Learning Rotations Online

In this paper we show that the matrix von Mises-Fisher (vMF) distribution is a reasonable distribution upon which to build an online density estimation scheme for rotation matrices. We also consider a special case, the unit circle, for initial experimentation. The vector and matrix vMF distributions admit online algorithms in terms of their expectation parameters as a direct result of their exponential family nature, however proving regret bounds for these algorithms is arrested by the complexity of the cumulant functions for these distributions. In closing, we volunteer hazards and suggestions for immediate future work.

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