trentmkelly/LessWrong-43k huggingface dataset:
Why the Modified Demski Prior is better than the original
by Scott Garrabrant — 2015-10-06T18:50:57.000Z

Often, when talking about the Modified Demski Prior, I get the question "Why is this any different than the original? The original could have sampled logical sentences that claim that all outputs of a given Turing machine are true, with only a bounded complexity penalty." This post gives an answer to this question.

At first it may seem that there is no siginificant difference between the Demski Prior, and the Modified Demski Prior. The former samples logical sentences, while the latter samples Turing machines (Which can be represented as logical sentences). However, there is a subtle difference that actually causes the two to have radically different behavior.

Consider a Turing machine T which outputs an infinite string of sentences. The Modified Demski prior might sample T, and the Demski prior might sample the sentence "Every sentence output by T is true." (There is a little complication here with needing a slightly different language, but that is not what makes the big difference.)

The big difference between the two Priors is that in the Demski Prior, you can sample a sentence of the form "Not every sentence output by T is true." If you do, then if you later sample "Every sentence output by T is true," you will have to throw it out. There is no analogous TM you can sample in the Modified Demski prior. T can only be contradicted by a earlier Turing machine which directly contradicts one (or a finite number) of the sentences output by T. If you sample a machine that outputs one sentence that says that T outputs at least one false sentence, and then later sample T, the model you will have will believe that T outputs a false sentence at some nonstandard time, while all the actual outputs of T are true.

This makes a huge difference when T only outputs tautologies. Note that this does not change the end prior, but it does change the approximation procedure. If T is a machine that only outputs tautologies, then eventually the Modified Demski algorithm will sample T, and will believe that any sentence output by T is true (Even if it does not see a proof yet). This happens eventually with probability 1, since there is no consistent set of sentences which could contradict any output of T. This was important for showing that the Modified Demski Prior was Uniformly Coherent.

On the other hand, the first sentence sampled by the Demski Prior may have been "Not every sentenc

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Optimal predictors for global probability measures
by Vanessa Kosoy — 2015-10-06T17:40:19.000Z

There are two commonly used formalisms in average case complexity theory: problems with a single global probability measure on parameter space or problems with a family of such probability measures. Previous posts about optimal predictors focused on the family approach. In this post we give the formalism for global measures.

Results

New notation

1 will denote the one-element set.

Given μ a probability measure on {0,1}∗, X a set, Q:{0,1}∗2alg−→X, TμQ(s) stands for the maximal runtime of Q(x,y) for x∈suppμ, y∈{0,1}s.

Definition 1

A unidistributional estimation problem is a pair (f,μ) where μ is a probability measure on {0,1}∗ and f:suppμ→[0,1] is an arbitrary function.

Definition 2

Given appropriate sets X, Y, consider P:N×X×{0,1}∗2alg−→Y, r:N→N polynomial and a:N→{0,1}∗. The triple ^P=(P,r,a) is called a (poly,log)-scheme of signature X→Y when

(i) The runtime of P(j,x,y,z) is bounded by p(j) with p polynomial.

(ii) |a(j)|≤c1+c2log(j+1) for some c1,c2∈N.

A (poly,log)-scheme of signature {0,1}∗→[0,1] will also be called a (poly,log)-predictor.

Given j∈N, x∈X, ^Pj(x) will denote the Y-valued random variable P(j,x,y,a(j)) where y is sampled from the probability measure Ur(j). We will also use the notation ^Pj(x,y):=P(j,x,y,a(j)).

Fix Δ an error space of rank 1.

Definition 3

Consider (f,μ) a unidistributional estimation problem and ^P=(P,r,a) a (poly,log)-predictor. ^P is called a Δ(poly,log)-optimal predictor for (f,μ) when for any (poly,log)-predictor ^Q=(Q,s,b), there is δ∈Δ s.t.

Eμ×Ur(j)[(^Pj(x)−f(x))2]≤Eμ×Us(j)[(^Qj(x)−f(x))2]+δ(j)

Δ(poly,log)-optimal predictors for unidistributional problems have properties and existence theorems analogical to Δ(poly,log)-optimal predictor schemes, where the role of the rank 2 error space Δ2avg is taken by the rank 1 error space Δ1ll (see Definition 8). The theorems are listed below. The proofs of Theorem 4, Theorem 8 (which is stated stronger than previous analogues) and Theorem 10 are given in the appendix. Adapting the other proofs is straightforward.

