Quantile Estimation

Quantile estimation focuses on estimating specific percentiles (quantiles) of a probability distribution, offering a more comprehensive view than simply focusing on the mean. Current research explores efficient algorithms for distributed and high-dimensional data, including adaptations for manifold-valued data and the use of neural networks and optimal transport theory. These advancements are crucial for robust decision-making in various fields, improving the reliability of predictions in applications ranging from risk assessment and reinforcement learning to environmental monitoring and data analysis. The development of improved algorithms with strong theoretical guarantees, particularly for large-scale and complex data, remains a key focus.