LessWrong 2.0 Reader

Multiple points, really. I believe that this calculation is flawed in specific ways, but I also think that most calculations that attempt to estimate the relative odds of two events that were both very unlikely a priori will end up being off by a large amount. These two points are not entirely unrelated.

The specific problems that I noticed were:

1. The probabilities are not independent of each other, so they cannot be multiplied together directly. A bear flipping over your tent would almost always immediately be preceded by the bear scratching your tent, so updating on both events would just be double-counting evidence.
2. The probabilities do not appear to be conditional probabilities. P(A&B&C&D) doesn't equal P(A)*P(B)*P(C)*P(D), it equals P(A)*P(B|A)*P(C|A&B)*P(D|A&B&C).
3. The "nonbear" hypothesis is lumping together several different hypotheses. P(A|notbear) & P(B|notbear) cannot be multiplied together to get P(A&B|notbear), because (among other reasons) there may be some types of notbears that are very likely to do A but very unlikely to do B, some that are very likely to do both, and so on. Once you've observed A, it should update you on what kind of notbear it could be, and thus change the probability it does B.
4. The "20% a bear would scratch my tent : 50% a notbear would" claim is incorrect for the reasons I mentioned above. If your tent would be scratched 50% of the time in the absence of a bear, and a bear would scratch it 20% of the time, then the chance it gets scratched if there is a bear is 1-(1-50%)(1-20%), or 60%. (Unless you're postulating that bears always scare off anything else that might scratch the tent - which it seems Luke is indeed claiming.)
5. I disagree with several of the specific claims about the probabilities, such as "95% chance a bear would look exactly like a fucking bear inside my tent" and "1% chance a notbear would."

And then the meta-problem: when you're multiplying together more than two or three probabilities that you estimated, particularly small ones, errors in your ability to estimate them start to add up. Which is why I don't think it's usually worthwhile to try and estimate probabilities like this.

But you have a fair point about it being a good idea to practice explicit calculations, even if they're too complicated to reliably get right in real life. So here's how I might calculate it:

P(bear encounters you): 1%.

P(tent scratched | bear): 60%, for the reasons I said above... unless we take into account it scaring away other tent-scratching animals, in which case maybe 40%.

P(tent flipped over | bear & tent scratched): 20%, maybe? I think if the bear has already taken an interest in your tent, it's more likely than usual to flip it over.

P(you see a bear-shaped object | bear & tent scratched & tent flipped over): Bears always look like bears. This is so close to 100% I wouldn't even normally include it in the calculation, but let's call it 99.99%.

P(you get eaten | bear & tent scratched & tent flipped over & you see a bear-shaped object): It's already pretty been aggressive so far, so I'd say perhaps 5%.

On the other side, there are almost no objects for which the probability of it looking exactly like a bear isn't infinitesimal; let's only consider Bigfoot and serial-killer-who's-a-furry for simplicity, then add them up.

P(Bigfoot exists): ...hmm. I am not an expert on the matter, but let's say 1%.

P(Bigfoot encounters you | Bigfoot exists): There can't be that many Bigfoots (Bigfeet?) out there, or else people would have caught one. 0.01%.

P(tent scratched | Bigfoot): Bigfeet are probably more aggressive than bears, so 70%.

P(tent flipped over | Bigfoot): Again, Bigfeet are supposed to be pretty aggressive, so 50%.

P(you see a bear-shaped object | Bigfoot & tent scratched & tent flipped over): Bigfoot looks similar enough to a bear that you'll almost certainly think he's a bear. 99%.

P(you get eaten | Bigfoot & tent scratched & tent flipped over & you see a bear-shaped object): Again, Bigfeet aggressive, 30%.

Then for the furry cannibal one:

P(furry cannibal stalking this forest): 0.000001% (that's one in a hundred million, if I got my zeroes right). I welcome you to prove me wrong on the matter by manually increasing the number of furry cannibals in a given forest.

P(furry cannibal encounters you | furry cannibal exists): How large of a forest is this? Well, he probably has his methods of locating prey, so let's say 10%. Wait, why did I assume he's a "he"? What gender is the typical furry cannibal? Probably a trans woman? Let's name this furry cannibal Susan.

