Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

all right welcome back cohort 5 we're in our first discussion for chapter 7 so Andrew thank you for facilitating feel free to take it from here um so yeah uh first meeting on chapter seven so I'll do what I did with chapter six and maybe just give a I'll attempt to give a brief rundown of the chapter outline sort of layout and what's going on um that said there's a lot going on in this chapter and I would say aside from chapter six those who are interested in getting started on building actor inference models are going to want to kind of give a a kind of special amount of weight to this particular chapter um we do we are introduced to Hidden Markov models and partially observable Markov decision-making processes which PP is a shorthand for that and it's it's just as of right now that's kind of the not completely ubiquitous but most widely used models for a variety of Behavioral experiments um that said U couple weeks from now we'll get into chapter eight where we talk more about continuous models and um that'll be for looking at instances where we're looking at very you know uh fast time scales and great for things like motor movements um and just with things that are much quicker but usually we're dealing with discret variables so um chapter 7 quick intro 7.1 uh we focus on models of categorical variables in discrete time with examples increasing in complexity so we're introduced to models of perceptual processing decision making info seeking learning and finally hierarchical inference um and the authors try to um kind of get at different sorts of emergent properties including measurable physiology and behavior from these models 7.2 were introduced to the hidden Markov model on a perceptual processing experiment um this is where where the the model is of our beliefs about how a musician's audible notes which are the observations or outcomes in the model are generated from a written musical score which are the hidden States the actually written notes um they're uh they simulate the Dynamics of basian belief updating induced by a sequence of her notes again the outcomes um and then from there it gets into before I move on to the next section it's just worth noting all of these experiments in this chapter more or less to note very specifically what are the hidden States uh what are the outcomes what are our matrices that we're looking at um the a matrix or likelihood Matrix probability of observation given State um our B matrices which is our beliefs about how one state moves to the next uh from time step to time step we have our D Vector which are our prior beliefs uh about States just starting at time step one that's it once you move on from there uh D is no longer it's in the equation but it's not repeatedly used at every time step um although it can be updated depending on how you're running an experiment such as from trial to trial um so we get to see how it evolves over time time there are five total time steps it's another thing important to note a lot of experiments you'll typically decide how many time steps occur or will occur over the course of your experiment so here there are five a total of five notes that are played thanks Daniel for going to figure 7.2 um I guess to get a little bit more in depth here uh upper left of that figure shows the the models kind of um posterior beliefs about States and it's confidence and so like these lines start to stretch outward at first it's getting the the right notes for time step one and time step two Suddenly at time step three we get an incorrect note or at least an unexpected note uh there's a difference between the observations which are in the lower right corner um a certain note is played twice in a row incorrectly versus um what should have happened or what we expect expected which is the top right graph unless you can see that lightly gray square that is and the model correctly inferred the right note one that's in black but it was thrown off by that incor incorrect…