Hi Benjamin, Thus quoth Benjamin Redelings at 20:46 on Thu, Jun 15 2017:
On 06/13/2017 12:30 PM, Sergiu Ivanov wrote:
Probabilistic programs are written using the probability monad.
I've implemented a Haskell interpreter in C++ that records execution traces of the Haskell programs. Is your probability monad an actual monad that you implemented in a Haskell package, or is it a consequence of the fact that you are running Haskell-like programs in your interpreter?
1. Its an actual monad. It allows probability distributions to be "performed" by a Haskell function that serves as an interpreter. But I haven't implemented it in GHC. There are actually two interpreters, which are at the top of this file. "IOAndPass" is <<=, and "IOAnd" is <<. Please forgive the extreme hackiness :-P https://github.com/bredelings/BAli-Phy/blob/master/modules/Distributions.hs
OK, I see. (I suppose you meant to say that IOAndPass is =<<).
The (sample) function performs a distribution d by generating an IO action to randomly sample from the distribution. The (sample') function performs a distribution by setting up a node in a (dynamic) graphical model, which is also an IO action.
OK, so the difference is in the presence or absence of the graphical representation of the model your are working with?
2. Actions in this monad can either * sample from a distribution. * specify that we should record samples of an expression.
Do you mean something like x <- doSomething `fmap` someDistribution where x <- someDistribution would sample someDistribution?
* alter properties of variables sampled in a given scope.
Oh, so you have a kind of state baked into your monad as well?
For example in the code below, I specify that we should sample a dirichlet containing n modifiable variables, but that MCMC should perform resampling of the variables at a rate of 1/sqrt(n). [...]
OK, I see, thanks for the example! What do you mean by "modifiable variables"? Are those just random variables?
So, the monad here is mainly used to tag variables sampled in a given scope. It might also be used to specify mcmc transition kernels for these variables.
OK.
I'm not quite sure how to handle scopes outside monads yet, but Venture does something like that, and it doesn't use monads.
Not sure what you mean by "handle scopes outside monads". Some kind of scopes are handled without monads in a lot of programming languages/frameworks :-)
3. The above code is "mochastic" because we perform the distribution in a monadic interpreter in order to sample from it. But we could also do something non-monadic like
let x=sample $ normal 0 1 y=sample $ gamma 1 1 in x*y
Yeah, sure, because every monad is a functor.
But Haskell itself isn't a monad. For example, x and y aren't sequenced.
Not sure what you mean here again. Something can be a monad or not a monad depending on how you look at it. If you see Haskell code as a sequence of strings fed into the compiler, it's quite monadic to my taste. You probably mean something else.
Are there Haskell libraries to "run" Haskell programs in different interpreters?
There is a number of different Haskell implementations [0] as well as haskell-src-exts [1] which is a parser of Haskell implemented as a Haskell library. But you probably mean something else by "different interpreters".
4. The low-level C++ interpreter for haskell in bali-phy is not monadic. Its basically a C++ implementation of something like the STG machine, but modified to do incremental computation for generic Haskell. I actually used Sestoft (1997) "Deriving a Lazy Abstract Machine" instead of the STG. I guess I could have tried to do this by modifying GHCi to track execution traces. I'm not really sure if that would be be a good idea or not. Any thoughts?
My question here would be: why do you chose to write a Haskell interpreter (or modifying an existing one) instead of writing everything in Haskell? (I believe that's also the question Olaf asked.) (I don't really have any ideas on what would be a good way of implementing a Haskell interpreter.)
More generally: how deep can the interoperability between your project and some other Haskell code go? Hmm.. well I guess we could implement *sampling* from the above monad in GHC just by making the interpreter call unsafePerformIO when it sees a probability distribution. But implementing MCMC inference would require reimplementing incremental computation for Haskell in GHC.
OK, so sampling can be natively implemented in Haskell. What do you mean by "incremental computation"?
The problem domain I've been focusing on is evolution of DNA sequences on binary trees. I'm very much interested in your project because I often look into non-deterministic evolution of some abstract computing devices, and you actually seem to be focusing on a similar use case. Hmm... I guess the idea is to represent a distribution on the possible execution histories of non-deterministic haskell programs. So, yeah, maybe there is some overlap.
Yes, that's what I kind of had in my brain.
Huh... that actually might work! Do you handle non-determinism probabilistically? Do you want to condition on observations, or just run the abstract machine many times and record the distribution of what happens?
When I did similar things for my research, I just explored all the non-deterministic branches of execution for a couple of steps. I used a clot of Perl code which could filter out some branches. I haven't considered using a probabilistic approach, but it may actually be quite interesting, I'll give it a think, thank you :-) -- Sergiu [0] https://wiki.haskell.org/Implementations [1] http://hackage.haskell.org/package/haskell-src-exts