Visualizing multiparameter probabilistic models in Minkowski space

Many complexity-rich dynamical systems necessitate the use of a multiparameter probabilistic model to capture the observed system behavior succinctly. Unfortunately, multiparameter probabilistic models of large systems suffer from the curse of dimensionality. To alleviate this problem, we recently proposed a manifold embedding approach that borrows a concept from special relativity: the intensive symmetrized Kullback Liebler (isKL) embedding [1]. This approach generates an analytically tractable embedding for model predictions in Minkowski space, for most common probability distributions and statistical models. In principle, this technique not only offers a low dimensional representation of high dimensional data, but it also allows one to uncover hidden exponential families that describe experiments or simulations. In this talk, we will showcase how this technique can be combined with a probabilistic neural network to study cartilage tissue and bird song data.

[1] Teoh, et al. Phys. Rev. Research 2.3 (2020): 033221