Theorem 1

Suppose (j+1)−1∈Δ. Consider (f,μ) a unidistributional estimation problem and ^P=(P,r,a) a Δ(poly,log)-optimal predictor for (f,μ). Suppose {pj∈[0,1]}j∈N, {qj∈[0,1]}j∈N are s.t.

∃ϵ>0∀j:(μ×Ur(j)){(x,y)∈{0,1}∗2∣pj≤^Pj(x,y)≤qj}≥ϵ

Define

ϕj:=Eμ×Ur(j)[f(x

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Meetup : Less Wrong NH Meet-up
by Tuk — 2015-10-06T03:39:12.318Z

Discussion article for the meetup : Less Wrong NH Meet-up

WHEN:
13 October 2015 07:00:00PM (-0400)

WHERE:
269 Pearl St Manchester NH

The fifth NH meet-up is Tuesday, 10/13, in Manchester, NH at 7 pm at a private residence. Light refreshments will be provided.

Have you read Rationality: from AI to Zombies, or any of the Sequences on Less Wrong? Maybe you're just a fan of Harry Potter and the Methods of Rationality. Come hang out with us and discuss optimization of whatever it is you want to optimize.

You may want to bring a notebook.

https://www.facebook.com/events/882067888545859/

Discussion article for the meetup : Less Wrong NH Meet-up
Meetup : LessWrong Sao Paulo
by leohmarruda — 2015-10-06T01:54:32.100Z

Discussion article for the meetup : LessWrong Sao Paulo

WHEN:
10 October 2015 02:00:00PM (-0300)

WHERE:
Rua Mourato Coelho, 25 Pinheiros, São Paulo Brazil

At Casa cafe (possibly on the second floor).
Monthly meeting of the budding rationalist meetup :)
We'll have a short presentation at the beginning and possibly board games. :D
Don't be shy!
Join our mail list https://groups.google.com/forum/#!forum/racionalidade

Discussion article for the meetup : LessWrong Sao Paulo
A few misconceptions surrounding Roko's basilisk
by Rob Bensinger — 2015-10-05T21:23:08.994Z

There's a new LWW page on the Roko's basilisk thought experiment, discussing both Roko's original post and the fallout that came out of Eliezer Yudkowsky banning the topic on Less Wrong discussion threads. The wiki page, I hope, will reduce how much people have to rely on speculation or reconstruction to make sense of the arguments.

While I'm on this topic, I want to highlight points that I see omitted or misunderstood in some online discussions of Roko's basilisk. The first point that people writing about Roko's post often neglect is:

Roko's arguments were originally posted to Less Wrong, but they weren't generally accepted by other Less Wrong users.

Less Wrong is a community blog, and anyone who has a few karma points can post their own content here. Having your post show up on Less Wrong doesn't require that anyone else endorse it. Roko's basic points were promptly rejected by other commenters on Less Wrong, and as ideas not much seems to have come of them. People who bring up the basilisk on other sites don't seem to be super interested in the specific claims Roko made either; discussions tend to gravitate toward various older ideas that Roko cited (e.g., timeless decision theory (TDT) and coherent extrapolated volition (CEV)) or toward Eliezer's controversial moderation action.

In July 2014, David Auerbach wrote a Slate piece criticizing Less Wrong users and describing them as "freaked out by Roko's Basilisk." Auerbach wrote, "Believing in Roko’s Basilisk may simply be a 'referendum on autism'" — which I take to mean he thinks a significant number of Less Wrong users accept Roko’s reasoning, and they do so because they’re autistic (!). But the Auerbach piece glosses over the question of how many Less Wrong users (if any) in fact believe in Roko’s basilisk. Which seems somewhat relevant to his argument...?

The idea that Roko's thought experiment holds sway over some community or subculture seems to be part of a mythology that’s grown out of attempts to reconstruct the original chain of events; and a big part of the blame for that mythology's existence lies on Less Wrong's moderation policies. Because the discussion topic was banned for several years, Less Wrong users themselves had little opportunity to explain their views or address misconceptions. A...
How could one (and should one) convert someone from pseudoscience?
by Vilx- — 2015-10-05T11:53:21.478Z

I've known for a long time that some people who are very close to me are somewhat inclined to believe the pseudoscience world, but it always seemed pretty benign. In their everyday lives they're pretty normal people and don't do any crazy things, so this was a topic I mostly avoided and left it at that. After all - they seemed to find psychological value in it. A sense of control over their own lives, a sense of purpose, etc.

