Rough Randomness

Rough randomness extends traditional notions of randomness to encompass the vagueness and dynamism found in real-world processes, particularly those involving rough paths or irregular data. Current research focuses on developing new mathematical frameworks and computationally efficient algorithms, such as those based on randomized signatures and "large-minded reasoners," to model and analyze these complex systems. This work has implications for improving machine learning techniques, especially in clustering and time series analysis of high-dimensional data from diverse fields like finance and physics, by offering more robust and efficient approaches.