In this article, we present a visual introduction to Gaussian Belief Propagation (GBP), a probabilistic inference algorithm that operates by passing messages between the nodes of arbitrarily structured factor graphs. A special case of loopy belief propagation, GBP updates rely only on local information and will converge independently of the message schedule. Our key argument is that, given recent trends in computing hardware, GBP has the right computational properties to act as a scalable distributed probabilistic inference framework for future machine learning systems.
a process to uniquely encode two natural numbers into a single natural number (Used in diagonal arguments to prove integers and rationals have the same cardinality)
g(x, y) = (x^2 + 2xy + y^2 + x + 3y)/2is called the /Cantor pairing function/. “The statement that this is the only quadratic pairing function is known as the Fueter–Pólya theorem . Whether this is the only polynomial pairing function is still an open question.”
/This sentence has five words. Here are five more words. Five-word sentences are fine. But several together become monotonous. Listen to what is happening. The writing is getting boring. The sound of it drones. It’s like a stuck record. The ear demands some variety. Now listen. I vary the sentence length, and I create music. Music. The writing sings. It has a pleasant rhythm, a lilt, a harmony. I use short sentences. And I use sentences of medium length. And sometimes, when I am certain the reader is rested, I will engage him with a sentence of considerable length, a sentence that burns with energy and builds with all the impetus of a crescendo, the roll of the drums, the crash of the cymbals–sounds that say listen to this, it is important./
I don’t have a strong opinion on the matter, but interesting debate.