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Isn't free-energy nothing more than a maximization approximation to Bayesian inference. p(u|x)=p(x|u)p(u)/p(x) + max in log space: max ln p(x|u) + ln p(u) +
by MrQuincle 9y ago
Isn't free-energy nothing more than a maximization approximation to Bayesian inference.
p(u|x)=p(x|u)p(u)/p(x)
+ max in log space: max ln p(x|u) + ln p(u)
+ use variational approximation, e.g. Kullback-Leibler: min ln KL(q(u)|p(x|u)) + ln p(u)
+ define free energy: F = ln p(u) - KL, so it can be maximized
Hence, rather than with KL where we minimize over a ratio with conditional p(x|u), we maximize over the joint 1/p(x,y). So we optimize for both likelihood and prior.
Sounds to me as a sloppy Bayesian approach. :-) Normally, the prior is intended to be used as full distribution. Not to get a max. probable value from.
In this approach we maximize for both prior and likelihood. Seems logical that we get all kind of possible trade-offs. Which should we choose? And why is free-energy so perfect?
- eli_gottlieb 9y agoThe "free-energy principle" in this case isn't just variational inference via a free-energy cost derived from the KL divergence. It involves treating action (control signals) as a variational parameter to the recognition density. The agent thus treats their likelihood function as a descriptive model of the world, and their prior as a prescriptive model: they update their beliefs (recognition density) to be accurate Bayesian inferences, but then act so as to reduce prior improbability (despite accumulation of likelihood data).