Probability Density Function

Probability density functions (PDFs) describe the likelihood of a continuous random variable taking on a given value, a fundamental concept across numerous scientific fields. Current research focuses on developing robust and efficient methods for estimating PDFs from data, including novel algorithms based on maximum likelihood estimation, kernel methods, and deep learning architectures like transformers and normalizing flows. These advancements are crucial for improving accuracy in diverse applications such as survival analysis, causal inference, and physical modeling, where accurate PDF estimation is essential for reliable predictions and informed decision-making. Furthermore, research explores the use of PDFs in novel contexts, such as representing point clouds and improving robustness in machine learning tasks.