Paper notes: lbcf: a large scale budget constrained causal forest algorithm

Original paper ：M. Ai et al., “LBCF: A Large-Scale Budget-Constrained Causal Forest Algorithm,” in Proceedings of the ACM Web Conference 2022, New York, NY, USA, 2022, pp. 2310–2319. doi: 10.1145/3485447.3512103.

Motivation

This work takes the gold coin distribution scene as the background , Evaluate the causal effect of the number of gold coins distributed on the viewing duration of users , Based on the evaluation results, a personalized distribution mechanism is designed .

challenge：

• Large scale users ;
• multi-treatment;

contribution：

• Put forward LBCF Method solves the above two problems ;
• A new model effect evaluation index is proposed ;
• Experiments were carried out on real data ;

related work:
This part is mainly about myself challenge The shortcomings of the existing work are described , There are two types ：

• The first category ：LBCF Criticize them for using greedy tactics in making decisions , And through examples, this kind of greedy strategy can not achieve treament effect The optimal value 【 surface 1】
• The second category ：LBCF It is pointed out that although the second kind uses the optimization algorithm to make decisions , However, the performance is insufficient in the face of large-scale data , Mainly ：1. They can only do cohort-level The optimization of the , It can't be done member-level The optimization of the ;2. They are solving multi-treatment Many trees were constructed causal forest, In this case , Different forest The feature space is different , So the result of the evaluation treatment effect Also incomparable .

Methodology

in the light of related work The problem in ,LBCF The corresponding solutions are put forward , Methodology is mainly divided into two parts ：

• The first part is causal forest The construction of , The main contribution of this part is to put forward a new split standard , And named their forest UDCF;
• The second part is the construction of the optimization problem , In this part, an optimization algorithm for large-scale data is proposed , The name for DGB;

Problem definition ：
It is worth mentioning that LBCF Yes multi-treatment Next CATE The definition of ：

They are in Y(T=0) For the baseline , Only consider Y(T=j) To Y(T=0) The difference between the .

UDCF

Author for multi-treatment problem , Think the forest they built （ namely UDCF） There are two requirements that need to be met ：

• Unified： Refer to ,UDCF Need to make each treatment Of effect The evaluation is in the same feature space ;
• Discriminative ： Refer to ,UDCF Need to make a difference treatment Corresponding effect Sufficiently heterogeneous ;

therefore ,UDCF The full name of is Unified Discriminative Causal Forest.

In order to meet the above two requirements , The author puts forward two New split criteria ：

• inter split： The standard is to GRF be used for CATE A little change has been made to the split criteria of , bring CF Can be applied to multi-treatment The circumstances of , To satisfy the Unified characteristic , Its formal expression is as follows ：
  
  Not familiar with GRF Step by step Paper notes ：GRF
  This split criterion continues to be used GRF Thought , You want to maximize the heterogeneity between child nodes ;
• Intra split： The standard is aimed at Discriminative Characteristics proposed 【 Assumptions are also attached 1】, The idea is to maximize the difference treatment Heterogeneity between , The formal expression is as follows ：
  
  Based on the above two split criteria , The author puts forward the calculation steps of node splitting ：
  1. First of all, according to the inter split Criteria filter out m A candidate ;
  2. According to intra split The criteria screen out the optimal split ;

DGB

It is also an optimization problem ：

The details are brief