andreas

"I design a cell to not fail and then assume it will and then ask the next 'what-if' questions," Sinnett said. "And then I design the batteries that if there is a failure of one cell it won't propagate to another. And then I assume that I am wrong and that it will propagate to another and then I design the enclosure and the redundancy of the equipment to assume that all the cells are involved and the airplane needs to be able to play through that."

—Mike Sinnett, Boeing's 787 chief project engineer

The game theory textbook "A Course in Microeconomic Theory" (Kreps) addresses this situation. Quoting from page 516:

We will give an exact analysis of this problem momentarily (in smaller type), but you should have no difficulty seeing the basic trade-off; too little punishment, triggered only rarely, will give your opponent the incentive to try to get away with the noncooperative strategy. You have to punish often enough and harshly enough so that your opponent is motivated to play [cooperate] instead of [defect]. But the more often/more harsh

I am more motivated to read the rest of your sequence if the summary sounds silly than if I can easily see the arguments myself.

Back when Eliezer was writing his metaethics sequence, it would have been great to know where he was going, i.e., if he had posted ahead of time a one-paragraph technical summary of the position he set out to explain. Can you post such a summary of your position now?

Now, citing axioms and theorems to justify a step in a proof is not a mere social convention to make mathematicians happy. It is a useful constraint on your cognition, allowing you to make only inferences that are actually valid.

When you are trying to build up a new argument, temporarily accepting steps of uncertain correctness can be helpful (if mentally tagged as such). This strategy can move you out of local optima by prompting you to think about what further assumptions would be required to make the steps correct.

Techniques based on this kind of r... (read more)

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See also: A Universal Approach to Self-Referential Paradoxes, Incompleteness and Fixed Points, which treats the Liar's paradox as an instance of a generalization of Cantor's theorem (no onto mapping from N->2^N).

The best part of this unified scheme is that it shows that there are really no paradoxes. There are limitations. Paradoxes are ways of showing that if you permit one to violate a limitation, then you will get an inconsistent systems. The Liar paradox shows that if you permit natural language to talk about its own truthfulness (as it - of course - does) then we will have inconsistencies in natural languages.

Do you think that your beliefs regarding what you care about could be mistaken? That you might tell yourself that you care more about being lazy than about getting cryonics done, but that in fact, under reflection, you would prefer to get the contract?

Please stop commenting on this topic until you have understood more of what has been written about it on LW and elsewhere. Unsubstantiated proposals harm LW as a community. LW deals with some topics that look crazy on surface examination; you don't want people who dig deeper to stumble on comments like this and find actual crazy.

Similarly, inference (conditioning) is incomputable in general, even if your prior is computable. However, if you assume that observations are corrupted by independent, absolutely continuous noise, conditioning becomes computable.

Consider marginal utility. Many people are working on AI, machine learning, computational psychology, and related fields. Nobody is working on preference theory, formal understanding of our goals under reflection. If you want to do interesting research and if you have the background to advance either of those fields, do you think the world will be better off with you on the one side or on the other?

Now suppose you are playing against another timeless decision theory agent. Clearly, the best strategy is to be that actor which defects no matter what. If both agents do this, the worst possible result for both of them occurs.

Which shows that defection was not the best strategy in this situation.

Yes, deriving mechanisms that take complex models and turn them into something tractable is mostly an open problem.

They don't work without continuous parameters. If you have a probabilistic program that includes both discrete and continuous parameters, you can use gradient methods to generate MH proposals for your continuous parameters. I don't think there are any publications that discuss this yet.

A pdf of the nature intro is here.

I was comparing the two choices people face who want to do inference in nontrivial models. You can either write the model in an existing probabilistic programming language and get inefficient inference for free or you can write model+inference in something like Matlab. Here, you may be able to use libraries if your model is similar enough to existing models, but for many interesting models, this is not the case.

Current universal inference methods are very limited, so the main advantages of using probabilistic programming languages are (1) the conceptual clarity you get by separating generative model and inference and (2) the ability to write down complex nonparametric models and immediately be able to do inference, even if it's inefficient. Writing a full model+inference implementation in Matlab, say, takes you much longer, is more confusing and less flexible.

That said, some techniques that were developed for particular classes of problems have a useful analog in the setting of programs. The gradient-based methods you mention have been generalized to work on any probabilistic program with continuous parameters.

Probabilistic inference in general is NP-hard, but it is not clear that (1) this property holds for the kinds of problems people are interested in and, even if it does, that (2) approximate probabilistic inference is hard for this class of problems. For example, if you believe this paper, probabilistic inference without extreme conditional probabilities is easy.

Combine this with speech-to-text transcription software and you get a searchable archive of your recorded interactions!

ETA: In theory. In practice, dictation software algorithms are probably not up to the task of turning noisy speech from different people into text with any reasonable accuracy.

The key idea behind Church and similar languages is that they allow us to express and formally reason about a large class of probabilistic models, many of which cannot be formalized in any concise way as Bayes nets.

Bayes nets express generative models, i.e. processes that generate data. To infer the states of hidden variables from observations, you condition the Bayes net and compute a distribution on the hidden variable settings using Bayesian inference or some approximation thereof. A particularly popular class of approximations is the class of sampling ... (read more)