Causal Inference | Answering causal questions

Key Takeaways

hey folks welcome back this is the second video in a three-part series on causality in this video i'll be talking about causal inference which aims at answering questions involving cause and effect so i'll start by giving um introduction to causal inference and sketching some big ideas and then i'll finish with a concrete example with code using the microsoft do y library in python so with that let's get into the video okay so here we're talking about causal inference which aims at answering questions about cause and effect so given a causal model here we have a directed acyclic graph which i talked about in the previous video and from that how can we estimate causal effects for example how can we estimate the effect of x on y so some examples of questions that fall under the umbrella of causal inference are did the treatment directly help those who took it or was it the marketing campaign that led to increased sales this month or the holiday or how big of an effect would increasing wages have on productivity so these are very practical and significant questions that may not be so readily answered using traditional means and i'll try to highlight what causal inference is good at through what i call the three gifs of causal inference so the first gift is the do operator and the do operator simply simulates a physical intervention and we're all familiar with interventions in the real world this is like when your friend's candy habit gets completely out of control and you just have to sit him or her down and say this has got to stop this is what the do operator does but for a causal model in other words it is a mathematical representation of an intervention so suppose we have this model on the left here we have z causes x which causes y what an intervention in x looks like in this mathematical representation is we delete all the incoming edges into x and manually set x to some predetermined value say x naught so significant contribution from judea pearl and colleagues are the rules of do calculus what these rules provide is a way to translate probabilities that include the do operator into probabilities that do not include the do operator so the power of this is that often we can't perform interventions in the real world this could be because it's physically impossible or unethical or whatever reason for example intervening in someone's height by making them taller to measure the response in basketball ability is not physically feasible or intervening in smoking by forcing someone to smoke a pack of cigarettes every day to measure the response in the risk of lung disease is unethical so in other words often in the real world we have no way to collect data about the interventional probability distribution that is we don't have access to data about probabilities that include the do operator in these situations the rules of do calculus may provide a way to re-express to rewrite probabilities that we are interested in but can't measure directly so the second gift of causal inference is clarifying this notion of confounding and confounding at least for me was something that did not have a clear definition until i read judea pearl's book the book of why so in his book pearl defines confounding as anything that makes the interventional distribution different from the observational distribution in other words anything that makes a probability of y given an intervention in x different from the probability of y given an observation in x so this is easy to see in the three variable case so here we have an example of a causal model which shows the relationship between age education and wealth in this example age is the confounder and this can be understood as age is a common cause of education and wealth which is an idea that's been around for a while as pearl discusses in his book many people took this kind of common cause definition as a definition for confounding but what pearl does in defining confounding in this way in terms of the interventional versus observational distribution is becomes much more easy to generalize this notion to much more than just three variables okay so what does this mean practically if we know age is a confounder this can help inform our analysis of data that we might collect of these three variables so suppose we have this data here of age education and income and we want to assess the impact of education on income if we don't take into consideration age bank a confounder the naive thing to do would be to just partition the data into two subgroups one group has just a high school education and the other group has a college education and just compare their difference in income but since age is confounder this wouldn't give you the best result so knowing what the confounders are of your problem allow you to perform this analysis a different way so in this specific case since age is a confounder we shouldn't compare data between age groups we should compare data within age groups so that's what i'm showing here you can imagine this single data set being split off into four separate data sets uh where we have the blue data set people in their 20s the yellow dataset people in the 30s people in the 40s in red people in the 50s in green and then we repeat the analysis i was talking about before where we kind of compare the incomes of people without just high school education versus college education so you may ask why do we care about this do operator why do we need to talk about interventional probabilities versus observational probabilities and so on ultimately what these tools provide are a way to estimate causal effects so a causal effect is a way to quantify the causal impact that one variable has on another and this is a core part of causal inference so this is what we were naturally doing in the previous slide when we were trying to assess the impact of education on income what we were really doing is quantifying the causal effect that education had on people's incomes but this is obviously applicable to other situations when we ask questions like what productivity be increased if we increase wages or how would sales change if we increase the marketing budget with these questions and several more we're talking about causal effects what is the causal impact of wages on productivity what is the causal effect of marketing spend on sales so looking at the same example as before we have a causal model including age education and wealth we know from the previous slide that age is a confounder because it creates a discrepancy between the interventional and observational probability distributions we can consider education to be a treatment and wealth to be a response to that treatment and then suppose with this causal model in hand we collect some data very similar to what we were talking about in the previous slide but now we're set up to do causal inference we're set up to ask and attempt to answer a question involving cause and effect so a question might be is grad school worth it which might be something someone watching this video is thinking about or something someone is reminiscing upon and wishing they would have known about causal inference before deciding to go to grad school and they're already waist deep into it either way one way to frame this question of is grad school worth it could be what is the treatment effect of education on wealth i'm not saying this is the best way to do it but this is a way we can do it so i'll use this opportunity to run through a concrete example with code in python so the example code is at the github link at the bottom here i also put the link in the description but basically here we're going to estimate the treatment effect of education on income so first we download some libraries load some data this is real census data from the uci university of california irvine the machine learning data repository i don't know the specific name but here is the uh link here to do the causal effect calculation i use the do y library which is a microsoft library for doing causal inference so the next step is we have to define our causal model so again the starting point of all causal inference is a causal model so we need to start with our dag which is the same as we saw in an earlier slide just that education now has a new name called has graduate degree and income has a different name which is greater than 50k so these are both boolean variables which means they're true or false variables so either someone can have a graduate degree or they don't or either they make more than fifty thousand dollars a year or they don't and then age is just an integer next we need a s demand which is basically a recipe for estimating our causal effect you can just do this in one line using the do y library and then finally we can estimate the causal effect so here we're using a t learner which is a type of meta learner i can link a paper talking about meta learners in the description i won't jump into all the details i'll just kind of jump to the result which is the average causal effect is 0.2 so one way to interpret this is having a graduate degree increases your chances of making more than 50 000 a year by 20 however we had a lot of samples in this data set and we've just reduced all those samples to a single number which was the average which may not always be the most representative number so it's always good to plot the distribution and when we plot the distribution so here we have on the x-axis the causal effect the y-axis is the count the number of records or people that had that individual causal effect we see that the distribution is not gaussian so if the distribution is not gaussian that means the average is not a very representative number for that distribution so in other words even though a lot of people had a 0.2 treatment effect there were also a significant number of people that had no treatment effect so it seems we're no closer to answering the question of is grad school worth it however one thing one could do is to dive into these different cohorts kind of look at the samples that had no causal effect from a graduate degree and then look at the people that had a significant causal effect and then you can start to answer the question like what kinds of people benefit from a graduate degree and what kinds of person don't benefit from a graduate degree and then maybe that can kind of help you answer this question so again codes on the github feel free to take it run with it do whatever you want extend the analysis further post your own youtube video about it i'll be really interested to see if anyone actually takes a look and tries to answer this question of is grad school worth it but i guess it's a little too late for me at this point so that was the second video in the three-part series on causality we talked about causal inference which aims at answering questions involving causality however the starting point of all causal inference is a causal model which may not be so easy to have in hand that's where the topic of the next video can be helpful which is causal discovery and that aims at obtaining causal structure from data alone so if you enjoyed this video consider liking subscribing sharing commenting your thoughts i'm always happy and interested in reading the comments check out the blog if you want to get some more details on causal inference and check out the github to get the example code talked about in this video and thanks for watching [Music]