2018/02/18 by Shiqing Yu, Mathias Drton, Yu, Shiqing +3 · 1 citation
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1802.06340
openalex publication_date 2018/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A common challenge in estimating parameters of probability density functions is the intractability of the normalizing constant. While in such cases maximum likelihood estimation may be implemented using numerical integration, the approach becomes computationally intensive. In contrast, the score matching method of Hyvärinen (2005) avoids direct calculation of the normalizing constant and yields closed-form estimates for exponential families of continuous distributions over ℝm. Hyvärinen (2007) extended the approach to distributions supported on the non-negative orthant ℝ+m. In this paper, we give a generalized form of score matching for non-negative data that improves estimation efficiency. We also generalize the regularized score matching method of Lin et al. (2016) for non-negative Gaussian graphical models, with improved theoretical guarantees.