Interaction Models and Generalized Score Matching for Compositional Data

Shiqing Yu, Mathias Drton, Ali Shojaie
Proceedings of the Second Learning on Graphs Conference, PMLR 231:20:1-20:25, 2024.

Abstract

Applications such as the analysis of microbiome data have led to renewed interest in statistical methods for compositional data, i.e., data in the form of relative proportions. In particular, there is considerable interest in modelling interactions among such proportions. To this end we propose a class of exponential family models that accommodate arbitrary patterns of pairwise interaction. Special cases include Dirichlet distributions as well as Aitchison’s additive logistic normal distributions. Generally, the distributions we consider have a density that features a difficult-to-compute normalizing constant. To circumvent this issue, we design effective estimation methods based on generalized versions of score matching.

Cite this Paper

BibTeX
@InProceedings{pmlr-v231-yu24a, title = {Interaction Models and Generalized Score Matching for Compositional Data}, author = {Yu, Shiqing and Drton, Mathias and Shojaie, Ali}, booktitle = {Proceedings of the Second Learning on Graphs Conference}, pages = {20:1--20:25}, year = {2024}, editor = {Villar, Soledad and Chamberlain, Benjamin}, volume = {231}, series = {Proceedings of Machine Learning Research}, month = {27--30 Nov}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v231/yu24a/yu24a.pdf}, url = {https://proceedings.mlr.press/v231/yu24a.html}, abstract = {Applications such as the analysis of microbiome data have led to renewed interest in statistical methods for compositional data, i.e., data in the form of relative proportions. In particular, there is considerable interest in modelling interactions among such proportions. To this end we propose a class of exponential family models that accommodate arbitrary patterns of pairwise interaction. Special cases include Dirichlet distributions as well as Aitchison’s additive logistic normal distributions. Generally, the distributions we consider have a density that features a difficult-to-compute normalizing constant. To circumvent this issue, we design effective estimation methods based on generalized versions of score matching.} }
Endnote
%0 Conference Paper %T Interaction Models and Generalized Score Matching for Compositional Data %A Shiqing Yu %A Mathias Drton %A Ali Shojaie %B Proceedings of the Second Learning on Graphs Conference %C Proceedings of Machine Learning Research %D 2024 %E Soledad Villar %E Benjamin Chamberlain %F pmlr-v231-yu24a %I PMLR %P 20:1--20:25 %U https://proceedings.mlr.press/v231/yu24a.html %V 231 %X Applications such as the analysis of microbiome data have led to renewed interest in statistical methods for compositional data, i.e., data in the form of relative proportions. In particular, there is considerable interest in modelling interactions among such proportions. To this end we propose a class of exponential family models that accommodate arbitrary patterns of pairwise interaction. Special cases include Dirichlet distributions as well as Aitchison’s additive logistic normal distributions. Generally, the distributions we consider have a density that features a difficult-to-compute normalizing constant. To circumvent this issue, we design effective estimation methods based on generalized versions of score matching.
APA
Yu, S., Drton, M. & Shojaie, A.. (2024). Interaction Models and Generalized Score Matching for Compositional Data. Proceedings of the Second Learning on Graphs Conference, in Proceedings of Machine Learning Research 231:20:1-20:25 Available from https://proceedings.mlr.press/v231/yu24a.html.

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