![]() If you trust you data to have good over in covariate space, matching is a good approach because there is always some nearby point with the opposite treatment. Ultimately, to choose your technique you need to make some assumptions about how you contruct you counter factual. While there are some automated techniques, like this paper, I haven't had a change to try them out. #AVERAGE TREATMENT EFFECT ON THE TREATED HOW TO#The remaining question is how to decide which method to use? This is not an easy question. I've now covered most the of the common techniques for causal inference from observational data. Let's see how it does one of our previous datasets: One way to approach this problem is to introduce two new random variables to our system: $Y_\right)$ In these situations we still want to be able to say something about what the effect of an intervention is - to do this we need to make some assumptions about the data generating process we are investigating. This is a useful question because there are lots of situations where running an A/B test to directly measure the effects of an intervention is impractical, unfeasable or unethical. The question these notes will try and answer is how we can reason about the interventional distribution, when we only have access to observational data. The distribution of $Y$ is then given by the interventional distribution When we force people to wear cool hats, we are making an intervention. In the previous example, when we make no intervention on the system, we have an observational distribution of $Y$, conditioned on the fact we observe $X$: This act of forcing a variable to take a certain value is called an "Intervention". To be precise, $X$ and $Y$ are random variables and the "effect" we want to know is how the distribution of $Y$ will change when we force $X$ to take a certain value. In the current context, I am using it to mean "What is the effect on $Y$ of changing $X$?" "Causality" is a vague, philosophical sounding word. The previous example demonstrates the old statistics saying: This removes the effect of any confounding variables which might be influencing the metric we care about.īecause we generated our dataset from a known process (in this case a function I wrote), we can intervene in it directly and measure the effect of an A/B test: Specifically, we want to randomize who gets cool hats and who doesn't, and look at the different values of $y$ we receive. The cleanest way to actually measure the effect of some change in a system is by running a randomized control trial. If the team lead does this they fundamentally change the system we are sampling from, potentially altering or even reversing any correlations we observed before. The problem comes if we try to use this information as an argument about whether or not the team lead should force people to wear cool hats. As long as we believe that they are "drawn from the same distribution" as our previous observations, we expect the same correlations to exist. We can use this information to make statements about what we might think about someone's probability if we see them wearing a cool hat. Being data drive, the Team Lead starts to record whether or not a team member wears a cool hat ($X=1$ for a cool hat, $X=0$ for no cool hat) and whether or not they are productive ($Y=1$ for productive, $Y=0$ for unproductive).Īfter making observations for a week, they end up with a dataset like the following: One day a team lead notices that some members of their team wear cool hats, and that these members of the team tend to be less productive. To begin, let's look at a motivating example. You can find the functions which generate these datasets in the accompanying file datagenerators.py on github here. samples from some distribution, returning the results as a pandas dataframe. These data generators all generate i.i.d. ![]() This has two advantages: we can and will generate datasets with specific properties, and we have the ability to "intervene" in the data generating system directly, giving us the ability to check whether our inferences are correct. #AVERAGE TREATMENT EFFECT ON THE TREATED SERIES#The author has a good series of blog posts on it's functionality.īecause most datasets you can download are static, throughout this post I will be using be using my own functions to generate data. In this post, I will be using the excellent CausalInference package to give an overview of how we can use the potential outcomes framework to try and make causal inferences about situations where we only have observational data. ![]()
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