commit 8313e5798dbd3f5f297473d48d99135b626b1f5a Author: Jared Tobin <jared@jtobin.ca> Date: Sun, 4 Nov 2012 22:42:16 +1300 Initial commit. Diffstat:
| A | .gitignore | | | 9 | +++++++++ |
| A | Examples/code/BNN_Flat.hs | | | 41 | +++++++++++++++++++++++++++++++++++++++++ |
| A | Examples/code/Booth_Flat.hs | | | 41 | +++++++++++++++++++++++++++++++++++++++++ |
| A | Examples/code/Himmelblau_Flat.hs | | | 41 | +++++++++++++++++++++++++++++++++++++++++ |
| A | Examples/code/Rosenbrock_Flat.hs | | | 39 | +++++++++++++++++++++++++++++++++++++++ |
| A | Examples/code/SPDE_Flat.hs | | | 45 | +++++++++++++++++++++++++++++++++++++++++++++ |
| A | Examples/data/input/inits-100d.dat | | | 200 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | Examples/data/input/inits-2d.dat | | | 100 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | LICENSE | | | 29 | +++++++++++++++++++++++++++++ |
| A | Numeric/MCMC/Flat.hs | | | 135 | +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ |
| A | README.md | | | 2 | ++ |
| A | flat-mcmc.cabal | | | 30 | ++++++++++++++++++++++++++++++ |
12 files changed, 712 insertions(+), 0 deletions(-)
diff --git a/.gitignore b/.gitignore @@ -0,0 +1,9 @@ +.git +dist +Setup.hs +demos +output +*swp +*.hi +*.o +.DS_Store diff --git a/Examples/code/BNN_Flat.hs b/Examples/code/BNN_Flat.hs @@ -0,0 +1,41 @@ +import System.IO +import System.Exit +import System.Environment +import System.Random.MWC +import Control.Monad +import Numeric.MCMC.Flat +import qualified Data.Vector as V + +target :: [Double] -> Double +target [x0, x1] = -0.5*(x0^2 * x1^2 + x0^2 + x1^2 - 8*x0 - 8*x1) +{-# INLINE target #-} + +main = do + args <- getArgs + when (args == []) $ do + putStrLn "(flat-mcmc) Bivariate non-normal density " + putStrLn "Usage: ./BNN_Flat <numSteps> <inits> " + putStrLn " " + putStrLn "numSteps : Number of Markov chain iterations to run." + putStrLn "inits : Filepath containing points at which to " + putStrLn " initialize the ensemble. " + exitSuccess + + inits <- readInits (args !! 1) + + let nepochs = read (head args) :: Int + params = Options target (V.length inits) 30 + config = MarkovChain inits 0 + + g <- create + results <- runChain params nepochs config g + + hPutStrLn stderr $ + let nAcc = accepts results + total = nepochs * V.length inits * length (V.head inits) + in show nAcc ++ " / " ++ show total ++ " (" ++ + show ((fromIntegral nAcc / fromIntegral total) :: Float) ++ + ") proposals accepted" + + + diff --git a/Examples/code/Booth_Flat.hs b/Examples/code/Booth_Flat.hs @@ -0,0 +1,41 @@ +import System.IO +import System.Exit +import System.Environment +import System.Random.MWC +import Control.Monad +import Numeric.MCMC.Flat +import qualified Data.Vector as V + +target :: [Double] -> Double +target [x0, x1] = (-1)*((x0 + 2*x1 -7)^2 + (2*x0 + x1 - 5)^2) +{-# INLINE target #-} + +main = do + args <- getArgs + when (args == []) $ do + putStrLn "(flat-mcmc) Booth density " + putStrLn "Usage: ./Booth_Flat <numSteps> <inits> " + putStrLn " " + putStrLn "numSteps : Number of Markov chain iterations to run." + putStrLn "inits : Filepath containing points at which to " + putStrLn " initialize the ensemble. " + exitSuccess + + inits <- readInits (args !! 1) + + let nepochs = read (head args) :: Int + params = Options target (V.length inits) 30 + config = MarkovChain inits 0 + + g <- create + results <- runChain params nepochs config g + + hPutStrLn stderr $ + let nAcc = accepts results + total = nepochs * V.length inits * length (V.head inits) + in show nAcc ++ " / " ++ show total ++ " (" ++ + show ((fromIntegral nAcc / fromIntegral total) :: Float) ++ + ") proposals accepted" + + + diff --git a/Examples/code/Himmelblau_Flat.hs b/Examples/code/Himmelblau_Flat.hs @@ -0,0 +1,41 @@ +import System.IO +import System.Exit +import System.Environment +import System.Random.MWC +import Control.Monad +import Numeric.MCMC.Flat +import qualified Data.Vector as V + +target :: [Double] -> Double +target [x0, x1] = (-1)*((x0*x0 + x1 - 11)^2 + (x0 + x1*x1 - 7)^2) +{-# INLINE target #-} + +main = do + args <- getArgs + when (args == []) $ do + putStrLn "(flat-mcmc) Himmelblau density " + putStrLn "Usage: ./Himmelblau_Flat <numSteps> <inits> " + putStrLn " " + putStrLn "numSteps : Number of Markov chain iterations to run." + putStrLn "inits : Filepath containing points at which to " + putStrLn " initialize the ensemble. " + exitSuccess + + inits <- readInits (args !! 