module Learning.IOHMM.Internal (
IOHMM (..)
, LogLikelihood
, init
, withEmission
, viterbi
, baumWelch
) where
import Prelude hiding (init)
import Control.Applicative ((<$>))
import Control.DeepSeq (NFData, force, rnf)
import Control.Monad (forM_, replicateM)
import Control.Monad.ST (runST)
import qualified Data.Map.Strict as M (findWithDefault)
import Data.Random.RVar (RVar)
import Data.Random.Distribution.Simplex (stdSimplex)
import qualified Data.Vector as V (
Vector, filter, foldl1', generate, map, replicateM, unsafeFreeze
, unsafeIndex , unsafeTail , zip, zipWith3
)
import qualified Data.Vector.Generic as G (convert)
import qualified Data.Vector.Generic.Util as G (frequencies)
import qualified Data.Vector.Mutable as MV (
unsafeNew, unsafeRead, unsafeWrite
)
import qualified Data.Vector.Unboxed as U (
Vector, fromList, length, map, sum, unsafeFreeze, unsafeIndex
, unsafeTail, unzip, zip
)
import qualified Data.Vector.Unboxed.Mutable as MU (
unsafeNew, unsafeRead, unsafeWrite
)
import qualified Numeric.LinearAlgebra.Data as H (
(!), Matrix, Vector, diag, fromColumns, fromList, fromLists
, fromRows, konst, maxElement, maxIndex, toColumns, tr
)
import qualified Numeric.LinearAlgebra.HMatrix as H (
(<>), (#>), sumElements
)
type LogLikelihood = Double
data IOHMM = IOHMM { nInputs :: Int
, nStates :: Int
, nOutputs :: Int
, initialStateDist :: H.Vector Double
, transitionDist :: V.Vector (H.Matrix Double)
, emissionDistT :: H.Matrix Double
}
instance NFData IOHMM where
rnf hmm = rnf m `seq` rnf k `seq` rnf l `seq` rnf pi0 `seq` rnf w `seq` rnf phi'
where
m = nInputs hmm
k = nStates hmm
l = nOutputs hmm
pi0 = initialStateDist hmm
w = transitionDist hmm
phi' = emissionDistT hmm
init :: Int -> Int -> Int -> RVar IOHMM
init m k l = do
pi0 <- H.fromList <$> stdSimplex (k1)
w <- V.replicateM m (H.fromLists <$> replicateM k (stdSimplex (k1)))
phi <- H.fromLists <$> replicateM k (stdSimplex (l1))
return IOHMM { nInputs = m
, nStates = k
, nOutputs = l
, initialStateDist = pi0
, transitionDist = w
, emissionDistT = H.tr phi
}
withEmission :: IOHMM -> U.Vector (Int, Int) -> IOHMM
withEmission model xys = model'
where
n = U.length xys
k = nStates model
l = nOutputs model
ss = [0..(k1)]
os = [0..(l1)]
ys = U.map snd xys
step m = fst $ baumWelch1 (m { emissionDistT = H.tr phi }) n xys
where
phi :: H.Matrix Double
phi = let zs = fst $ viterbi m xys
fs = G.frequencies $ U.zip zs ys
hs = H.fromLists $ map (\s -> map (\o ->
M.findWithDefault 0 (s, o) fs) os) ss
hs' = hs + H.konst 1e-9 (k, l)
ns = hs' H.#> H.konst 1 k
in hs' / H.fromColumns (replicate l ns)
ms = iterate step model
ms' = tail ms
ds = zipWith euclideanDistance ms ms'
model' = fst $ head $ dropWhile ((> 1e-9) . snd) $ zip ms' ds
euclideanDistance :: IOHMM -> IOHMM -> Double
euclideanDistance model model' =
sqrt $ sum $ H.sumElements ((phi phi') ** 2) :
map (\i -> H.sumElements ((w i w' i) ** 2)) is
where
is = [0..(nInputs model 1)]
w = V.unsafeIndex (transitionDist model)
w' = V.unsafeIndex (transitionDist model')
phi = emissionDistT model
phi' = emissionDistT model'
viterbi :: IOHMM -> U.Vector (Int, Int) -> (U.Vector Int, LogLikelihood)
viterbi model xys = (path, logL)
where
n = U.length xys
deltas :: V.Vector (H.Vector Double)
psis :: V.Vector (U.Vector Int)
(deltas, psis) = runST $ do
ds <- MV.unsafeNew n
ps <- MV.unsafeNew n
let (_, y0) = U.unsafeIndex xys 0
MV.unsafeWrite ds 0 $ log (phi' H.! y0) + log pi0
forM_ [1..(n1)] $ \t -> do
d <- MV.unsafeRead ds (t1)
let (x, y) = U.unsafeIndex xys t
dws = map (\wj -> d + log wj) (w' x)
