6 ms·

I've read Pearl's book too and it wasn't clear if it was possible to systematically "observe interventions" instead of doing them yourself and what the rules wo

I've read Pearl's book too and it wasn't clear if it was possible to systematically "observe interventions" instead of doing them yourself and what the rules would be for that. I mean there was some stuff about instrumental variables but it seems the theory is a bit incomplete in that area. What distinguishes an intervention vs just normal observable randomness? Does it have to do with the complexity of the entity performing the "intervention", with the fact that this entity can observe and act on knowledge? I guess it's kind of the debate about where determinism ends and free will begins. Are there mathematical bounds to help us sort it out though? Maybe there is something information theoretic? It's very unclear in my mind. This is all about fitting generative models that are robust to counterfactual changes, that remain predictive even if you run your models with data you've never observed, this beyond simple interpolation/extrapolation. Are there priors in model structure that tend to naturally make models much more robust to counterfactual changes and that make models work well beyond the data? Do these priors get more effective when they include some latent variables that distinguish between observations and interventions? How to you train these latent variables?

zwaps 6y ago
Pearl has a particular pet model for causality, but there are other approaches. I have yet to see someone actually apply Pearl's model in prominent research, but we are probably getting there. I think the question that is really on your mind is the one of (causal) identification. For ML researchers, this may be explained as follows: How, and to what degree, can we find a "deep" parameter that is a general or constant relationship between our inputs and outputs? Is this possible? When? Under which assumptions? If we do this, THEN we can run counterfactuals with our model. But as it turns out, to convince yourself that your model really generalizes, you will have to prove to yourself that there exists a set of general relationships (parameters) in the data - which may for example be general because they are causal parameters - and that your model is sufficient to "identify" these parameters given the data source. You will quickly find that you need to examine both the model, and the data (and assumptions that you have about it). Generally, no "model" itself is ever causal. It's always the combination of model and DGP. One way to have a causal model is to simply assume some physical relationship exists, and estimate parameters from data. This is called structural modeling in econometrics and scientific ML in, well, physics mostly. You bring in prior science and knowledge - like how weather fronts move, or how prices relate to costs - and use this structure to contrain your model. If you do this well, then this may be enough to identify causal parameters! Or ranges thereof. Here is a technical treatment of such issues: http://fmwww.bc.edu/EC-P/wp957.pdf http://fmwww.bc.edu/EC-P/wp957.pdf Another way is to find some measure of interest that you can derive without a complete model. For example, you may be able to "identify" so-called average marginal/treatment effects of some input variable without a parametric model. Then, as long as the changes in your inputs are "exogenous" in some sense, you can get a causal parameter. In experiments, the differences in inputs are randomized. What remains as group differences between placebo and treatment are the causal effects. In observational data, you may look for "natural experiments". Here, some exogenous variation can be found that identifies a similar treatment effect between individuals that are affected, and those that are not. Depending on your issue at hand, further techniques may be necessary to identify causal effects. Let's make an example: You built your start up to a huge and successful company, made up of programming teams. As CEO, you finally think about realizing your dream: Firing every non-technical team lead (say, everyone with an MBA). What effect would this have on productivity in the short term? Well, you have lots of data about your teams, and have certainly fired a lot of people, so you build a model. That model tells you, that firing such team leads is super good for productivity. However, after you do the firing, you find that productivity drops. What happened? Your model did not identify a causal effect. In this case, the firings you have observed probably occurred because the team lead was simply a bad manager. However, that data does not identify the "casual effect" of firing team leads. The "intervention" or the "treatment" you observed was not "exogenous". Okay, let's do more science here. Let's say you try to find