P(tent scratched | Susan): Probably not that high; she doesn't want to wake you up too soon. 30%.

P(tent flipped over | Susan & tent scratched): She might just sneak in, but let's say 90%.

P(you see a bear-shaped object | Susan & tent scratched & tent flipped over): She's wearing a bear costume, as hypothesized; 99.99%.

P(you get eaten | Susan & tent scratched & tent flipped over & you see a bear-shaped object): Yes, of course this happens; this was her whole kink in the first place! 99%.

So for "bear," we have 1%*40%*20%*99.99%*5% = 0.004%. For "Bigfoot," we have 1%*0.01%*70%*50%*99%*30% = 0.00001%. For "Susan," we have 0.000001%*10%*30%*90%*99.99%*99% = .000000027%. Looks like Bigfoot was so much more likely than Susan that we can pretty much just forget the Susan possibility altogether. It's 0.004 to 0.00001, so 400 to 1 chance that you're being eaten by a bear.

(Although I actually think you should be even more confident than 400 to 1 that it's a bear rather than Bigfoot, and that I just was off by an order of magnitude for one reason or another, as happens when you're doing these sorts of calculations. And if you ever actually observe all of these things, the most likely hypothesis is that you're dreaming.)

This is one of the key reasons that the term alignment was invented and used instead of control; I can be aligned with the interests of my infant, or my pet, without any control on their part.

the research management frame would be more helpful.

I think btw it gets more value than scholar support because it's a proactive service we offer to all scholars on a given stream, rather than waiting for them to only come to us when there's a problem.

the role of the RM should shift from writing the reports for mentors to helping the fellows prepare their own reports for mentors.

I spend a fair amount of time on my projects helping people prep for meetings with their supervisors, yeah. I also used to have scholars edit my written reports before sending to Ethan.

my language progression on something, becoming increasingly general: goals/value function -> decision policy (not all functions need to be optimizing towards a terminal value) -> output policy (not all systems need to be agents) -> policy (in the space of all possible systems, there exist some whose architectures do not converge to output layer)

(note: this language isn't meant to imply that systems behavior must be describable with some simple function, in the limit the descriptive function and the neural network are the same)

I'm not sure I'm following your actual objection. Is your point that this algorithm is wrong and won't update towards the right probabilities even if you keep feeding it new pieces of evidence, that the explanations and numbers for these pieces of evidence don't make sense for the implied story, that you shouldn't try to do explicit probability calculations this way, or some fourth thing?

If this algorithm isn't actually equivalent to Bayes in some way, that would be really useful for someone to point out. At first glance it seems like a simpler (to me anyway) way to express how making updates works, not just on an intuitive "I guess the numbers move that direction?" way but in a way that might not get fooled by e.g. the mammogram example. 

If these explanations and numbers don't make exact sense for the implied story, that seems fine? "A train is moving from east to west at a uniform speed of 12 m/s, ten kilometers west a second train is moving west to east at a uniform speed of 15 m/s, how far will the first train have traveled when they meet?" is a fine word problem even if that's oversimplified for how trains work. 

If you don't think it's worth doing explicit probability calculations this way, even to practice and try and get better or as a way to train the habit of how the numbers should move, that seems like a different objection and one you would have with any guide to Bayes. That's not to say you shouldn't raise the objection, but that doesn't seem like an objection that someone did the math wrong!

And of course maybe I'm completely missing your point.

Generally: in maneuver warfare you seek to make your opponent spend more energy per unit of reaction/movement than you do, wearing them down or putting them in a position of weakness.

You can just try to estimate the base rate of a bear attacking your tent and eating you, then estimate the base rate of a thing that looks identical to a bear attacking your tent and eating you, and compare them. Maybe one in a thousand tents get attacked by a bear, and 1% of those tent attacks end with the bear eating the person inside. The second probability is a lot harder to estimate, since it mostly involves off-model surprises like "Bigfoot is real" and "there is a serial killer in these woods wearing a bear suit," but I'd have trouble seeing how it could be above one in a billion. (Unless we're including possibilities like "this whole thing is just a dream" - which actually should be your main hypothesis.)

