Moment Problem

The moment problem focuses on reconstructing probability distributions or functions from a limited set of their moments (e.g., mean, variance). Current research emphasizes developing efficient algorithms, often leveraging neural networks (like Physics-Informed Neural Networks or deep neural network priors) or Gaussian processes, to solve this inverse problem in various contexts, including signal processing, computational physics, and machine learning applications like video moment retrieval. These advancements aim to improve accuracy and computational efficiency, particularly in high-dimensional spaces and when dealing with noisy data, leading to better solutions for problems ranging from density estimation to orbit recovery. The impact spans diverse fields, offering improved modeling and analysis capabilities where direct observation is difficult or computationally expensive.