Theoretical Impediments to Machine Learning with Seven Sparks from Causality | Hacker News Reader

Theoretical Impediments to Machine Learning with Seven Sparks from Causality

arxiv.org

71 pointsmagoghm15 comments

His best observation is "Anthropologists like N. Harari, and S. Mithen are in general agreement that the decisive ingredient that gave our Homo sapiens ancestors the ability to achieve global dominion, about 40,000 years ago, was their ability to choreograph a mental representation of their environment, interrogate that representation, distort it by mental acts of imagination and finally answer “What if?” kind of questions." I can agree with that.

I've been saying something like that since the 1980s, but less abstractly. I've argued that "common sense" is the ability to examine a proposed course of short term action and predict generally what will happen. I used to work on this at a low level, along the lines of "much of life is about getting through the next 15 seconds in the real world without falling down or bumping into anything". That's needed to survive in the real world. That led me into automatic driving, legged running, grasping by touch, and similar low level problems. Most of the brain in lower level mammals manages things at that level. Once you've got that, maybe some higher level can back-seat drive the short-term system to achieve higher level goals. I argued for getting the lower level right first. AI still isn't very good at this, which is why mobile robots are not yet useful.

It's clear that machine learning as we know it today has real problems doing strong AI. We all know that. But this paper does not demonstrate that the author's pet approach is any better. There are no examples. No working systems. Also, trying to hammer the world into predicate calculus just doesn't work. I went through Stanford at the peak of that idea in the mid-1980s, and watched all the big names hit a wall.

Trying to hammer the world into predicate calculus just doesn't work. Trying to hammer the world into "thought vectors" doesn't work either. Where to?

Geometry? Maybe probabilistic geometry, like SLAM.

>Once you've got that, maybe some higher level can back-seat drive the short-term system to achieve higher level goals.

http://slatestarcodex.com/2017/09/05/book-review-surfing-unc...

Some say some books need to be chewed and digested, but that it is worth the effort. Well, I've been chewing this from time to time since his 2011 Turing prize; and I have yet to be able to build an understanding around it. Understanding Michael StoneBreaker's was much easier. Build great databases. Several times. Get prizes.

It feels like this causality formulation begs for modelling, and for a program to be able to execute and test its own do-calculus actions; to provide the world with a compelling 'Hello World'. Maybe emit some counterfactuals too.

Reinforcement Learning seems to yield way better results at exploring the world; at producing actions that help model and test (and then influence) the world.

Why is not more used? What's the story around it?

turbocodes, belief propagation, bayes nets are more significant in industry

Judea Pearl is tough going for me. I've never met him but he comes across as arrogant and condescending through his writing. I also find his writing very tough to follow. Even so, his Do-calculus is a valuable perspective on causal inference. Dawid is my go to source for clear exposition of causal concepts. Hard to find a clearer thinker and better writer in this area.

I agree that this article came off as a bit condescending.

Pearl has a more general-audience book coming out this year coauthored with Dana Mackenzie called The Book of Why: The Science of Cause and Effect. I'm hoping that it will be a more gentle introduction to the topic. I'll check out Dawid in the meantime.

can you clarify what Dawid you're referring to? The one who authored https://www.ucl.ac.uk/statistics/research/pdfs/rr279.pdf ?

>Such systems cannot reason about interventions and retrospection and, therefore, cannot serve as the basis for strong AI.

Can't they, though? Humans can't reason about quite a lot of their own behavior either. Another question, as a complete outsider to the topic: can't reasoning be implemented as a higher order abstraction over a statistical model?

>> To appreciate the extent of this denial, readers would be stunned to know that only a few decades ago scientists were unable to write down a mathematical equation for the obvious fact that “mud does not cause rain.” Even today, only the top echelon of the scientific community can write such an equation and formally distinguish “mud causes rain” from “rain causes mud.” And you would probably be even more surprised to discover that your favorite college professor is not among them.

