{"type":"ScholarlyArticle","title":"Disentangling Direct and Indirect Interactions in Polytomous Item Response Theory Models","authors":[{"name":"Frank Nussbaum","slug":"frank-nussbaum","given":"Frank","family":"Nussbaum","affiliation":"Friedrich-Schiller University , Jena , Germany; DLR Institute of Data Science , Jena , Germany"},{"name":"Joachim Giesen","slug":"joachim-giesen","given":"Joachim","family":"Giesen","affiliation":"Friedrich-Schiller University , Jena , Germany"}],"abstract":"Measurement is at the core of scientific discovery.  However, some quantities, such as economic behavior or intelligence, do not allow for direct measurement. They represent latent constructs that require surrogate measurements. In other scenarios, non-observed quantities can influence the variables of interest. In either case, models with latent variables are needed.  Here, we investigate fused latent and graphical models that exhibit continuous latent variables and discrete observed variables. These models are characterized by a decomposition of the pairwise interaction parameter matrix into a group-sparse component of direct interactions and a low-rank component of indirect interactions due to the latent variables. We first investigate when such a decomposition is identifiable. Then, we show that fused latent and graphical models can be recovered consistently from data in the high-dimensional setting. We support our theoretical findings with experiments on synthetic and real-world data from polytomous item response theory studies.","doi":"10.24963/ijcai.2020/310","url":"https://ijcai.org/proceedings/2020/310","pdf":"https://ijcai.org/proceedings/2020/0310.pdf","markdown":"https://ijcai.org/proceedings/2020/310.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/310","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Machine Learning","track":"Main track","number":310,"pages":{"first":2241,"last":2247},"keywords":["Multidisciplinary Topics and Applications: Social Sciences","Machine Learning: Learning Graphical Models","Machine Learning: Feature Selection; Learning Sparse Models"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25230/file_25230.m3u8","length_sec":288,"provider":"hls"}],"references":[{"position":1,"raw":"[Allman et al., 2009] Elizabeth S. 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