Pattern-by-Pattern方法在缺失数据下表现优异，尤其适用于非随机缺失场景。
When Pattern-by-Pattern Works: Theoretical and Empirical Insights for Logistic Models with Missing Values
- 为每种缺失模式分别训练逻辑回归模型，提升预测准确性。
- 在小样本时均值填补表现良好，大样本时Pattern-by-Pattern更优。
- 适合处理非随机缺失数据，对高维复杂场景有较强鲁棒性。
在输入缺失的情况下，即使参数估计也难以实现准确预测。针对逻辑回归模型中无闭式解的最优预测问题，本文证明了模式逐个处理（PbP）策略在高斯模式混合模型（GPMM）下能准确逼近贝叶斯概率。该结论适用于标准缺失机制（MCAR、MAR），并延伸至传统方法失效的非随机缺失（MNAR）场景。实验对比了PbP、插补法与EM方法在分类、概率估计、校准与推断任务中的表现。结果显示：小样本时均值插补可作基准；大样本时PbP高效且性能佳；而包含响应标签的非线性多重迭代插补（如带响应标签的随机森林MICE）表现最佳，但计算成本较高。
原文摘要 · Abstract (English)
Predicting with missing inputs challenges even parametric models, as parameter estimation alone is insufficient for prediction on incomplete data. While several works study prediction in linear models, we focus on logistic models, where optimal predictors lack closed-form expressions. We prove that a Pattern-by-Pattern strategy (PbP), which learns one logistic model per missingness pattern, accurately approximates Bayes probabilities under a Gaussian Pattern Mixture Model (GPMM). Crucially, this result holds across standard missing data scenarios (MCAR and MAR) and, notably, in Missing Not at Random (MNAR) settings where standard methods often fail. Empirically, we compare PbP against imputation and EM methods across classification, probability estimation, calibration, and inference. Our analysis provides a comprehensive view of logistic regression with missing values. It reveals that mean imputation can be used as baseline for low sample sizes and PbP for large sample sizes, as both methods are fast to train and may have good performances in some settings. The best performances are achieved by non-linear multiple iterative imputation techniques that include the response label (Random Forest MICE with response), which are more computationally expensive.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。