MV.unsafeWrite ds t $ log (phi' H.! y) + H.fromList (map H.maxElement dws)
MV.unsafeWrite ps t $ U.fromList (map H.maxIndex dws)
ds' <- V.unsafeFreeze ds
ps' <- V.unsafeFreeze ps
return (ds', ps')
where
pi0 = initialStateDist model
w' = H.toColumns . V.unsafeIndex (transitionDist model)
phi' = emissionDistT model
deltaE = V.unsafeIndex deltas (n1)
path = runST $ do
ix <- MU.unsafeNew n
MU.unsafeWrite ix (n1) $ H.maxIndex deltaE
forM_ [nl | l <- [1..(n1)]] $ \t -> do
i <- MU.unsafeRead ix t
let psi = V.unsafeIndex psis t
MU.unsafeWrite ix (t1) $ U.unsafeIndex psi i
U.unsafeFreeze ix
logL = H.maxElement deltaE
baumWelch :: IOHMM -> U.Vector (Int, Int) -> [(IOHMM, LogLikelihood)]
baumWelch model xys = zip models (tail logLs)
where
n = U.length xys
step (m, _) = baumWelch1 m n xys
(models, logLs) = unzip $ iterate step (model, undefined)
baumWelch1 :: IOHMM -> Int -> U.Vector (Int, Int) -> (IOHMM, LogLikelihood)
baumWelch1 model n xys = force (model', logL)
where
m = nInputs model
k = nStates model
l = nOutputs model
(xs, ys) = U.unzip xys
(alphas, cs) = forward model n xys
betas = backward model n xys cs
(gammas, xis) = posterior model n xys alphas betas cs
pi0 = V.unsafeIndex gammas 0
w = let xis' i = V.map snd $ V.filter ((== i) . fst) $ V.zip (G.convert $ U.unsafeTail xs) xis
ds = V.foldl1' (+) . xis'
ns i = ds i H.#> H.konst 1 k
in V.map (\i -> H.diag (H.konst 1 k / ns i) H.<> ds i) (V.generate m id)
phi' = let gs' o = V.map snd $ V.filter ((== o) . fst) $ V.zip (G.convert ys) gammas
ds = V.foldl1' (+) . gs'
ns = V.foldl1' (+) gammas
in H.fromRows $ map (\o -> ds o / ns) [0..(l1)]
model' = model { initialStateDist = pi0
, transitionDist = w
, emissionDistT = phi'
}
logL = (U.sum $ U.map log cs)
forward :: IOHMM -> Int -> U.Vector (Int, Int) -> (V.Vector (H.Vector Double), U.Vector Double)
forward model n xys = runST $ do
as <- MV.unsafeNew n
cs <- MU.unsafeNew n
let (_, y0) = U.unsafeIndex xys 0
a0 = (phi' H.! y0) * pi0
c0 = 1 / H.sumElements a0
MV.unsafeWrite as 0 (H.konst c0 k * a0)
MU.unsafeWrite cs 0 c0
forM_ [1..(n1)] $ \t -> do
a <- MV.unsafeRead as (t1)
let (x, y) = U.unsafeIndex xys t
a' = (phi' H.! y) * (w' x H.#> a)
c' = 1 / H.sumElements a'
MV.unsafeWrite as t (H.konst c' k * a')
MU.unsafeWrite cs t c'
as' <- V.unsafeFreeze as
cs' <- U.unsafeFreeze cs
return (as', cs')
where
k = nStates model
pi0 = initialStateDist model
w' = H.tr . V.unsafeIndex (transitionDist model)
phi' = emissionDistT model
backward :: IOHMM -> Int -> U.Vector (Int, Int) -> U.Vector Double -> V.Vector (H.Vector Double)
backward model n xys cs = runST $ do
bs <- MV.unsafeNew n
let bE = H.konst 1 k
cE = U.unsafeIndex cs (n1)
MV.unsafeWrite bs (n1) (H.konst cE k * bE)
forM_ [nl | l <- [1..(n1)]] $ \t -> do
b <- MV.unsafeRead bs t
let (x, y) = U.unsafeIndex xys t
b' = w x H.#> ((phi' H.! y) * b)
c' = U.unsafeIndex cs (t1)
MV.unsafeWrite bs (t1) (H.konst c' k * b')
V.unsafeFreeze bs
where
k = nStates model
w = V.unsafeIndex (transitionDist model)
phi' = emissionDistT model
posterior :: IOHMM -> Int -> U.Vector (Int, Int) -> V.Vector (H.Vector Double) -> V.Vector (H.Vector Double) -> U.Vector Double -> (V.Vector (H.Vector Double), V.Vector (H.Matrix Double))
posterior model _ xys alphas betas cs = (gammas, xis)
where
gammas = V.zipWith3 (\a b c -> a * b / H.konst c k)
alphas betas (G.convert cs)
xis = V.zipWith3 (\a b (x, y) -> H.diag a H.<> w x H.<> H.diag (b * (phi' H.! y)))
alphas (V.unsafeTail betas) (G.convert $ U.unsafeTail xys)
k = nStates model
w = V.unsafeIndex (transitionDist model)
phi' = emissionDistT model