Recently I found out however that at least one of them seriously believes Bruce Lipton, who in essence preaches that happy thoughts cure cancer. Now I'm starting to get worried...

Thus I'm wondering - what can I do about it? This is in essence a religious question. They believe this stuff with just anecdotal proof. How do I disprove it without sounding like "Your religion is wrong, convert to my religion, it's right"? Pseudoscientists are pretty good at weaving a web of lies that sound quite logical and true.

The one thing I've come up with is to somehow introduce them to classical logical fallacies. That at least doesn't directly conflict with their beliefs. But beyond that I have no idea.

And perhaps more important is the question - should I do anything about it? The pseudoscientific world is a rosy one. You're in control of your life and your body, you control random events, and most importantly - if you do everything right, it'll all be OK. Even if I succeed in crushing that illusion, I have nothing to put in its place. I'm worried that revealing just how truly bleak the reality is might devastate them. They seem to be drawing a lot of their happiness from these pseudoscientific beliefs, either directly or indirectly.

And anyway, more likely that I won't succeed but just ruin my (healthy) relationship with them. Maybe it's best just not to interfere at all? Even if they end up hurting themselves, well... it was their choice. Of course, that also means that I'll be standing idly by and allowing bullshit to propagate, which is kinda not a very good thing. However right now they are not very pushy about their beliefs, and only talk about them if the topic comes up naturally, so I guess it's not that bad.

Any thoughts?
Open thread, Oct. 5 - Oct. 11, 2015
by MrMind — 2015-10-05T06:50:59.444Z

If it's worth saying, but not worth its own post (even in Discussion), then it goes here.

Notes for future OT posters:

1. Please add the 'open_thread' tag.

2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)

3. Open Threads should be posted in Discussion, and not Main.

4. Open Threads should start on Monday, and end on Sunday.
The Bayes Score Meliorizer
by Scott Garrabrant — 2015-10-05T05:50:03.000Z

We came up with another logical predictor proposal at MIRIxLA today. We were excited about it for a while, but it turned out to not to do much better than the Benford learner. I am writing it up, in case I or someone else wants to think about it later.

Consider the following probabilistic algorithm, which assigns probabilities to logical sentences (encoded by Godel numbers)

Input N.

Sample a sequence of N Turing machines, each of which output an infinite sequence of rational numbers.

Interpret each TM as a partial function fi from N to [0,1], where fi sends n to the nth number output, and in undefined if the output is not between 0 and 1

Restrict the sequence to only machines that output the first n bits in time 2n and only machines whose functions are defined on N.

The first function in the sequence starts out as the king. Each Turing machine one at a time in order tries to dethrone the current king.

To check whether or not the nth Turing machine dethrones the current king:
a. Consider the set S of all inputs on which both fn and the king are defined.
b. Run a theorem prover for N steps on each of these sentences in order, until you find one that can neither be proven or disproven in time N.
c. Let S′ be the subset S of sentences proven or disproven this way.
d. Compute the probability P which is the product of all the probabilities that fn assigns to the correct answer in S′.
e. Compute the probability Q which is the product of all the probabilities that the king assigns to the correct answer in S′.
f. If P is at least nQ, fn becomes the new king.

Output the probability that the king assigns to N.

This algorithm did not turn out to be as good as I originally thought it would be, and I probably wont do a good write up on all the properties of this algorithm. (If this opinion changes, I will write a lot more.) However, let me give a proof sketch that this algorithm is at least reasonable enough to get the Generalized Benford Test for subsequences s which are indistinguishable from a rational probability p coin.

Proof Sketch: Consider the machine T which only outputs probabilities on the subsequence s, and always outputs p . When N is large, with probability almost 1, thin Turing machine will be sampled. With probability 1−ε, all of the Turing machines sampled before T will have complexity at most k, where k is a function only of T and ε.

