Inductive Geometric Matrix Midranges

Geometric Learning of Hidden Markov Models via a Method of Moments Algorithm

“…The development and analysis of statistical procedures and optimization algorithms on manifolds and nonlinear spaces more broadly have been the subject of intense and growing research interest in recent decades due to the ubiquity of manifold-valued data in a wide range of applications [17][18][19][20][21][22][23]. Since the application of Euclidean algorithms to such data often has a significantly negative impact on the accuracy and interpretability of the results, it is necessary to devise algorithms that respect the intrinsic geometry of the data.…”

“…which yields a relative approximation error of P − P F P F = 0.050 (23) with respect to the Frobenius norm. The mean error in the estimated transition probabilities is…”