The mediation condition is that when you condition on the latent, the mutual information between any one variable and the joint distribution of all other variables is low. In the case of the energy and temperature, once you know the energy and temperature, all the variables are now independent, and so you get no mutual information. However, with the parity, the rest of the variables let you figure out the last, so we fail mediation.
For redundancy, the energy and temperature is for the most part determined by any (n-1) variable subset, becaues averages. This isn’t true of the parity—the last bit being 50⁄50 means you still have total uncertainty over the parity.
You clearly have some idea of what “mediation” and “redundancy” means for these particular scenarios and why they matter. I still have no clue what you mean by those words, why I should care about these properties, or how they related to the notion of insensitivity.
Ah, I was talking about the conditions for natural latents, the main research program of the post author. See this post for a good math intro containing those definitions.
I now have the definitions, but I still don’t see the relation to insensitivity. Yes, natural latents are natural ontologies, but natural ontologies are not necessarily natural latents.
At the very least, the stochastic redund condition feels like a pretty minimal version of what ‘insensitivity’ could mean. The parity is still pretty maximally insensitive—if you’re trying to reduce your uncertainty about what the parity is, learning about (n-1) bits doesn’t even help you until you learn the last one! I doubt a good definition of “insensitivity” would call the parity insensitive.
What do you mean by “the stochastic redund condition”? Here’s what I feel like you’re doing: you have some unformalized intuitions. It seems to be the case that ‘insensitive’ stuff matches your intuition about redundancy for uncontrived examples. You then went and contrived an example where it didn’t match your intuition.
If I were in your situation, I would conclude, “my intuition is missing something, let me try to formalize this and see where I went wrong.”
I’m still really confused by your opening salvo:
“No, the reason why we should have insensitivity is not quite that.”
What do you mean??? What is “that”, what is “the reason why we should have insensitivity”? I think the reason we should have insensitivity is so the oracle can make predictions.
Also, I’m not going to continue responding. I do not think you have anything here. I think you are just confused, and you have not done the work to figure out what you yourself mean.
The mediation condition is that when you condition on the latent, the mutual information between any one variable and the joint distribution of all other variables is low. In the case of the energy and temperature, once you know the energy and temperature, all the variables are now independent, and so you get no mutual information. However, with the parity, the rest of the variables let you figure out the last, so we fail mediation.
For redundancy, the energy and temperature is for the most part determined by any (n-1) variable subset, becaues averages. This isn’t true of the parity—the last bit being 50⁄50 means you still have total uncertainty over the parity.
You clearly have some idea of what “mediation” and “redundancy” means for these particular scenarios and why they matter. I still have no clue what you mean by those words, why I should care about these properties, or how they related to the notion of insensitivity.
Ah, I was talking about the conditions for natural latents, the main research program of the post author. See this post for a good math intro containing those definitions.
I now have the definitions, but I still don’t see the relation to insensitivity. Yes, natural latents are natural ontologies, but natural ontologies are not necessarily natural latents.
At the very least, the stochastic redund condition feels like a pretty minimal version of what ‘insensitivity’ could mean. The parity is still pretty maximally insensitive—if you’re trying to reduce your uncertainty about what the parity is, learning about (n-1) bits doesn’t even help you until you learn the last one! I doubt a good definition of “insensitivity” would call the parity insensitive.
What do you mean by “the stochastic redund condition”? Here’s what I feel like you’re doing: you have some unformalized intuitions. It seems to be the case that ‘insensitive’ stuff matches your intuition about redundancy for uncontrived examples. You then went and contrived an example where it didn’t match your intuition.
If I were in your situation, I would conclude, “my intuition is missing something, let me try to formalize this and see where I went wrong.”
I’m still really confused by your opening salvo:
“No, the reason why we should have insensitivity is not quite that.”
What do you mean??? What is “that”, what is “the reason why we should have insensitivity”? I think the reason we should have insensitivity is so the oracle can make predictions.
Also, I’m not going to continue responding. I do not think you have anything here. I think you are just confused, and you have not done the work to figure out what you yourself mean.