I see. so -
If P(H) = 1.0 - ϵ1
And P(E|H) = 0 + ϵ2
Then it equals "infinite confusion".
Am i correct?
and also, when you use epsilons, does it mean you get out of the "dogma" of 100%? or you still can't update down from it?
And what i did in my post may just be another example of why you don't put an actual 1.0 in your prior, cause then evidence of the same strength in the other direction would demand that you divide zero by zero. right?ryan_b on Declarative Mathematics
This is a great post! Thank you in particular for the Stephen Boyd recommendation.
In terms of frameworks and ML, you might be interested in this blog post announcing the release of the DiffEqFlux.jl package in the Julia programming language. I was reminded of this because it seems to be an example of merging already-mature frameworks, specifically a machine learning framework (Flux) and a differential equation framework (DifferentialEquations.jl).
A recent paper called Neural Ordinary Differential Equations explored the problem of parameterizing a term in an ODE instead of specifying a sequence of layers, using ML techniques. The benefit of the combined framework is that it allows us to incorporate what we already know about the structure of the problem via the ODE, and apply neural networks to the parts we don't.
I'm not deeply familiar with either framework, but I have been following DifferentialEquations.jl for a while because I had hoped it would let me tackle a few problems I have had my eye on.
I feel like Geometric Algebra is pointing in a similar direction to what you describe. It is not directly an applied framework, but rather a kind of ur-framework for teaching and developing other frameworks on top of it. The idea is that they make geometric objects elements of the algebra, which really boils down to making the math match the structure of space and in this way preserve geometric intuitions throughout. Its advocates hope it will serve as a unified framework for physics and engineering applications. The primary theorist is David Hestenes, and his argument for why this was necessary is found here; there are surveys/tutorials from other people who have done work in the field here and here.
Geometric Algebra and its extension Geometric Calculus are both still pretty firmly in the 'reorganizing math' kind of endeavor, with lots of priority put on proving results and developing algorithms. But there are a few areas where they are growing into an applied framework of the kind you describe, specifically robotics, computer graphics, and computer vision.
It was through the robotics applications that I found it; they promised an intuitive explanation of quaternions, which otherwise were just this scary way to calculate motion.jimrandomh on Can a Bayesian agent be infinitely confused?
The latter; it could be anything, and by saying the probabilities were 1.0 and 0.0, the original problem description left out the information that would determine it.yoav-ravid on Can a Bayesian agent be infinitely confused?
Thanks for the answer! i was somewhat amused to see that it ends up being a zero divided by zero.
Does the ratio between 1epsilon over 2epsilon being undefined means that it's arbitrarily close to half (since 1 over two is half, but that wouldn't be exactly it)? or means that we get the same problem i specified in the question, where it could be anything from (almost) 0 to (almost) 1 and we have no idea what exactly?eh_yo_lexa on New Entry at the Stanford Encyclopedia of Philosophy on the Pragmatic Theory of Truth
I personally find this subject (pragmatism generally) interesting, but others here might not. If you're going to link to an external source, could you please write a post detailing what is being explained in the external source and why people here might find it relevant plus why they should care about it? I strong-downvoted your post because simply link-posting with no context or explanation about why the topic is relevant/why people should care, is almost always a non-useful thing for people, and if one is going to post things here, they ought to be useful for the community.
Cheersjimrandomh on Can a Bayesian agent be infinitely confused?
If you do out the algebra, you get that P(H|E) involves dividing zero by zero:
There are two ways to look at this at a higher level. The first is that the algebra doesn't really apply in the first place, because this is a domain error: 0 and 1 aren't probabilities, in the same way that the string "hello" and the color blue aren't.
The second way to look at it is that when we say P(H)=1.0 and P(E|H)=0, what we really meant was that P(H)=1.0−ϵ1 and P(E|H)=0+ϵ2; that is, they aren't precisely one and zero, but they differ from one and zero by an unspecified, very small amount. (Infinitesimals are like infinities; ϵ is arbitrarily-close-to-zero in the same sense that an infinity is arbitrarily-large). Under this interpretation, we don't have a contradiction, but we do have an underspecified problem, since we need the ratio ϵ1ϵ2 and haven't specified it.william_s on The Main Sources of AI Risk?
Is this future AI catastrophe? Or is this just a description of current events being a general gradual collapse?
This seems like what is happening now, and has been for a while. Existing ML systems are clearly making Type-I problems, already quite bad before ML was a thing at all, much worse, to the extent that I don't see much ability left of our civilization to get anything that can't be measured in a short term feedback loop - even in spaces like this, appeals to non-measurable or non-explicit concerns are a near-impossible sell.
Part II problems are not yet coming from ML systems, exactly, But we certainly have algorithms that are effectively optimized and selected for the ability to gain influence; the algorithm gains influence, which causes people to care about it and feed into it, causing it to get more. If we get less direct in the metaphor we get the same thing with memetics, culture, life strategies, corporations, media properties and so on. The emphasis on choosing winners, being 'on the right side of history', supporting those who are good at getting support. OP notes that this happens in non-ML situations explicitly, and there's no clear dividing line in any case.
So if there is another theory that says, this has already happened, what would one do next?dagon on Intuitions on Negative Utilitarianism
On the "a day in hell cannot be outweighed" question, do you have any analysis of that intuition? Are you assuming that you'll remember that day and be broken by it, or is there some other negative value you're putting on it. Do you evaluate "a day in hell, 1000 years in heaven, then termination" differently from "1000 years in heaven, then a day in hell, then termination"? How about "a day in hell, mind-reset to prior state, then 1000 years in heaven"?
The reason I ask is that I'm trying to understand what's being evaluated. Are you comparing value of instantaneous experience integrated over time, or are you comparing value of effect that experiences have on your identity?