2022/03/08 by Yuqi Gu, Gu, Yuqi
Computer Science · Psychology · #Bayesian Modeling and Causal Inference #Data Visualization and Analytics #FOS: Computer and information sciences #FOS: Mathematics #Mental Health Research Topics #Methodology (stat.ME) #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2203.04403
openalex publication_date 2022/03/08 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
Identifiability of discrete statistical models with latent variables is known\nto be challenging to study, yet crucial to a model's interpretability and\nreliability. This work presents a general algebraic technique to investigate\nidentifiability of discrete models with latent and graphical components.\nSpecifically, motivated by diagnostic tests collecting multivariate categorical\ndata, we focus on discrete models with multiple binary latent variables. We\nconsider the BLESS model in which the latent variables can have arbitrary\ndependencies among themselves while the latent-to-observed measurement graph\ntakes a "star-forest" shape. We establish necessary and sufficient graphical\ncriteria for identifiability, and reveal an interesting and perhaps surprising\ngeometry of blessing-of-dependence: under the minimal conditions for generic\nidentifiability, the parameters are identifiable if and only if the latent\nvariables are not statistically independent. Thanks to this theory, we can\nperform formal hypothesis tests of identifiability in the boundary case by\ntesting marginal independence of the observed variables. In addition to the\nBLESS model, we also use the technique to show identifiability and the\nblessing-of-dependence geometry for a more flexible model, which has a general\nmeasurement graph beyond a start forest. Our results give new understanding of\nstatistical properties of graphical models with latent variables. They also\nentail useful implications for designing diagnostic tests or surveys that\nmeasure binary latent traits.\n