TY - JOUR
T1 - Innovation representation of stochastic processes with application to causal inference
AU - Painsky, Amichai
AU - Rosset, Saharon
AU - Feder, Meir
N1 - Publisher Copyright:
© 1963-2012 IEEE.
PY - 2020/2
Y1 - 2020/2
N2 - Typically, real-world stochastic processes are not easy to analyze. In this paper, we study the representation of different 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 on entropic causal inference, which has recently demonstrated promising performance, compared to alternative methods.
AB - Typically, real-world stochastic processes are not easy to analyze. In this paper, we study the representation of different 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 on entropic causal inference, which has recently demonstrated promising performance, compared to alternative methods.
KW - Cause effect analysis
KW - independent component analysis
KW - signal representation
KW - stochastic processes
UR - http://www.scopus.com/inward/record.url?scp=85078405545&partnerID=8YFLogxK
U2 - 10.1109/TIT.2019.2927530
DO - 10.1109/TIT.2019.2927530
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AN - SCOPUS:85078405545
SN - 0018-9448
VL - 66
SP - 1136
EP - 1154
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 2
M1 - 8758213
ER -