Another plot: rewards vs effort costs (how much you're paying or how many resources you have)
In One and Done paper: as samples get costly, you want to get fewer of them.
(utility is rewards minus cost)
Thought experiment: a participant comes into a laboratory and you give them ten dollars. humans write down their beliefs, you distort it depending on how much they pay you. Try to imagine it as something concrete/physical.
What if you noisify your category belief, how does that effect your ability to generalize to other coins (not the one at hand)
The lower value (coin weight) is continuous and has more specific values. We want to capture the fact that it's cheaper to keep around the abstract information because it's less information to keep (heavy vs light is less complex than an actual coin weight). Question: when you're dealing with a hierarchical model, when is it better to keep around the abstract information versus the specific information? We've discovered a case where forgetting the abstract is ok because it's the specific that you're using for predictions. But maybe it's cheaper overall to keep the simpler abstract information. But what if you want to generalize to another coin? If you forget abstract for that, you are more in trouble. That's a case where it'd be costly to lose the abstract information. There's a situation though where you could reconstruct the abstract information, because all of the information is shared. Like, bottom level information can tell you what the upper level might be. You can't keep around all the data, you can only keep around beliefs.
What if you reset the coin category but keep around the coin weight? You're going to mix it with your new prior around the weight... it might be similar but should be a little bit flatter. What is the result of that reset?
For our plots, how do we interpret our axes?
Another plot: rewards vs effort costs (how much you're paying or how many resources you have)
In One and Done paper: as samples get costly, you want to get fewer of them.
(utility is rewards minus cost)
Thought experiment: a participant comes into a laboratory and you give them ten dollars. humans write down their beliefs, you distort it depending on how much they pay you. Try to imagine it as something concrete/physical.
What if you noisify your category belief, how does that effect your ability to generalize to other coins (not the one at hand)
The lower value (coin weight) is continuous and has more specific values. We want to capture the fact that it's cheaper to keep around the abstract information because it's less information to keep (heavy vs light is less complex than an actual coin weight). Question: when you're dealing with a hierarchical model, when is it better to keep around the abstract information versus the specific information? We've discovered a case where forgetting the abstract is ok because it's the specific that you're using for predictions. But maybe it's cheaper overall to keep the simpler abstract information. But what if you want to generalize to another coin? If you forget abstract for that, you are more in trouble. That's a case where it'd be costly to lose the abstract information. There's a situation though where you could reconstruct the abstract information, because all of the information is shared. Like, bottom level information can tell you what the upper level might be. You can't keep around all the data, you can only keep around beliefs.
What if you reset the coin category but keep around the coin weight? You're going to mix it with your new prior around the weight... it might be similar but should be a little bit flatter. What is the result of that reset?