1) + + let nepochs = read (head args) :: Int + params = Options target (V.length inits) 30 + config = MarkovChain inits 0 + + g <- create + results <- runChain params nepochs config g + + hPutStrLn stderr $ + let nAcc = accepts results + total = nepochs * V.length inits * length (V.head inits) + in show nAcc ++ " / " ++ show total ++ " (" ++ + show ((fromIntegral nAcc / fromIntegral total) :: Float) ++ + ") proposals accepted" + + + diff --git a/Examples/code/Rosenbrock_Flat.hs b/Examples/code/Rosenbrock_Flat.hs @@ -0,0 +1,39 @@ +import System.IO +import System.Exit +import System.Environment +import System.Random.MWC +import Control.Monad +import Numeric.MCMC.Flat +import qualified Data.Vector as V + +target :: [Double] -> Double +target [x0, x1] = (-1)*(5*(x1 - x0^2)^2 + 0.05*(1 - x0)^2) +target _ = error "explode" + +main = do + args <- getArgs + when (args == []) $ do + putStrLn "(flat-mcmc) Rosenbrock density " + putStrLn "Usage: ./Rosenbrock_Flat <numSteps> <inits> " + putStrLn " " + putStrLn "numSteps : Number of Markov chain iterations to run." + putStrLn "inits : Filepath containing points at which to " + putStrLn " initialize the ensemble. " + exitSuccess + + inits <- readInits (args !! 1) + + let nepochs = read (head args) :: Int + params = Options target (V.length inits) 20 + config = MarkovChain inits 0 + + g <- create + results <- runChain params nepochs config g + + hPutStrLn stderr $ + let nAcc = accepts results + total = nepochs * V.length inits * length (V.head inits) + in show nAcc ++ " / " ++ show total ++ " (" ++ + show ((fromIntegral nAcc / fromIntegral total) :: Float) ++ + ") proposals accepted" + diff --git a/Examples/code/SPDE_Flat.hs b/Examples/code/SPDE_Flat.hs @@ -0,0 +1,45 @@ +import System.IO +import System.Exit +import System.Environment +import System.Random.MWC +import Control.Monad +import Numeric.MCMC.Flat +import qualified Data.Vector as V + +target :: [Double] -> Double +target xs = go 0 0 xs + where go t0 t1 [] = (- t0 / (2*h)) - (0.5 * h * t1) + go t0 t1 (u:us:uss) = go (t0 + (us - u)^2) (t1 + v (us + u)) uss + h = 1 / fromIntegral (length xs) + v x = (1 - x^2)^2 +{-# INLINE target #-} + +main = do + args <- getArgs + when (args == []) $ do + putStrLn "(flat-mcmc) Stochastic partial differential equation " + putStrLn "Usage: ./SPDE_Flat <numSteps> <inits> <granularity> " + putStrLn " " + putStrLn "numSteps : Number of Markov chain iterations to run." + putStrLn "inits : Filepath containing points at which to " + putStrLn " initialize the ensemble. " + putStrLn "granularity : Parallel granularity (smaller is finer). " + exitSuccess + + inits <- readInits (args !! 1) + + let nepochs = read (head args) :: Int + gran = read (args !! 2) :: Int + params = Options target (V.length inits) gran + config = MarkovChain inits 0 + + g <- create + results <- runChain params nepochs config g + + hPutStrLn stderr $ + let nAcc = accepts results + total = nepochs * V.length inits * length (V.head inits) + in show nAcc ++ " / " ++ show total ++ " (" ++ + show ((fromIntegral nAcc / fromIntegral total) :: Float) ++ + ") proposals accepted" + diff --git a/Examples/data/input/inits-100d.dat b/Examples/data/input/inits-100d.dat @@ -0,0 +1,200 @@ +-0.378157 -0.3936388 -0.3492082 -0.8053676 0.3257766 0.5612745 -0.1579117 0.4207219 0.2071167 -0.2250999 0.5720361 0.08261235 -0.9802909 0.4948627 0.2703137 -0.9593947 