For N s

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Logical predictors cannot dominate their own complexity class
by Scott Garrabrant — 2015-10-05T04:45:49.000Z

One good property for a logical predictor (A Turing machine which tries to guess the output of an environment E that is too complex to simulate) is that it is able to to do asymptotically at least as well as any other logical predictor in some class.

We say that a logical predictor L dominates all the logical predictors in a set S if for every s in S, we get P(s,E,n)∈O(P(L,E,n)), where P(x,E,n) is the probability that x and E agree on the first n bits. That is to say that the probability L assigns to the correct environment is at least a constant times the probability that s assigns the correct environment is the limit.

Theorem: It is not in general possible for a machine L which runs in O(f(n)) time to dominate the class of all functions which run in O(f(n)).

Proof: Consider an environment E which flips pseudorandom coins for its output, such that the nth bit output by E could be computed it time 2ng(n), where g(n) is the number of times 2 divides n. Given less than this amount of time, there is no way to predict the coin flips that does asymptotically better than random.

Let L be a Turing machine which outputs the nth bit in c⋅2n time. Consider the set of all n with g(n)>c. L can do no better than random guessing, and so can get the first k such bits correct with probability at most 2−k. However, there exists a Turing machine which runs in time O(2n), and computes the correct answer for all n with g(n)≤c+1, and guess randomly on the rest. This algorithm does is twice as likely on average to get each n with g(n)=c+1. Therefore, the probability that this algorithm gets the first k elements correct divided by the probability that L gets the first k elements correct must go to infinity.

In principle, it is still possible for a logical predictor that runs in time f(n) to dominate any logical predictor that runs in time g(n), where f and g are any functions with g∈o(f). I am working on trying to find a predictor with this property.
Detach the grim-o-meter
by So8res — 2015-10-05T03:00:00.000Z
Link: https://mindingourway.com/detach-the-grim-o-meter/

I'm betting that the last three posts have given many readers an incorrect impression about my demeanor. It's easy to read those posts and conclude that I must be a grim, brooding character who goes around with his jaw set all day long.

Which is understandable, but silly. You don't need to carry a grim demeanor to draw strength from seeing the dark world. It's quite possible to deeply want the world to be different than it is, and tap into a deep well of cold resolve, and still also be curious, playful, and relaxed in turn.

This isn't a story, and we don't need to pretend to archetypes.

I've met many who are under the impression that when you realize the world is in deep trouble, you're obligated to respond by feeling more and more grim. Like a movie about a detective that's trying to save a kidnapped child: as the detective learns that the child is in more and more danger, they lock their jaw and become more and more grim and determined. Their respite comes only when the child is rescued.

That's narrative thinking, and we aren't in a narrative. You can break the trope. (In fact, I encourage you to break tropes as soon as you realize that you're acting them out.)

Many people seem to have this internal grim-o-meter which measures how grim the state of the world is, and they dutifully try to keep this calibrated. When they hear that they might be failing a class, they get a bit more grim, and this helps them buckle down. When they hear that there was an earthquake in Napal, they get a little more grim, and they maybe even feel guilty if they can't feel appropriately grim for appropriately long.

I say, it's good to have a grim-o-meter, but stop calibrating it against the state of the world. That's a terrible plan!

I mean, look at humanity at large. People are killing each other like it's going out of style, while millions die from disease each year and civilization careens towards self-destruction.

Now look at your grim-o-meter. It has, like, seven different settings. Maybe twelve, on a good day.

That detective in the movie about the kidnapped child might be able to faithfully use a twelve-setting grim-o-meter to track the grimness of their own situation.

But the real world? The one with billions of people each with rich inner lives, and astronomical future potential hanging by a pale blue thread in Time? There's no way you can justifiably connect a twelve-setting grim-o...
Logical counterfactuals using optimal predictor schemes
by Vanessa Kosoy — 2015-10-04T19:48:23.000Z

We give a sufficient condition for a logical conditional expectation value defined using an optimal predictor scheme to be stable on counterfactual conditions.

Definition

Given Δ an error space of rank r, the stabilizer of Δ, denoted stabΔ is the set of functions γ:Nr→R>0 s.t. for any δ∈Δ we have γδ∈Δ.

Theorem

Consider Δ an error space of rank 2, D⊆{0,1}∗, μ a word ensemble and ^PD a Δ(poly,log)-optimal predictor scheme for (χD,μ). Assume ϵ:N2→R>0 is s.t.

