indicate that FIML is most effective for MNAR data among the tested approaches. TSRE excels in handling MAR data, while missForest is only advantageous in limited conditions with a combination of very skewed distributions, very large sample sizes (e.g., n larger than 1000), and low missing data rates.