Many of you who have followed the evolution of this variational inference discussion (over the past ten blogposts), may be wondering where to start. This would be particularly true for readers who are not necessarily familiar with the variational-anything literature, and would like to begin with the easiest, most intuitive-explanatory articles possible, and then gently… Continue reading Variational Free Energy: Getting-Started Guide and Resource Compendium
Tag: Matthew Beal
Variational Free Energy and Active Inference: Pt 5
The End of This Story This blogpost brings us to the end of a five-part series on variational free energy and active inference. Essentially, we’ve focused only on that first part – on variational free energy. Specifically, we’ve been after Karl Friston’s Eqn. 2.7 in his 2013 paper, “Life as We Know It,” and similarly… Continue reading Variational Free Energy and Active Inference: Pt 5
Variational Free Energy and Active Inference: Pt 4
Today, we interpret the q(Psi | r) and p(Psi, s, a, r | m) in Friston’s (2013) “Life as We Know It” (Eqn. 2.7) and Friston et al. (2015) “Knowing One’s Place” (Eqn. 3.2). This discussion moves forward from where we left off in the previous post, identifying how Friston’s notation builds on Beal’s (2003)… Continue reading Variational Free Energy and Active Inference: Pt 4
Variational Free Energy and Active Inference: Pt 3
When we left off in our last post, we’d determined that Friston (2013) and Friston et al. (2015) reversed the typical P and Q notation that was commonly used for the Kullback-Leibler divergence. Just as a refresher, we’re posting those last two images again. The following Figure 1 was originally Figure 5 in last week’s… Continue reading Variational Free Energy and Active Inference: Pt 3
Variational Free Energy and Active Inference: Pt 2
Our intention with this post is to cover not only the notion, but the notation, used by Karl Friston in his 2013 paper, “Life as We Know It.” (Actually, we’re addressing a very small notational subset – albeit one that needs to be treated with great care and caution.) To do this, we’re also discussing… Continue reading Variational Free Energy and Active Inference: Pt 2
Variational Free Energy and Active Inference: Pt 1
Overarching Story Line This new blogpost series, on variational free energy and active inference, presents tutorial-level studies centered on the free energy equation (Eq. 2.7) of Karl Friston’s 2013 paper, “Life as We Know It.” Specifically, we’re focused on the free energy equation shown in Figure 1 below. Over this blogpost series, we will reinforce… Continue reading Variational Free Energy and Active Inference: Pt 1
Kullback-Leibler, Etc. – Part 3 of 3: The Annotated Resources List
I thought it would be (relatively) straightforward to wrap this up. Over the past several posts in this series, we’ve discussed the Kullback-Leibler (K-L) divergence and free energy. In particular, we’ve described free energy as the “universal solvent” for artificial intelligence and machine learning methods. This next (and last) post in this series was intended… Continue reading Kullback-Leibler, Etc. – Part 3 of 3: The Annotated Resources List
The Kullback-Leibler Divergence, Free Energy, and All Things Variational – Part 1.5 of 3
Let’s talk about the Kullback-Leibler divergence. (Sometimes, we call this the “K-L divergence.”) It’s the foundation, the building block, for variational methods. The Kullback-Leibler divergence is a made-up measure. It’s not one of those “fundamental laws of the universe.” It’s strictly a made-up human thing. Nevertheless, it’s become very useful – and is worth our… Continue reading The Kullback-Leibler Divergence, Free Energy, and All Things Variational – Part 1.5 of 3
The Kullback-Leibler Divergence, Free Energy, and All Things Variational (Part 1 of 3)
Variational Methods: Where They Are in the AI/ML World The bleeding-leading edge of AI and machine learning (ML) deals with variational methods. Variational inference, in particular, is needed because we can’t envision every possible instance that would comprise a good training and testing data set. There will ALWAYS be some sort of oddball thing that… Continue reading The Kullback-Leibler Divergence, Free Energy, and All Things Variational (Part 1 of 3)