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Title: Generalized score matching for regression Authors:  Jiazhen Xu - Australian National University (Australia) [presenting]
Tao Zou - The Australian National University (Australia)
Andrew Wood - Australian National University (Australia)
Janice Scealy - Australian National University (Australia)
Abstract: Many probabilistic models are developed with an intractable normalizing constant and have been extended to contain covariates. Since the evaluation of the exact full likelihood is difficult or even impossible for these models, score matching was proposed to avoid explicit computation of the normalizing constant. Score matching has been so far limited to the models in which the observations are independent and identically distributed (IID). However, the IID assumption does not hold in the traditional fixed design setting for regression-type models. To deal with the estimation of these covariate-dependent models, a novel score matching approach is presented for independent but not necessarily identically distributed(INID) data under a general framework for both continuous and discrete responses. In particular, we introduce a novel generalized score matching method for count response regression. We prove that our proposed score matching estimators are consistent and asymptotically normal under mild regularity conditions. The theoretical results are supported by numerical studies. Additionally, our simulation results indicate that, compared to the approximate maximum likelihood estimation, the generalized score matching produces estimates with smaller biases in an application to high school attendance data.