Discrete Probability Example (Try 3) #558
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| coin : Coin =>Float = [0.2, 0.8] | ||
| dice_1 : Dice => Float = for i. 1.0 / 6.0 | ||
| dice_2 : Dice => Float = [0.5, 0.1, 0.1, 0.1, 0.1, 0.1] |
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nit: dice_1 -> fair_dice, dice_2 -> unfair_dice?
| ' Distributions are easy to create. Here are a couple simple ones. | ||
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| def normalize (x: m=>Float) : Dist m = AsDist for i. x.i / sum x | ||
| def uniform : Dist m = normalize for i. 1.0 |
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nit: slightly faster to just make it for i. (1.0 / size m)
| concat $ for i. select (x.i > 0.0) (AsList 1 [(i, x.i)]) mempty | ||
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| instance [Show m] Show (Dist m) | ||
| show = \a. |
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nit: the indentation seems really deep?
| roll = \i . (i - 1)@ Dice | ||
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| None = Fin 1 | ||
| nil = 0@None |
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You might be able to use Unit and () instead of None and nil, but that's up to you. I kind of like this too.
| def Var (a:Type) : Type = a => Float | ||
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| ' These can either be observed or latent. | ||
| If a random variable is observed then we use an indicator. |
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It was a little unclear to me initially that by indicator you meant that it is one for exactly one event. It's a bit confusing that "indicator variable" is defined in terms of an "indicator". But it might be just me not having this nomenclature in my head.
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| ' We also define a Markov version of our sample function. | ||
| Instead of summing out over the usage of its result, | ||
| it constructs a matrix a vector. |
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Will make more clear. This part was me trying to follow @duvenaud 's particle filter and rewrite it as an associative Accum.
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Oh bummer. I was hoping that this would be easier to read. It was the indicator part where I lost you? I'll try to add some better explanations and use the more standard |
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@srush would you like to rephrase this or should we just fix the minor things and merge this? |
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I'll send an updated version soon. Been a bit busy the last couple weeks. |
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There's no hurry from our side, take your time. I just came form vacation and I'm trying to make sure that we didn't drop the ball on any of your excellent PRs! Please ping us if you think that we forgot about any of them. |
(This is somewhere between an example and a blog post, but it uses a ton of Dex features so I thought I would submit for comments)
Implements an exact PPL for typed, discrete probability. This allows for concisely solving many elementary probability
brain teasers in dex.
Features:
Embedded modeling language using "table continuations" Here is what a bayes net looks like
Clean separation of model and explicit observations.
Differential posterior inference, i.e. using auto differentiation for exact posterior calculation.
A small set of combinators for discrete probability (expectations, printing, arb)
Examples for a bunch of undergrad level brain teasers (coin flips, monty hall, wet grass, hmm)