对比因果与反因果合并预测器，揭示其在泛化能力上的差异
Causal vs. Anticausal merging of predictors
- 用因果最大熵框架融合预测变量，区分因果与反因果方向
- 全数据下分别退化为逻辑回归和线性判别分析，决策边界不同
- 部分数据时反因果方向更利于跨变量泛化，适合小样本场景
我们研究在相同数据下，以因果与反因果方向合并预测器所产生的差异。重点考察一个简单模型：以一个二值变量为目标，两个连续变量为预测器。采用因果最大熵（CMAXENT）作为归纳偏置进行融合，但预期类似差异也适用于其他考虑因果不对称性的融合方法。结果表明，当观察到所有双变量分布时，CMAXENT 解在因果方向退化为逻辑回归，在反因果方向退化为线性判别分析（LDA）。此外，我们分析了仅观测部分双变量分布时，两种方向决策边界的不同，揭示了对离变量外（OOV）泛化的影响。
原文摘要 · Abstract (English)
We study the differences arising from merging predictors in the causal and anticausal directions using the same data. In particular we study the asymmetries that arise in a simple model where we merge the predictors using one binary variable as target and two continuous variables as predictors. We use Causal Maximum Entropy (CMAXENT) as inductive bias to merge the predictors, however, we expect similar differences to hold also when we use other merging methods that take into account asymmetries between cause and effect. We show that if we observe all bivariate distributions, the CMAXENT solution reduces to a logistic regression in the causal direction and Linear Discriminant Analysis (LDA) in the anticausal direction. Furthermore, we study how the decision boundaries of these two solutions differ whenever we observe only some of the bivariate distributions implications for Out-Of-Variable (OOV) generalisation.
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