Problem Setting#

Suppose we have a dataset containing observations from $N$ individuals. For each individual $i$, we have $\{{\mathit{S}}_i,A_i,R_i\}$, $i=1,\cdots ,N$. ${\mathit{S}}_i$ includes the feature information, $A_i$ is the action taken, and $R_i$ is the observed reward received.

Real Data#

1. Fetch_hillstrom

Fetch_hillstrom is a dataset from the scikit-uplift package with a single decision point. This study aims to assess the effectiveness of an e-mail campaign ($A$). The primary outcome of the interest is the money spent by customers during the two weeks following the e-mail campaign. By selecting only the individuals who purchased merchandise (spend>0), the dataset we used in this chapter comprises 578 customers ($N=578$). For each customer, there are nine features available:

• recency: # of months since the last purchase;

• history: total dollars spent in the past year;

• mens: binary, =1 if purchased Men’s merchandise in the past year;

• womens: binary, =1 if purchased Women’s merchandise in the past year;

• newbie: binary, =1 if the customer is a new customer in the past year;

• zip_code_Surburban: binary, =1 if zip_code is classified as Suburban;

• zip_code_Urban: binary, =1 if zip_code is classified as Urban;

• channel_Phone: binary, =1 if the customer purchased from Phone in the past year;

• channel_Web: binary, =1 if the customer purchased from Web in the past year.

Note, if zip_code_Surburban =0 and zip_code_Urban=0, then the zip_code is classified as Rural; if channel_Phone=0 and channel_Web=0, then the customer purchased from multichannel in the past year.

There are two different types of action space that are available for us to specify:

• Binary Treatment: Considering a binary action space, each customer would either receive an e-mail campaign ($A=1$) or receive no e-mail ($A=0$).

• Multi Treatments: Considering a multinomial action space, each customer would either receive no e-mail ($A=0$) or receive an e-mail campaign featuring Women’s merchandise ($A=1$) or receive an e-mail campaign featuring Men’s merchandise ($A=2$)

After two weeks following the e-mail campaign, each customer’s total dollar spent ($R$) is recorded.

The observed data are independent and identically distributed $\{{\text{recency}}_i,{\text{history}}_i,{\text{mens}}_i,{\text{womens}}_i,{\text{newbie}}_i,{\text{zip\_code\_Surburban}}_i,{\text{zip\_code\_Urban}}_i,{\text{channel\_Phone}}_i,{\text{channel\_Web}}_i,A_i,R_i\}$, for $i=1,\dots ,N$,

where larger values of $R$ are considered better.

• How to get the data?

  1. from causaldm._util_causaldm import *

  2. if binary treatment, S,A,R = get_data(target_col = ‘spend’, binary_trt = True); otherwise, S,A,R = get_data(target_col = ‘spend’, binary_trt = Flase)

More details about the original dataset can be found in https://blog.minethatdata.com/2008/03/minethatdata-e-mail-analytics-and-data.html.