0.4992166 0.8249822 -0.6257682 -0.006402534 -0.5830307 -0.3410036 0.6020871 0.1435127 -0.8199525 -0.9833688 0.5195233 -0.3122609 0.8902204 -0.01877975 0.4551275 -0.6727086 -0.6372498 0.5232103 0.4302569 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Tobin + +Redistribution and use in source and binary forms, with or without +modification, are permitted provided that the following conditions are +met: + + 1. Redistributions of source code must retain the above copyright + notice, this list of conditions, and the following disclaimer. + + 2. Redistributions in binary form must reproduce the above + copyright notice, this list of conditions, and the following + disclaimer in the documentation and/or other materials provided + with the distribution. + + 3. The name of the author may not be used to endorse or promote + products derived from this software without specific prior + written permission. + +THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR +IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED +WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE +DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, +INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES +(INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR +SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, +STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING +IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +POSSIBILITY OF SUCH DAMAGE. diff --git a/Numeric/MCMC/Flat.hs b/Numeric/MCMC/Flat.hs @@ -0,0 +1,135 @@ +{-# OPTIONS_GHC -Wall #-} + +module Numeric.MCMC.Flat ( + MarkovChain(..), Options(..), Ensemble + , runChain, readInits + ) where + +import Control.Arrow +import Control.Monad +import Control.Monad.Reader +import Control.Monad.Primitive +import System.Random.MWC +import qualified Data.Vector as V +import qualified Data.Vector.Unboxed as U +import Control.Monad.Par (NFData) +import Control.Monad.Par.Scheds.Direct +import Control.Monad.Par.Combinator + +-- | Parallel map with a specified granularity. +parMapChunk :: NFData b => Int -> (a -> b) -> [a] -> Par [b] +parMapChunk n f xs = do + xss <- parMap (map f) (chunk n xs) + return (concat xss) + where chunk _ [] = [] + chunk m ys = let (as, bs) = splitAt m ys + in as : chunk m bs + +-- | State of the Markov chain. Current ensemble position is held in 'theta', +-- while 'accepts' counts the number of proposals accepted. +data MarkovChain = MarkovChain { ensemble :: Ensemble + , accepts :: {-# UNPACK #-} !Int } + +-- | Display the current state. This will be very slow and should be replaced. +instance Show MarkovChain where + show config = filter (`notElem` "[]") $ unlines $ map show (V.toList (ensemble config)) + +-- | Options for the chain. The target (expected to be a log density), as +-- well as the size of the ensemble. The size should be an even number. Also +-- holds the specified parallel granularity as 'csize'. +data Options = Options { _target :: [Double] -> Double + , _size :: {-# UNPACK #-} !Int + , _csize :: {-# UNPACK #-} !Int } + +-- | An ensemble of particles. +type Ensemble = V.Vector [Double] + +-- | A result with this type has a view of the chain's options. +type ViewsOptions = ReaderT Options + +-- | Generate a random value from a distribution having the property that +-- g(1/z) = zg(z). +symmetricVariate :: PrimMonad m => Gen (PrimState m) -> m Double +symmetricVariate g = do + z <- uniformR (0 :: Double, 1 :: Double) g + return $! 