R. Bogacz delivers a detailed and beautifully made tutorial on a subject that can be very difficult to understand, Variational Bayes, as seen from Karl Fristons perspective; Namely invoking the Free-Energy principle to motivate Active Inference.

In the last decade, Active Inference has gained traction with the wider neuroscientific community, and recently Karl was measured to be the most influential neuroscientist in the modern era. I use the same notation as in R. Bogacz.

The code implements and refers to equations in the paper, and network graphs were provided by Bogacz himself. A simple organism is trying to infer the size v” role=”presentation”>vv of a food item.

The only source of noisy information is one photoreceptor that signals the light reflected from this item, we denote this u” role=”presentation”>uu. The non-linear function that relates size v” role=”presentation”>vv to photosensory input u” role=”presentation”>uu is assumed to be g(v)=v2″ role=”presentation”>g(v)=v2g(v)=v2.

We assume that this signal is normally distributed with mean g(v)” role=”presentation”>g(v)g(v) and variance Σv” role=”presentation”>ΣvΣv. We can write of the the likelihood function (probability of a size v” role=”presentation”>vv given a signal u” role=”presentation”>uu) as is the normal distribution with mean μ” role=”presentation”>μμ and variance Σ” role=”presentation”>ΣΣ. Read more from tmorville.github.io…

thumbnail courtesy of tmorville.github.io