The fundamental problem of causal inference says that only one potential outcome is observed for each unit.

What happen if both outcomes from control and treatment can be observed? Can we still make use of analysis tool like causal tree to understand heterogeneous treatment effect?

As a concrete example, suppose we are an online searching engine and want to better understand how to serve ads. Each time a user enters a search query (request), we pick an ads from a collection of N ads and show it to the user. For each of these N ads, there are 2 versions, one with image and one without. We randomize users into control group and treatment group (same distribution of users in each group), where users in control group will see ads without image and users in treatment group will see ads with image. By the end of the experiment, for each ads we record total number of clicks by users in control group as well as treatment group.

In this particular case, each ads is an experiment unit, and we are able to observe outcomes from both treatment and control. We want to understand if we should add an image to the ads or not. In addition, each ad has its feature (e.g., associated company, promoted product, etc.), and we want to understand which group of ads will benefit the most from the addition of images. My question is  , in such case, can we follow the routine in treatment effect analysis? If not, what's a more suitable framework?

The fundamental problem of causal inference says that only one potential outcome is observed for each unit.

What happens if both outcomes from control and treatment can be observed? Can we still make use of analysis tools like causal trees to understand heterogeneous treatment effects?

As a concrete example, suppose we are an online search engine and want to better understand how to serve ads. Each time a user enters a search query (request), we pick an ad from a collection of $N$ ads and show it to the user. For each of these $N$ ads, there are 2 versions, one with an image and one without. We randomize users into a control group and a treatment group (same distribution of users in each group), where users in the control group will see ads without an image and users in the treatment group will see ads with an image. By the end of the experiment, for each ad we record the total number of clicks by users in the control group as well as in the treatment group.

In this particular case, each ad is an experimental unit, and we are able to observe outcomes from both the treatment group and the control group. We want to understand if we should add an image to the ads or not. 

In addition, each ad has its feature (e.g., associated company, promoted product, etc.), and we want to understand which group of ads will benefit the most from the addition of images. My question is, in such a case, can we follow the routines in treatment effect analysis? If not, what's a more suitable framework?

The fundamental problem of causal inference says that only one potential outcome is observed for each unit.

What happen if both outcomes from control and treatment can be observed? Can we still make use of analysis tool like causal tree to understand heterogeneous treatment effect?

As a concrete example, suppose we are an online searching engine and want to better understand how to serve ads. Each time a user enters a search query (request), we pick an ads from a collection of N ads and show it to the user. For each of these N ads, there are 2 versions, one with image and one without. We randomize user request into control group and treatment group, where users in control group will see ads without image and users in treatment group will see ads with image. By the end of the experiment, for each ads we record total number of clicks by users in control group as well as treatment group.

In this particular case, each ads is an experiment unit, and we are able to observe outcomes from both treatment and control. We want to understand if we should add an image to the ads or not. In addition, each ad has its feature (e.g., associated company, promoted product, etc.), and we want to understand which group of ads will benefit the most from the addition of images. My question is , in such case, can we follow the routine in treatment effect analysis? If not, what's a more suitable framework?

The fundamental problem of causal inference says that only one potential outcome is observed for each unit.

What happen if both outcomes from control and treatment can be observed? Can we still make use of analysis tool like causal tree to understand heterogeneous treatment effect?

As a concrete example, suppose we are an online searching engine and want to better understand how to serve ads. Each time a user enters a search query (request), we pick an ads from a collection of N ads and show it to the user. For each of these N ads, there are 2 versions, one with image and one without. We randomize users into control group and treatment group (same distribution of users in each group), where users in control group will see ads without image and users in treatment group will see ads with image. By the end of the experiment, for each ads we record total number of clicks by users in control group as well as treatment group.

In this particular case, each ads is an experiment unit, and we are able to observe outcomes from both treatment and control. We want to understand if we should add an image to the ads or not. In addition, each ad has its feature (e.g., associated company, promoted product, etc.), and we want to understand which group of ads will benefit the most from the addition of images. My question is , in such case, can we follow the routine in treatment effect analysis? If not, what's a more suitable framework?