I know who Judea Pearl is, but this is just conceited. "Only the top echelon of the scientific community"? What, of _any_ field?

More importantly, the scientific community can express "mud does not cause rain" in a formal manner and they have been able to do this since the beginning of the last century:

  ¬Causes(mud, rain) ∧ Causes(rain, mud)

It's not specifically an equation -it's a theory- but it does the job in a formal language with Turing equivalent expressive power. So does this:

  p(mud | rain) = 1.0
  p(rain | mud) = p(rain)

Additionally, in modern machine learnign there are theoretical results that prove the learnability of all computable functions by various different classes of algorithm -inverse deduction for symbolists (like myself), backpropagation for the connectionists and so on [1]. It's really hard to reconcile such theoretical results with the claim that there are, basically, things you can't learn with, say, neural networks or genetic algorithms, but can learn with counterfactuals.

_____________

[1] Nice little talk by Pedro Domingos summarising his "Master Algorithm" ideas, including a bit about Judea Pearl's favourite type of machine learning:

https://www.youtube.com/watch?v=B8J4uefCQMc

  >  p(mud | rain) = 1.0
  >  p(rain | mud) = p(rain)

I'm not sure these statements say what you think they do. Assuming P(rain) > 0, the first statement

  p(mud | rain) = 1.0

is equivalent to

  p(mud & rain) = p(rain).

The second statement therefore implies

  p(rain | mud) = p(mud & rain).

Thus

  p(rain & mud) / p(mud) = p(mud & rain).

This, however, leads to the surprising conclusion

  p(mud) = 1.0.

According to your theory, it is always muddy.

I think what's meant is something like p(mud_{t+1} | rain_{t}) = 1 and p(rain_{t+1} | mud_{t}) = p(rain). Say during 10 units of time it rains at points 1, 3, 4, 6, and 10 and it's muddy IFF it rained in the previous period. Then the above probability statements are true and it's only muddy 40% of the time.

OK, but that's not a big problem. My theory only needs to say that mud doesn't cause rain. Judea Pearl says that only his addition to Bayesian probabilities can do that.

I guess I could have thought of a better example, but I like how ryanmonroe's comment interprets it, below.

> p(mud | rain) = 1.0

> p(rain | mud) = p(rain)

tr352 has already detailed below why this doesn't work, but I think it's worth noting why this is fundamentally the wrong thing. When you look at P(X|Y), you're conditioning on everything you can infer having seen Y -- you're not limiting yourself to causal connections. So in fact, you're not correct to say that P(rain|mud) = P(rain); P(rain|mud) will be greater than P(rain); the fact that it's muddy out does indeed tell you that it is more likely to be raining out, even though the causality does not run that way.

(Indeed, in general, P(X|Y)>P(X) if and only if P(Y|X)>P(Y) -- this occurs if and only if X and Y are positively correlated -- but causality is not symmetric, so you certainly cannot represent causality with "being positively correlated", a symmetric relation! Similarly P(X|Y)=P(X) if and only if P(Y|X)=P(Y); this occurs if and only if X and Y are independent. I'm pretty sure you don't mean to say that rain and mud are independent of one another, but that's what we must conclude from your equations.)

Basically, you're talking about P(rain|mud), but what you actually want is something like P(rain|do(mud)); it is indeed the case that P(rain|do(mud))=P(rain). But pure probability theory can't capture that, which is the point of what Pearl is saying. Probability theory really does not work like causality works, and cannot capture the same information, and if you ignore this and try to use probability theory as if it were causality anyway you are going to end up with some seriously nonsensical results, like thinking that rain and mud are independent of one another.

(Meanwhile, the problem with your first attempt, namely,

> ¬Causes(mud, rain) ∧ Causes(rain, mud)

is, well... it's not wrong, it's just completely unhelpful. OK, so you've made "causes" into a primitive relation. Great. Now how do we reason about that? All you've done is rephrased a statement, what we need here is a system of reasoning.)

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