Textbook Group meeting for Parr, Pezzulo, Friston 2022 .

Welcome everyone to the Active Inference Institute textbook reading group. This is cohort 7 continuing on with chapter 8 of the textbook. We already know that we are in the second half of the textbook, meaning we're much more focused on practice uh rather than theory uh which we had in the first part. In chapter 2, we were introduced in chapter six, excuse me, in part two, we were introduced in chapter six to a recipe for building active inference models. So we're familiar with all of uh you know the core fundamentals including what is your system of interest or your agent or your generative model that you are looking at and then what is on the other hand uh to use Mark Solmes's words uh just as we identified a system of interest we have to figure out our not system that is what is not the system of interest what is the environment or other variables uh that you know exist in the world but are not um part and parcel with our agent. Right? So that's that means identifying what is our generative uh process or the environment or the not system. And so we are familiar with a lot of the core components. We look at things like hidden states, observations and uh actions or policies which are sequences of actions. And then we identify the variables of the models, the different parameters. And from there we just build upward and we look at what kind of model is necessary for understanding our particular system of interest. And uh so we looked at chapter 7 which had to do with discrete state space models and that covered largely the hidden Markov model in the musician example and then built up to the POMDP or partially observable Markov decision-m process uh which is sort of the exemplar discrete state space model and that uh was illustrated through use of the T-mase example mouse choosing left or So we know already with the discrete state space that we if we followed up to the end of chapter 7, we can build models where there are discrete actions being taken like the mouse chooses the left or the right arm of the maze or it chooses to visit the informative cue along the way. But these ultimately amount to three different actions per time step. Um they are not a continuous state space. Right? So for those who are very familiar with anything from just general statistics linear regression up to machine learning and deep learning models that work with continuous state spaces often times we want to create models that can predict continuous values such as 37.99 as opposed to choose left in the teammates right and that also means being able to read continuous data such as from data streams IoT devices um financial data uh there's a plethora of different kinds of continuous uh data to look at. So that's what brings us here to chapter 8 looking at continuous time models. The these are arguably where active inference started. Um neuronal signals are usually measured continuously including from uh electronphilography or EEG uh devices as well as uh fMRI and looking at bolt signals as well as a variety of other physiological data including things like heart rate. So whenever we get into chapter eight, uh we turn to continuous state space models which the authors state are well suited for modeling physical fluctuations impinging on sensory receptors and for the continuous motion of the aectors, eg the muscles we used to change the world around us with model examples for the dynamical systems involved in motor control as well as the concept of generalized synchrony and finally constructing hybrid models for combining discrete and continuous variables at different levels which features at the end of the chapter. So largely we're introduced to notation for stochastic equations uh which invol are involved in continuous time models. Uh we see a lot of similar notation to what we've seen so far earlier on in the textbook. The authors largely use y to denote uh observations and x to denote hidden states. here. This is not terribly different, but we…