Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

all right welcome back cohort 7 and all Andrew to you and just take it however sure all right um yeah so welcome everyone we're uh cohort 7 here discussing chapter two of the active inference textbook by friston par at all and uh here we're looking at the low road to active inference so uh as we saw in the previous chapter there was a kind of schematic showing uh there might be two general paths that that one can take to to reach an understanding of active inference so one of them is kind of starting from uh something like basium mechanics and statistics which is what the low road is all about that's what we'll be talking about today and then from the other angle one can approach active inference by starting with the free energy principle and General uh imperative for for organisms to uh act and perceive and so on in order to achieve homeostasis uh where possible and again we can reach active inference from there so I was just going to give a hopefully brief uh summary of of chapter two um starting from the first section uh it begins with the helm holian or perhaps Conan perspective of perception as unconscious inference as well as the basy and brain hypothesis and so with this framework we're treating the cognitive mechanisms of perception action planning and learning as Basi and inference problems as well as deriving a variational approximation uh to overcome the typical intractability problems which arise when attempting to compute exact basian inference uh those Concepts or something we'll be getting into later in the chapter so uh to start with there's perception is inference uh the authors claim perception is not just a bottomup process of turning sensory States or observations into internal representations of the outside as if it were a one-way process from from outside in uh despite the fact that this has been argued historically in various cognitive science Traditions they say instead it is an inferential process that combines top- down prior information about the most likely causes of Sensations with bottomup sensory stimuli so it's more of an inside out process uh we could liken this to comparing a prior hypothesis with the outcomes of an experiment which act as our confirmatory or disconfirmatory evidence for our hypothesis so um from there we can relate this idea of priors and observations or evidence uh using B's rule so uh bases rule we can we can break that down into these kind of component parts so we have our priors probability of X is the nomenclature that's used in this chapter more frequently used for describing continuous time active inference models uh and then we have uh our marginal probability of observations evidence U probability of Y and then these get related through a fun uh what called a likelihood model or function which is probability of Y given X or the probability of the evidence given your priors and then we can flip that through the equation and use incoming new evidence to update uh what would be called our posterior probability of X conditioned on y so our probability of pin States given the New Evidence um we're given a kind of a brief refresher of course this is this is basing in probabilities so we're dealing with probabil uh probabilistic reasoning so uh for anyone in the math group or or otherwise who was still getting a feel for some of the mathematics going on here it's good to familiarize yourself at least at first with some of the simpler uh ideas behind probabilistic reasoning including the the sum Rule and and product rules regarding like probability distributions sum to one uh there are no negative probability values maybe you know in the process of computing your final result you might have something like that but in any case in the final outcome no negative values and um as well as like marginalization those kinds of things so we're given um we're given a example of like for uh someone who's visually perceiving an object and they're trying to decide is it a frog or an…