Cumulative Distribution Function

The cumulative distribution function (CDF) describes the probability that a random variable takes a value less than or equal to a given value, serving as a fundamental tool in probability and statistics. Current research focuses on efficiently computing and modeling CDFs, particularly for multivariate and high-dimensional data, employing techniques like probabilistic circuits, neural networks (including transformers and normalizing flows), and orthogonal polynomials. These advancements improve the accuracy and efficiency of probabilistic inference, enabling better uncertainty quantification in diverse applications such as survival analysis, time series forecasting, and robust machine learning under distribution shifts.