# AB实验人群定向HTE模型2 - Causal Tree with Trigger

• Trigger：对不同群体的treatment选择个性化阈值。 E.g优惠券力度，红包金额
• 新的Node Penalty: 旨在增强模型generalization

### 论文

C. Tran and E. Zheleva, “Learning triggers for heterogeneous treatment effects,” in Proceedings of the AAAI Conference on Artificial Intelligence, 2019

### 模型

#### Trigger

Trigger的计算主要用在treatment是一个潜在连续变量，例如服药的剂量，优惠券的金额等等。这时实验希望得到的不仅是优惠券是否能提升用户留存，而且是对哪些用户使用多少金额的优惠券能最大化ROI。

\begin{align} T = {t_i}&\quad \text{treatment的所有可能取值}\\ \theta_l &\quad \text{最优treatment阈值}\\ F^t(S_l) &= max_{\theta_l}F(S_l)\\ \end{align}

#### Node Penalty

\begin{align} & {(X_i, Y_i,T_i): X_i \in X} \\ & \text{where X是特征，Y是Response，T是AB实验分组}\\ &T_i \in {0,1} \quad \\ &Y_i = \begin{cases} Y(1) & \quad T_i = 0\\ Y(0) & \quad T_i = 1\\ \end{cases}\\ &CATE: \tau(x) = E(Y_i(1)-Y_i(0)|X=x)\\ \end{align}

\begin{align} &S_l = {(X_i, Y_i,T_i): X_i \in X_l} \quad \text{叶节点-局部样本}\\ &\hat{\mu_t}(S_l) = \frac{1}{N_{l,t}}\sum_{T_i=t, i \in S_l}Y_i \quad \text{AB组Y的均值} \\ &\hat{\tau}(S_l) = \hat{\mu_1}(S_l) -\hat{\mu_0}(S_l) \quad \text{叶节点CATE}\\ &F(S_l) = N_l * \hat{\tau}^2(S_l)\\ & \text{cost fucntion}: max \sum_{i=1}^L F(S_i)\\ \end{align}

\begin{align} &penalty = N_L^{val} * |\hat{\tau}(S_l^{val}) -\hat{\tau}(S_l^{train}) | \\ &cost = \frac{(1-\lambda)F(S_l^{train}) - \lambda * penalty}{|N_l^{train} - N_l^{val}| +1}\\ \end{align}

posted @ 2019-10-22 10:32  风雨中的小七  阅读(800)  评论(0编辑  收藏