{"ID":22918837,"CreatedAt":"2026-09-17T01:02:08.507062015Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.17942","arxiv_id":"2609.17942","title":"On the Identifiability of Mixed Ordinal and Exponential Family Causal DAGs under Linear Parametric Models","abstract":"The problem of identifiability in linear parametric models (LPMs) whose nodes follow either an ordered logit model or a regular one-parameter exponential family is evaluated. The results go beyond classical structural equation models as well as results for nodes with observations from a homogeneous family of distributions. The main result establishes that the orientation of every edge joining an ordinal node to an exponential-family node is identifiable from the joint distribution alone at every parameter value, provided the ordinal node has at least three categories and the exponential-family node at least three points of support, with no restriction on the sufficient statistic. Converses show that both requirements are necessary: the three-category requirement is binding only for affine sufficient statistics, and the three-point requirement is binding under the canonical link. The guarantee extends to orienting every such mixed ordinal-exponential family edge of a given $d$-node undirected skeleton. Numerical experiments illustrate the theoretical results by successfully separating orientations within a Markov equivalence class, which are indistinguishable by conditional independence alone.","short_abstract":"The problem of identifiability in linear parametric models (LPMs) whose nodes follow either an ordered logit model or a regular one-parameter exponential family is evaluated. The results go beyond classical structural equation models as well as results for nodes with observations from a homogeneous family of distributi...","url_abs":"https://arxiv.org/abs/2609.17942","url_pdf":"https://arxiv.org/pdf/2609.17942v1","authors":"[\"Sambit Mishra\",\"Urbashi Mitra\"]","published":"2026-09-16T00:01:50Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"math.ST\",\"stat.ME\",\"stat.ML\"]","methods":"[]","has_code":false}