out the effect of technical ability of the team lead on team productivity. You run your fancy ML models, and again conclude that more technical ability of the manager makes for a better team. But when you implement your effective training measures (or hiring measures, for that matter), the benefit is less than you expect. Again, what happened? Well, you might have a selection effect. Technically competent team leads may select into productive teams. Or, there is endogenity: productive teams mean that the team lead learns technical stuff, instead of managing chaos. The effect is actually reversed: good teams make leaders more competent. Your estimation - your model - overestimates the causal effect. It is not sufficient to create a counterfactual, simply because you did not find the real causal chain. Some key words to look into that are probably simpler than Pearl's full framework (and more practical, as they are applied every day): Natural Experiments, Instrumental Variables, Difference-in-Difference, Synthetic Controls, Matching, Heckman Selection If you are a person into technical papers, here's an approach that combines ML with causal analysis https://economics.mit.edu/files/12538 https://economics.mit.edu/files/12538
- BenoitEssiambre 6y ago
  Thanks for that detailed answer. That was great.
- omeze 6y ago
  As someone who has only read 1/3rd of Pearls book (for fun, just an engineer by day), this was a great answer and convinced me to pick it back up after surveying the non-Pearl world - thank you!
  - zwaps 6y ago
    I should add that if you are interested in some other perspective, but maybe not in mostly technical discussions, then the authors Angrist and Pischke have a couple of books - one if even a comic book - about causal analysis.
ordu 6y ago
> What distinguishes an intervention vs just normal observable randomness? The difference is your knowledge that value of some variable is controlled and independent from anything else in this situation. If causal model is some kind of a puzzle, then you could see how it would work if some parts of model are made dysfunctional by your intervention. X causes Y means that changes in X lead to changes in Y. If you changed X than Y would change also. By observation you can witness correlation, which says nothing about causes. You could add temporal element, like "X happened earlier than Y" it means that Y couldn't be the cause of X. But it doesn't answer the question about cause, it just rejects some hypothesis about cause, and is all uncertain: we could easily devise an example when such a rejection would be a mistake. For example people could act because they are able predict something will happen. So something is not happened yet, but already is the cause of some events. But when changes to X were made by you, then you know exactly when X was changed, you know that it was no changed to changes of Y or some Z which is a confounder. Here we also could make a mistakes, for example, because we do not know exactly how we make decisions and our behavior could be a confounder or mediator or something like. So we devised randomized controlled trials, double-blind experiments to make experiment really independent. > I guess it's kind of the debate about where determinism ends and free will begins. No need to get to that length. If your behavior is independent from the process which you research, than you'll get a "practical free will": free from influences of studied variables. This practical and situational free will definition is enough for learning about causes.
- zwaps 6y ago
  It also depends on your model. If you do not need to estimate the entire distribution, but are fine with getting some moment estimates (aka - an average effect, the marginal of the expected output and so forth) then you do not even need independence. What you need is no correlation with confounders. Since this includes latent factors, the philosophical issue is, of course, the same.
vladf 6y ago
I think the problem with observing interventions is it will result in impractically large sample complexity to derive the same causal conclusion as causal calculus armed with assumptions of DAG structure. I think metaphysically speaking the approaches (observing interventions vs causal calc) aren’t meaningfully different in terms of inferences you can make with infinite data, see my similar observations to yours: https://vladfeinberg.com/2019/12/01/metaphysics-of-causality.html https://vladfeinberg.com/2019/12/01/metaphysics-of-causality... But if you can presume a fixed DAG you can get away with fewer observations bc then you can derive some minimal/cheap set of vars to randomize over such that the resulting experiment measures a causal effect. All causal calc does is give you a framework for clarifying assumptions necessary to derive such a set. In high dims performing randomization is exponentially costly.

