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What are the relationships and the differences between causal inference and prediction (both classification and regression)?

In the prediction context, we have the predictor/input variables and response/output variables. Does that mean that there is causal relation between input and output variables? So, does prediction belong to causal inference?

If I understand correctly, causal inference considers to estimate conditional distribution of one random variable given another random variable, and often use graphical models to represent the conditional independence between random variables. So, causal inference, in this sense, isn't prediction, is it?

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    $\begingroup$ Have you had a look at this Kaggle competition? kaggle.com/c/cause-effect-pairs you might find something interesting $\endgroup$ – Simone Apr 23 '13 at 0:17
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    $\begingroup$ This paper talks about the difference: Galit Shmueli, To Explain or to Predict?, Statist. Sci. Volume 25, Number 3 (2010), 289-310. $\endgroup$ – Shu Zhang Apr 16 '18 at 22:04
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Causal inference is focused on knowing what happens to $Y$ when you change $X$. Prediction is focused on knowing the next $Y$ given $X$ (and whatever else you've got).

Usually, in causal inference, you want an unbiased estimate of the effect of $X$ on Y. In prediction, you're often more willing to accept a bit of bias if you and reduce the variance of your prediction.

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    $\begingroup$ This answer neglects the difference between causal and associational models. $\endgroup$ – Neil G Jul 20 '14 at 19:47
  • $\begingroup$ Well, isn't associational basically the default? And wouldn't causal be nested within associational? I've never heard of anyone ever talk about an ''associational model'', except perhaps disparagingly in the case of one where the supposedly causal effects were confounded. $\endgroup$ – generic_user Jul 27 '14 at 12:59
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    $\begingroup$ Okay, I see your point that associational is the default and that causal models are "nested" in the sense that they are more powerful. The question is what is the difference between a causal model and regression or classification (an associational model). And the main difference is that: While you can do regression from causes to their effect, or from effects to some hypothetical cause; in a causal model, the relationships are directed (causes to effects). These directions are required to support interventional reasoning, which associational models cannot support. $\endgroup$ – Neil G Jul 28 '14 at 2:53
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Causal inference requires a causal model. Such a model can be used to infer (predict) some variables given observations and interventions at other variables. Regression and classification have no such causal requirement and therefore have nothing to do with interventional reasoning.

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