Innovation Representation of Stochastic Processes with Application to Causal Inference
Abstract
Typically, real-world stochastic processes are not easy to analyze. In this work we study the representation of any stochastic process as a memoryless innovation process triggering a dynamic system. We show that such a representation is always feasible for innovation processes taking values over a continuous set. However, the problem becomes more challenging when the alphabet size of the innovation is finite. In this case, we introduce both lossless and lossy frameworks, and provide closed-form solutions and practical algorithmic methods. In addition, we discuss the properties and uniqueness of our suggested approach. Finally, we show that the innovation representation problem has many applications. We focus our attention to Entropic Causal Inference, which has recently demonstrated promising performance, compared to alternative methods.
Cite
@article{arxiv.1811.10071,
title = {Innovation Representation of Stochastic Processes with Application to Causal Inference},
author = {Amichai Painsky and Saharon Rosset and Meir Feder},
journal= {arXiv preprint arXiv:1811.10071},
year = {2018}
}
Comments
arXiv admin note: text overlap with arXiv:1611.04035 by other authors