0.5*(z + 1)^(2 :: Int) + +-- | The result of a single-particle Metropolis accept/reject step. This +-- compares a particle's state to a perturbation made by an affine +-- transformation based on a complementary particle. Non-monadic to +-- more easily be used in the Par monad. +metropolisResult :: [Double] -> [Double] -- Target and alternate particles + -> Double -> Double -- z ~ g(z) and zc ~ rand + -> ([Double] -> Double) -- Target function + -> ([Double], Int) -- Result and accept counter +metropolisResult w0 w1 z zc target = + let val = target proposal - target w0 + (fromIntegral (length w0) - 1) * log z + proposal = zipWith (+) (map (*z) w0) (map (*(1-z)) w1) + in if zc <= min 1 (exp val) then (proposal, 1) else (w0, 0) + +-- | Execute Metropolis steps on the particles of a sub-ensemble by +-- perturbing them with affine transformations based on particles +-- in a complementary ensemble, in parallel. +executeMoves :: (Functor m, PrimMonad m) + => Ensemble -- Target sub-ensemble + -> Ensemble -- Complementary sub-ensemble + -> Int -- Size of the sub-ensembles + -> Gen (PrimState m) -- MWC PRNG + -> ViewsOptions m (Ensemble, Int) -- Updated ensemble and # of accepts +executeMoves e0 e1 n g = do + Options t _ csize <- ask + + zs <- replicateM n (lift $ symmetricVariate g) + zcs <- replicateM n (lift $ uniformR (0 :: Double, 1 :: Double) g) + js <- fmap U.fromList (replicateM n (lift $ uniformR (1:: Int, n) g)) + + let w0 k = e0 `V.unsafeIndex` (k - 1) + w1 k ks = e1 `V.unsafeIndex` ((ks `U.unsafeIndex` (k - 1)) - 1) + + result = runPar $ parMapChunk csize + (\(k, z, zc) -> metropolisResult (w0 k) (w1 k js) z zc t) + (zip3 [1..n] zs zcs) + (newstate, nacc) = (V.fromList . map fst &&& sum . map snd) result + + return (newstate, nacc) + +-- | Perform a Metropolis accept/reject step on the ensemble by +-- perturbing each element and accepting/rejecting the perturbation in +-- parallel. +metropolisStep :: (Functor m, PrimMonad m) + => MarkovChain -- State of the Markov chain + -> Gen (PrimState m) -- MWC PRNG + -> ViewsOptions m MarkovChain -- Updated sub-ensemble +metropolisStep state g = do + Options _ n _ <- ask + let n0 = truncate (fromIntegral n / (2 :: Double)) :: Int + (e, nacc) = (ensemble &&& accepts) state + (e0, e1) = (V.slice (0 :: Int) n0 &&& V.slice n0 n0) e + + -- Update each sub-ensemble + result0 <- executeMoves e0 e1 n0 g + result1 <- executeMoves e1 (fst result0) n0 g + + return $! + MarkovChain (V.concat $ map fst [result0, result1]) + (nacc + snd result0 + snd result1) + +-- | Diffuse through states. +runChain :: Options -- Options of the Markov chain + -> Int -- Number of epochs to iterate the chain + -> MarkovChain -- Initial state of the Markov chain + -> Gen RealWorld -- MWC PRNG + -> IO MarkovChain -- End state of the Markov chain, wrapped in IO +runChain params nepochs initConfig g + | nepochs == 0 = return initConfig + | otherwise = do + result <- runReaderT (metropolisStep initConfig g) params + print result + runChain params (nepochs - 1) result g + +-- | A convenience function to read and parse ensemble inits from disk. +-- Assumes a text file with one particle per line, where each particle +-- element is separated by whitespace. +readInits :: FilePath -> IO Ensemble +readInits p = fmap (V.fromList . map (map read . words) . lines) (readFile p) + diff --git a/README.md b/README.md @@ -0,0 +1,2 @@ +Check the acceptance ratio calculation. + diff --git a/flat-mcmc.cabal b/flat-mcmc.cabal @@ -0,0 +1,30 @@ +-- Initial flat_mcmc.cabal generated by cabal init. For further +-- documentation, see http://haskell.org/cabal/users-guide/ + +name: flat-mcmc +version: 0.1.0.0 +synopsis: Painless general-purpose sampling. +-- description: +homepage: http://jtobin.github.com/flat-mcmc +-- license: +license-file: LICENSE +author: Jared Tobin +maintainer: jared@jtobin.ca +-- copyright: +category: Numeric, Machine Learning, Statistics +build-type: Simple +cabal-version: >=1.8 +Description: + + A general-purpose sampler for anisotropic distributions. + +Source-repository head + Type: git + Location: http://github.com/jtobin/flat-mcmc.git + +library + exposed-modules: Numeric.MCMC.Flat + -- other-modules: + build-depends: base ==4.*, mtl ==2.1.*, primitive ==0.4.*, mwc-random ==0.12.*, vector ==0.9.*, monad-par ==0.3.*, monad-par-extras ==0.3.* + ghc-options: -Wall +