Spline Interpolation on the Manifold of Probability Density Functions

This chapter delves into the challenge of spline interpolations on \(\mathcal {P}\) , the space of probability density functions, especially when dealing with a limited set of observations \(p_i \in \mathcal {P}\) . Fitting a set of PDFs points constitutes a vital area of research in theoretical and computational statistics, with widespread applications in fields such as machine learning, medical imaging, computer vision, signal/video processing, and beyond