The hardest part of this project is the beginning and once we get a workflow it'll get easier. Noah is also very excited.
There was a model we went through this past week on learning trajectories. Given an amount of data, what can you infer about the fairness of the coin?
We talked about in class about p(h|d1, d2)p(h) = p(h|d2)p(h|d1). You can map over the first 19 data points and get the posterior, and that becomes the prior for your 20th data point. (yesterday's posterior = today's prior)
For example, you can have a model (idealLearner) that makes two observations, or a model (model1a) that makes one observation and a second one (model1b) that samples from the first. These end up being equivalent. You can then write a model that is the "remembered" version of the model (model1a) generating your posterior (prior for the second model), where noise is added.
To think about for next week:
What are the details of this noisify function? What are the effects of the noise? What if the original model is not just one parameter but multiple parameters, with information at different hierarchies? What resources do the user has, how much can they spend to keep memories (can think of it as currency, e.g. as was done in the "One and Done" paper). Define what your resources are and how you can allocate them. E.g. for a fair coin, it is worth remembering the weight or a higher order variable?
We should start out with something simple such as a coin example, and then build up. We'll think about objects with properties after next week's hierarchical model lectures. We should play around with MH's model that he wrote out today with different levels of noise. Maybe it's costly to keep a parameter low (to retain the memory). (maybe I have to choose which k variables to store out of n total variables)
For next week the three of us should read papers, meet up to play around with code and ideas. We should think about what's the right target behavior and a reward associated with that: a model pays a cost to remember something, makes prediction, makes money. How should it balance the costs and rewards? (Maybe it finds out that it doesn't have to pay so much to get good results.) We'll initially try to figure out the optimal way for people to store memory, just to nail down a definition of the cost of memory. (Maybe some memories are more costly than others, or maybe the model needs to save up for some end goal.)
The hardest part of this project is the beginning and once we get a workflow it'll get easier. Noah is also very excited.
There was a model we went through this past week on learning trajectories. Given an amount of data, what can you infer about the fairness of the coin?
We talked about in class about p(h|d1, d2)p(h) = p(h|d2)p(h|d1). You can map over the first 19 data points and get the posterior, and that becomes the prior for your 20th data point. (yesterday's posterior = today's prior)
For example, you can have a model (idealLearner) that makes two observations, or a model (model1a) that makes one observation and a second one (model1b) that samples from the first. These end up being equivalent. You can then write a model that is the "remembered" version of the model (model1a) generating your posterior (prior for the second model), where noise is added.
To think about for next week:
What are the details of this noisify function? What are the effects of the noise? What if the original model is not just one parameter but multiple parameters, with information at different hierarchies? What resources do the user has, how much can they spend to keep memories (can think of it as currency, e.g. as was done in the "One and Done" paper). Define what your resources are and how you can allocate them. E.g. for a fair coin, it is worth remembering the weight or a higher order variable?
We should start out with something simple such as a coin example, and then build up. We'll think about objects with properties after next week's hierarchical model lectures. We should play around with MH's model that he wrote out today with different levels of noise. Maybe it's costly to keep a parameter low (to retain the memory). (maybe I have to choose which k variables to store out of n total variables)
For next week the three of us should read papers, meet up to play around with code and ideas. We should think about what's the right target behavior and a reward associated with that: a model pays a cost to remember something, makes prediction, makes money. How should it balance the costs and rewards? (Maybe it finds out that it doesn't have to pay so much to get good results.) We'll initially try to figure out the optimal way for people to store memory, just to nail down a definition of the cost of memory. (Maybe some memories are more costly than others, or maybe the model needs to save up for some end goal.)