In general, when you're dealing with very low or very high probabilities, I'd recommend you just try to use your intuition instead of trying to calculate everything out explicitly.* The main reason is this: if you estimate a probability as being 30% instead of 50%, it won't usually affect the result of the calculation that much. On the other hand, if you estimate a probability as being 1/10^5 instead of 1/10^6, it can have an enormous impact on the end result. However, humans are a lot better at intuitively telling apart 30% from 50% than they are at telling apart 1/10^5 from 1/10^6.

If you try to do explicit calculations about probabilities that are pretty close to 1:1, you'll probably get a pretty accurate result; if you try to do explicit calculations about probabilities that are several orders of magnitude away from each other, you'll probably be off by at least one order of magnitude. In this case, you calculated that even if a person on a camping trip is being eaten by something that looks identical to a bear, there's still about a 2.6% chance that it's not a bear. When you get a result that ridiculous, it doesn't mean there's a nonbear eating you, it means you're doing the math wrong.

*The situations in which you can get useful information from an explicit calculation on low probabilities are situations where you're fine with being off by substantial multiplicative factors. Like, if you're making a business decision where you're only willing to accept a <5% chance of something happening, and you calculate that there's only a one in a trillion chance, then it doesn't actually matter whether you were off by a factor of a million to one. (Of course, you still do need to check that there's no way you could be off by an even larger factor than that.)

What loop? They are all various viewpoints on the nature of reality, not steps you have to go through in some order or anything. (1) is a more useful viewpoint than the rest, and you can adopt that one for 99%+ of everything you think about and only care about the rest as basically ideas to toy with rather than live by.

I don't know about you (assuming you even exist in any sense other than my perception of words on a screen), but to me a model that an external reality exists beyond what I can perceive is amazingly useful for essentially everything. Even if it might not be actually true, it explains my perceptions to a degree that seems incredible if it were not even partly true. Even most of the apparent exceptions in (2) are well explained by it once your physical model includes much of how perception works.

So while (4) holds, it's to such a powerful degree that (2) to (6) are essentially identical to (1).

You could have a Q&A superintelligence that is passive and reactive - it gives the best answer to a question, on the basis of what it already knows, but it takes no steps to acquire more information, and when it's not asked a question, it just sits there... But any agent that uses it, would de facto become a superintelligence with agency. 

By imitating other players

As Jay Bailey mentioned, you can look at how other players approached challenges, and copy the approaches that worked. Pablo Repetto’s playthroughs of three early .scis seem particularly worthwhile given your situation, both because of how comprehensive & well-written they are, and because they were made by someone in the process of learning to use code on data science problems (the first playthrough was done in pure Excel, the other two were handled in Python).

By following a sensible strategy

Below is my standard plan for investigating a dataset, synthetic or otherwise (cribbed from an otherwise-mediocre Udacity course I took most of a decade ago, and still worth following).

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Univariate Analysis: How is each feature distributed when considered in isolation? You should probably make a histogram for each column.

Bivariate Analysis: Construct and check the correlation matrix between all features. Are there clusters? Create scatterplots (or equivalent) for any pair of features which correlate unusually strongly, any pair of features where at least one is a response variable, and any pair of features you find yourself curious about.

Feature Derivation: Based on what you’ve seen so far – and/or common sense – are there meaningful features you can create from what you’ve been provided? (i.e., if you’re given "Number of Wizards", "Number of Sorcerors" and "Number of Druids" for each row, it might be worth creating a “Total Number of Magic Users” column.) Investigate how these features interact with others.

ML Modelling: If you can, and it seems like a good idea, build an ML model predicting the important/unknown features from those you have. If constructed successfully, this becomes an oracle you can ask about the outcome of any possible choice you could make. (XGBoost and similar tools are extremely versatile, and have pretty good performance on most problems.)

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(The above is just a rough guide for what to do when you don’t know what to do. If you follow it, you should pretty quickly find yourself with a list of rabbitholes to fall down; you should probably err on the side of dropping everything and deviating from the path as soon as you find something interesting.)

By playing easier D&D.Scis

Difficulty of D&D.Sci games tends to be both high and high-variance; it’s usually assumed that players will have both data-manipulation and model-building skills. For what it’s worth, I can confirm that two relatively-approachable scenarios where not-using-ML won't put you at a disadvantage are (spoilered because this technically leaks information about them):