Minimum Stein Discrepancy Estimators
Minimum Stein Discrepancy Estimators
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发表时间：
2019-06
影响因子：
5.2
通讯作者：
A. Barp;François‐Xavier Briol;A. Duncan;M. Girolami;Lester W. Mackey
中科院分区：
文献类型：
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作者：
A. Barp;François‐Xavier Briol;A. Duncan;M. Girolami;Lester W. Mackey
当最大似然估计不可行时，人们经常求助于得分匹配、对比发散或最小概率流来获得易于处理的参数估计。我们提供了这些技术作为最小Stein差异估计器的统一视角，并利用这种透镜设计了具有互补优势的新的扩散核Stein差异(DKSD)和扩散分数匹配(DSM)估计器。我们建立了DKSD和DSM估计量的相合性、渐近正态和稳健性，并给出了有效优化的随机黎曼梯度下降算法。我们方法的主要优点是它的灵活性，它允许我们通过仔细选择Stein差异来为手头的特定模型设计具有理想特性的估计器。我们用分数匹配中的几个具有挑战性的问题来说明这一优势，例如非光滑、重尾或轻尾密度。
When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as minimum Stein discrepancy estimators, and use this lens to design new diffusion kernel Stein discrepancy (DKSD) and diffusion score matching (DSM) estimators with complementary strengths. We establish the consistency, asymptotic normality, and robustness of DKSD and DSM estimators, then derive stochastic Riemannian gradient descent algorithms for their efficient optimisation. The main strength of our methodology is its flexibility, which allows us to design estimators with desirable properties for specific models at hand by carefully selecting a Stein discrepancy. We illustrate this advantage for several challenging problems for score matching, such as non-smooth, heavy-tailed or light-tailed densities.