[26] Bernd Streitberg. Lancaster interactions revisited. The Annals of Statistics, pages 1878-1885, 1990.
[27] Edward H Ip, Yuchung J Wang, and Yeong-nan Yeh. Structural decompositions of multivariate distributions with applications in moment and cumulant. Journal of multivariate analysis, 89(1):119-134, 2004.
[28] Arthur Gretton, Kenji Fukumizu, Choon Teo, Le Song, Bernhard Schölkopf, and Alex Smola. A kernel statistical test of independence. Advances in neural information processing systems, 20, 2007.
[29] Kacper Chwialkowski and Arthur Gretton. A kernel independence test for random processes. In International Conference on Machine Learning, pages 1422-1430. PMLR, 2014.
[30] Felix Laumann, Julius von Kugelgen, and Mauricio Barahona. Kernel two-sample and independence tests for nonstationary random processes. Engineering Proceedings, 5(1), 2021.
[31] Felix Laumann, Julius von Kugelgen, and Maurizio Barahona. Non-linear interlinkages and key objectives amongst the paris agreement and the sustainable development goals. arXiv preprint arXiv:2004.09318, 2020.
[32] Niklas Pfister, Peter Buhlmann, Bernhard Scholkopf, and Jonas Peters. Kernel-based tests for joint independence. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 80(1):5-31, 2018.
[33] Zhaolu Liu, Robert L. Peach, Felix Laumann, Sara Vallejo Mengod, and Mauricio Barahona. Kernel-based joint independence tests for multivariate stationary and nonstationary time-series. arXiv preprint arXiv:2305.08529, 2023.
[34] Dino Sejdinovic, Arthur Gretton, and Wicher Bergsma. A kernel test for three-variable interactions. Advances in Neural Information Processing Systems, 26, 2013.
[35] Paul K Rubenstein, Kacper P Chwialkowski, and Arthur Gretton. A kernel test for three-variable interactions with random processes. arXiv preprint arXiv:1603.00929, 2016.
[36] Garrett Birkhoff. Lattice theory, volume 25. American Mathematical Soc., 1940.
[37] TP Speed. Cumulants and partition lattices 1. Australian Journal of Statistics, 25(2):378-388, 1983.
[38] Ginestra Bianconi. Higher-order networks. Cambridge University Press, 2021.
[39] S-I Amari. Information geometry on hierarchy of probability distributions. IEEE transactions on information theory, 47(5):1701-1711, 2001.
[40] Mahito Sugiyama, Hiroyuki Nakahara, and Koji Tsuda. Tensor balancing on statistical manifold. In International Conference on Machine Learning, pages 3270-3279. PMLR, 2017.
[41] Edward H Ip, Yuchung J Wang, and Yeong-nan Yeh. Some equivalence results concerning multiplicative lattice decompositions of multivariate densities. Journal of multivariate analysis, 84(2):403-409, 2003.
[42] Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Scholkopf, and Alexander Smola. A kernel two-sample test. The Journal of Machine Learning Research, 13(1):723-773, 2012.
[43] George A Gratzer. Lattice theory: foundation, volume 2. Springer, 2011.
[44] Peter McCullagh. Tensor methods in statistics. Chapman and Hall/CRC, 2018.
[45] Eric Temple Bell. The iterated exponential integers. Annals of Mathematics, pages 539-557, 1938.
[46] Miklos Bona and Istvan Mezo. Real zeros and partitions without singleton blocks. European Journal of Combinatorics, 51:500-510, 2016.