Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

all right welcome back cohort 6 it's 219 and we're in our first discussion of chapter 2 so Oli thank you for facilitating and kick it off and then let's see what we go okay thank you uh all right so in chapter two uh we delve into I mean uh the main uh compon one of the main components of active inference Theory uh namely uh how to formulate action and perception uh based on variational approaches so for perception uh the optimization parameter that needs to be minimized is the variational free energy and for the uh action counterpart the similar parameter would be uh the expected free energy uh so basically uh in this chapter we encounter two of the central equations of active inference Theory uh which are equations 2.5 and 2.6 uh one for the variation of free energy which formulates how uh the agent or the cognitive agent optimizes uh the variation free energy as its minimization parameter and similarly in equation uh 2.6 uh we see the same uh same mechanism as applied to a minimization of the expected free energy in the case of action uh but before uh going into the details of uh what those equations show and how how they work uh in the context of active inference it might be helpful to just uh go through the whole chapter um I mean uh in case uh there's any there's I mean any Gap in the understanding of what the whole picture here is so uh first uh as the title of the section 2.2 suggest perception as inference is one of the motors of active inference because uh as we know sometimes uh in the computational or the traditional cognitive science uh we treat perception as uh simple information processing um mechanism but here in active inference perception uh is treated as a kind of inference and not just symbol processing or information processing approach and the way to do that is uh to formulate it in terms of uh basian theor uh base Theory so uh in box 2.1 uh there is this fundamental rule of probability about I mean sumon product rules which is which are used uh in base Theory and then in equation 2 .1 uh The Familiar uh base theorem uh uh is introduced and then uh through an example in figure 2.1 it shows how exactly priors and beliefs are formulated and expressed in base theorem and later by using uh by by using those summon product rules uh we can write the posteriors uh and specifically the posteriors in the denominator as a kind of marginalization over uh over the probabilities of observations so that's basically what's been done in equation 2.2 and then uh here on page 20 there's this a useful distinction between the notion of surprise as applied in Psychology or at least folk psychology and the notion of surprise an active inference or namely the basian surprise sometimes it's called surprisal surprisal function uh so uh basically the difference between those two concepts are uh they are obviously related but they're not actually identical so when we talk about psychological surprise it connotes something about the effective uh notion of that surprise I mean uh we need to be uh we need to be affected by uh By An Unexpected observation in order for us to be surprised but here when we talk about basium surprise it's much more formal and it only describes uh the degree or the extent of the unexpected event regardless of how effectively it influences us as human observers or cognitive observers so it's just basically um uh something very formal and statistical so um one other key movements of active inference formulation is the use of callback lier Divergence uh for the comparison uh uh I mean uh for the comparison between the prediction and The observed uh data so uh the the justification to use callback lier Divergence comes from uh neon Pearson Lemma uh which I don't think is stated explicitly in the text because uh in uh non Pearson Lema uh it states that the most efficient statistic to compare two distributions is the logarithm of their likelihood ratios so basically that's what callback lier Divergence is it's…