Closed-Form Diffeomorphic Transformations for Time Series Alignment. (arXiv:2206.08107v1 [cs.LG])

Web: http://arxiv.org/abs/2206.08107

Time series alignment methods call for highly expressive, differentiable and
invertible warping functions which preserve temporal topology, i.e
diffeomorphisms. Diffeomorphic warping functions can be generated from the
integration of velocity fields governed by an ordinary differential equation
(ODE). Gradient-based optimization frameworks containing diffeomorphic
transformations require to calculate derivatives to the differential equation's
solution with respect to the model parameters, i.e. sensitivity analysis.
Unfortunately, deep learning frameworks typically lack
automatic-differentiation-compatible sensitivity analysis methods; and implicit
functions, such as the solution of …

arxiv lg time time series