提出一种抗污染的得分匹配方法，可稳定估计非高斯图模型参数。
Robust Score Matching
- 用几何均值中位数增强得分匹配，提升鲁棒性。
- 在数据受污染时仍能准确恢复模型结构，无污染时性能相当。
- 适合无法计算归一化常数的非高斯指数族图模型。
得分匹配（score matching）由Hyvärinen（2005）提出，是一种无需计算分布归一化常数的参数估计方法。本文利用几何均值中位数构建一种鲁棒得分匹配，可在观测数据受污染时仍获得一致的参数估计。该方法在指数族模型中保持凸性，特别适用于非高斯、归一化常数难以计算的指数族图模型。本文提供了存在污染时的支撑集恢复保证，并通过数值实验和降水数据集验证：无污染时性能与标准得分匹配相当，污染情况下显著更优。
原文摘要 · Abstract (English)
Proposed in Hyvärinen (2005), score matching is a parameter estimation procedure that does not require computation of distributional normalizing constants. In this work we utilize the geometric median of means to develop a robust score matching procedure that yields consistent parameter estimates in settings where the observed data has been contaminated. A special appeal of the proposed method is that it retains convexity in exponential family models. The new method is therefore particularly attractive for non-Gaussian, exponential family graphical models where evaluation of normalizing constants is intractable. Support recovery guarantees for such models when contamination is present are provided. Additionally, support recovery is studied in numerical experiments and on a precipitation dataset. We demonstrate that the proposed robust score matching estimator performs comparably to the standard score matching estimator when no contamination is present but greatly outperforms this estimator in a setting with contamination.
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