Generalized Score Matching for Non-Negative Data.

IF 4.3 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Journal of Machine Learning Research Pub Date : 2019-04-01
Shiqing Yu, Mathias Drton, Ali Shojaie
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引用次数: 0

Abstract

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. 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 R m . 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. As an example, we consider a general class of pairwise interaction models. Addressing an overlooked inexistence problem, we generalize the regularized score matching method of Lin et al. (2016) and improve its theoretical guarantees for non-negative Gaussian graphical models.

Abstract Image

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非负数据的广义分数匹配。
估计概率密度函数参数的一个常见挑战是归一化常数的难处。虽然在这种情况下,最大似然估计可以使用数值积分来实现,但这种方法的计算量很大。Hyvärinen(2005)的得分匹配方法避免了直接计算归一化常数,并对R m上的连续分布的指数族产生了封闭形式的估计。Hyvärinen(2007)将该方法扩展到非负正交R + m上支持的分布。本文给出了一种非负数据的分数匹配的广义形式,提高了估计效率。作为一个例子,我们考虑一类一般的两两交互模型。为了解决一个被忽视的不存在问题,我们推广了Lin等人(2016)的正则化分数匹配方法,并改进了其对非负高斯图模型的理论保证。
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来源期刊
Journal of Machine Learning Research
Journal of Machine Learning Research 工程技术-计算机:人工智能
CiteScore
18.80
自引率
0.00%
发文量
2
审稿时长
3 months
期刊介绍: The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online. JMLR has a commitment to rigorous yet rapid reviewing. JMLR seeks previously unpublished papers on machine learning that contain: new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature; experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems; accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods; formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks; development of new analytical frameworks that advance theoretical studies of practical learning methods; computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.
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