(i) ϵ−1∈stabΔ

(ii) ^PkjD≥ϵ(k,j)

Consider f:D∩suppμ→[0,1]
and ^P1, ^P2 Δ(poly,log)-optimal predictor schemes for (f,μ∣D). Then, ^P1μ≃Δ^P2.

Note

This result can be interpreted as stability on counterfactual conditions since the similarity is relative to μ rather than only relative to μ∣D. That is, ^P1 and ^P2 are similar outside of D as well.

Proof of Theorem

We will refer to the previously established results about Δ(poly,log)-optimal predictor schemes by L.N where N is the number in the linked post. Thus Theorem 1 there becomes Theorem L.1 here and so on.

By Theorem L.A.7

E(μk∣D)×Ur1(k,j)+r2(k,j)[(^Pkj1(x)−^Pkj2(x))2]∈Δ

Eμk×Ur1(k,j)+r2(k,j)[χD(x)(^Pkj1(x)−^Pkj2(x))2]μk(D)∈Δ

Eμk×Ur1(k,j)+r2(k,j)[χD(x)(^Pkj1(x)−^Pkj2(x))2]∈Δ

On the other hand, by Lemma L.B.3

Eμk×Ur(k,j)+r1(k,j)+r2(k,j)[(^PkjD(x)−χD(x))(^Pkj1(x)−^Pkj2(x))2]∈Δ

Combining the last two statements we conclude that

Eμk×Ur(k,j)+r1(k,j)+r2(k,j)[^PkjD(x)(^Pkj1(x)−^Pkj2(x))2]∈Δ

It follows that

Eμk×Ur1(k,j)+r2(k,j)[(^Pkj1(x)−^Pkj2(x))2]=ϵ(k,j)−1Eμk×Ur1(k,j)+r2(k,j)[ϵ(k,j)(^Pkj1(x)−^Pkj2(x))2]

Eμk×Ur1(k,j)+r2(k,j)[(^Pkj1(x)−^Pkj2(x))2]≤ϵ(k,j)−1Eμk×Ur(k,j)+r1(k,j)+r2(k,j)[^PkjD(x)(^Pkj1(x)−^Pkj2(x))2]

Eμk×Ur1(k,j)+r2(k,j)[(^Pkj1(x)−^Pkj2(x))2]∈Δ
[Link] Tetlock on the power of precise predictions to counter political polarization
by Stefan_Schubert — 2015-10-04T15:19:32.558Z

The prediction expert Philip Tetlock writes in New York Times on the power of precise predictions to counter political polarization. Note the similarity to Robin Hanson's futarchy idea.

IS there a solution to this country’s polarized politics?

Consider the debate over the nuclear deal with Iran, which was one of the nastiest foreign policy fights in recent memory. There was apocalyptic rhetoric, multimillion-dollar lobbying on both sides and a near-party-line Senate vote. But in another respect, the dispute was hardly unique: Like all policy debates, it was, at its core, a contest between competing predictions.

Opponents of the deal predicted that the agreement would not prevent Iran from getting the bomb, would put Israel at greater risk and would further destabilize the region. The deal’s supporters forecast that it would stop (or at least delay) Iran from fielding a nuclear weapon, would increase security for the United States and Israel and would underscore American leadership.

The problem with such predictions is that it is difficult to square them with objective reality. Why? Because few of them are specific enough to be testable. Key terms are left vague and undefined. (What exactly does “underscore leadership” mean?) Hedge words like “might” or “could” are deployed freely. And forecasts frequently fail to include precise dates or time frames. Even the most emphatic declarations — like former Vice President Dick Cheney’s prediction that the deal “will lead to a nuclear-armed Iran” — can be too open-ended to disconfirm.

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Non-falsifiable predictions thus undermine the quality of our discourse. They also impede our ability to improve policy, for if we can never judge whether a prediction is good or bad, we can never discern which ways of thinking about a problem are best.

The solution is straightforward: Replace vague forecasts with testable predictions. Will the International Atomic Energy Agency report in December that Iran has adequately resolved concerns about the potential military dimensions of its nuclear program? Will Iran export or dilute its quantities of low-enriched uranium in excess of 300 kilograms by the deal’s “implementation day” early next year? Within the next six months, will any disputes over I.A.E.A. access to Iranian sites be referred

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