Density Estimation

Density estimation seeks to describe how probability is distributed across possible observations, which supports tasks such as anomaly detection, forecasting, scientific inference, and data generation. Approaches range from kernel density estimation and Gaussian mixtures to copulas, probabilistic circuits, normalizing flows, and diffusion or energy-based models. Researchers also develop conditional and discrete estimators, with guarantees studied through measures such as likelihood, Hellinger distance, and total variation, including in high-dimensional and privacy-constrained settings. A central challenge is balancing flexible models and accurate density estimates with tractable computation, reliable uncertainty, and performance when data are sparse, shifted, or concentrated on lower-dimensional structure.