zwaps 6y ago

Pearl has a particular pet model for causality, but there are other approaches. I have yet to see someone actually apply Pearl's model in prominent research, but we are probably getting there. I think the question that is really on your mind is the one of (causal) identification. For ML researchers, this may be explained as follows: How, and to what degree, can we find a "deep" parameter that is a general or constant relationship between our inputs and outputs? Is this possible? When? Under which assumptions? If we do this, THEN we can run counterfactuals with our model. But as it turns out, to convince yourself that your model really generalizes, you will have to prove to yourself that there exists a set of general relationships (parameters) in the data - which may for example be general because they are causal parameters - and that your model is sufficient to "identify" these parameters given the data source. You will quickly find that you need to examine both the model, and the data (and assumptions that you have about it). Generally, no "model" itself is ever causal. It's always the combination of model and DGP. One way to have a causal model is to simply assume some physical relationship exists, and estimate parameters from data. This is called structural modeling in econometrics and scientific ML in, well, physics mostly. You bring in prior science and knowledge - like how weather fronts move, or how prices relate to costs - and use this structure to contrain your model. If you do this well, then this may be enough to identify causal parameters! Or ranges thereof. Here is a technical treatment of such issues: http://fmwww.bc.edu/EC-P/wp957.pdf http://fmwww.bc.edu/EC-P/wp957.pdf Another way is to find some measure of interest that you can derive without a complete model. For example, you may be able to "identify" so-called average marginal/treatment effects of some input variable without a parametric model. Then, as long as the changes in your inputs are "exogenous" in some sense, you can get a causal parameter. In experiments, the differences in inputs are randomized. What remains as group differences between placebo and treatment are the causal effects. In observational data, you may look for "natural experiments". Here, some exogenous variation can be found that identifies a similar treatment effect between individuals that are affected, and those that are not. Depending on your issue at hand, further techniques may be necessary to identify causal effects. Let's make an example: You built your start up to a huge and successful company, made up of programming teams. As CEO, you finally think about realizing your dream: Firing every non-technical team lead (say, everyone with an MBA). What effect would this have on productivity in the short term? Well, you have lots of data about your teams, and have certainly fired a lot of people, so you build a model. That model tells you, that firing such team leads is super good for productivity. However, after you do the firing, you find that productivity drops. What happened? Your model did not identify a causal effect. In this case, the firings you have observed probably occurred because the team lead was simply a bad manager. However, that data does not identify the "casual effect" of firing team leads. The "intervention" or the "treatment" you observed was not "exogenous". Okay, let's do more science here. Let's say you try to find out the effect of technical ability of the team lead on team productivity. You run your fancy ML models, and again conclude that more technical ability of the manager makes for a better team. But when you implement your effective training measures (or hiring measures, for that matter), the benefit is less than you expect. Again, what happened? Well, you might have a selection effect. Technically competent team leads may select into productive teams. Or, there is endogenity: productive teams mean that the team lead learns technical stuff, instead of managing chaos. The effect is actually reversed: good teams make leaders more competent. Your estimation - your model - overestimates the causal effect. It is not sufficient to create a counterfactual, simply because you did not find the real causal chain. Some key words to look into that are probably simpler than Pearl's full framework (and more practical, as they are applied every day): Natural Experiments, Instrumental Variables, Difference-in-Difference, Synthetic Controls, Matching, Heckman Selection If you are a person into technical papers, here's an approach that combines ML with causal analysis https://economics.mit.edu/files/12538 https://economics.mit.edu/files/12538

BenoitEssiambre 6y ago
Thanks for that detailed answer. That was great.
omeze 6y ago
As someone who has only read 1/3rd of Pearls book (for fun, just an engineer by day), this was a great answer and convinced me to pick it back up after surveying the non-Pearl world - thank you!
- zwaps 6y ago
  I should add that if you are interested in some other perspective, but maybe not in mostly technical discussions, then the authors Angrist and Pischke have a couple of books - one if even a comic book - about causal analysis.

ordu 6y ago

> What distinguishes an intervention vs just normal observable randomness? The difference is your knowledge that value of some variable is controlled and independent from anything else in this situation. If causal model is some kind of a puzzle, then you could see how it would work if some parts of model are made dysfunctional by your intervention. X causes Y means that changes in X lead to changes in Y. If you changed X than Y would change also. By observation you can witness correlation, which says nothing about causes. You could add temporal element, like "X happened earlier than Y" it means that Y couldn't be the cause of X. But it doesn't answer the question about cause, it just rejects some hypothesis about cause, and is all uncertain: we could easily devise an example when such a rejection would be a mistake. For example people could act because they are able predict something will happen. So something is not happened yet, but already is the cause of some events. But when changes to X were made by you, then you know exactly when X was changed, you know that it was no changed to changes of Y or some Z which is a confounder. Here we also could make a mistakes, for example, because we do not know exactly how we make decisions and our behavior could be a confounder or mediator or something like. So we devised randomized controlled trials, double-blind experiments to make experiment really independent. > I guess it's kind of the debate about where determinism ends and free will begins. No need to get to that length. If your behavior is independent from the process which you research, than you'll get a "practical free will": free from influences of studied variables. This practical and situational free will definition is enough for learning about causes.

zwaps 6y ago
It also depends on your model. If you do not need to estimate the entire distribution, but are fine with getting some moment estimates (aka - an average effect, the marginal of the expected output and so forth) then you do not even need independence. What you need is no correlation with confounders. Since this includes latent factors, the philosophical issue is, of course, the same.

vladf 6y ago

I think the problem with observing interventions is it will result in impractically large sample complexity to derive the same causal conclusion as causal calculus armed with assumptions of DAG structure. I think metaphysically speaking the approaches (observing interventions vs causal calc) aren’t meaningfully different in terms of inferences you can make with infinite data, see my similar observations to yours: https://vladfeinberg.com/2019/12/01/metaphysics-of-causality.html https://vladfeinberg.com/2019/12/01/metaphysics-of-causality... But if you can presume a fixed DAG you can get away with fewer observations bc then you can derive some minimal/cheap set of vars to randomize over such that the resulting experiment measures a causal effect. All causal calc does is give you a framework for clarifying assumptions necessary to derive such a set. In high dims performing randomization is exponentially costly.