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-rw-r--r--LICENSE202
-rw-r--r--Setup.hs2
-rw-r--r--src/Numeric/StreamingHistogram.hs100
-rw-r--r--src/Numeric/StreamingHistogram/Internal.hs23
-rw-r--r--streaming-histogram.cabal58
-rw-r--r--tests/BenchStreamingHist.hs21
-rw-r--r--tests/TestStreamingHist.hs92
7 files changed, 498 insertions, 0 deletions
diff --git a/LICENSE b/LICENSE
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--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,202 @@
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diff --git a/Setup.hs b/Setup.hs
new file mode 100644
index 0000000..9a994af
--- /dev/null
+++ b/Setup.hs
@@ -0,0 +1,2 @@
+import Distribution.Simple
+main = defaultMain
diff --git a/src/Numeric/StreamingHistogram.hs b/src/Numeric/StreamingHistogram.hs
new file mode 100644
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--- /dev/null
+++ b/src/Numeric/StreamingHistogram.hs
@@ -0,0 +1,100 @@
+{-# LANGUAGE GADTs #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module : Numeric.StreamingHistogram
+-- Maintainer : Tom Hunger
+-- Stability : experimental
+-- Portability : portable
+--
+-- A very inefficient implementation of lossy online histograms based
+-- on the following paper:
+--
+-- * A Streaming Parallel Decision Tree Algorithm by Ben-Haim and
+-- Tom-Tov:
+-- <http://www.jmlr.org/papers/volume11/ben-haim10a/ben-haim10a.pdf>
+--
+-- __NB__ This library is very experimental and inefficient. Numerical
+-- stability has not been tested (yet).
+
+module Numeric.StreamingHistogram
+ ( empty
+ , update
+ , Hist(..)
+ , merge
+ , sum
+ ) where
+
+import qualified Data.List as L
+import qualified Data.Map as M
+import Numeric.StreamingHistogram.Internal (shrink)
+import Prelude hiding (sum, pi)
+
+import Debug.Trace
+
+data Hist where
+ Hist ::
+ { nBins :: Int
+ , histData :: M.Map Double Int} -> Hist
+ deriving (Show, Eq)
+
+-- | Creates an empty histogram to be updated with 'update'
+empty :: Int -- ^ Maximum number of values to keep
+ -> Hist -- ^ The empty histogram
+empty nBins' = Hist { nBins = nBins', histData = M.empty }
+
+
+-- | Adds a single 'value' to the histogram.
+update :: Double -- ^ Value to add
+ -> Hist -- ^ Lossy histogram to update
+ -> Hist -- ^ Histogram with the value incorporated
+update value h =
+ let updated = M.insertWith (+) value 1 (histData h)
+ data' | M.size updated > nBins h = (M.fromList . shrink . M.assocs) updated
+ | otherwise = updated
+ in
+ h { histData = data' }
+
+-- | Merges two histograms. Returns Nothing if they don't have the same
+-- number of values. TODO: Use more efficient algorithm.
+merge :: Hist -- ^ Histogram a
+ -> Hist -- ^ Histogram b
+ -> Maybe Hist -- ^ Returns Nothing if a and b disagree on how
+ -- many values to keep.
+merge ha hb =
+ let union = M.unionWith (+) (histData ha) (histData hb)
+ data' u
+ | length u > nBins ha = data' (shrink u)
+ | otherwise = u
+ in
+ case (nBins ha) == (nBins hb) of
+ True -> Just (ha { histData = M.fromList (data' (M.assocs union)) })
+ False -> Nothing
+
+-- | Estimates how many points lie in the interval [-infinity, b].
+sum :: Double -- ^ The cutoff value b
+ -> Hist -- ^ A histogram
+ -> Double -- ^ Estimated number of points
+sum b hist =
+ result
+ where
+ -- pad the data on both sides to make sure we always have a (p,
+ -- p+1) pair even when (b < min histData) or (b > max histData).
+ -- TODO (1e300 is probably not a good boundary value..).
+ sorted = M.assocs (histData hist)
+ result = discover 0.0 ((-1e300, 0) : sorted ++ [(1e300, 0)])
+
+ -- Find split point for b and keep track of s so far
+ discover :: Double -> [(Double, Int)] -> Double
+ discover sSoFar ((pi, mi):(pj, mj):xs)
+ | trace (show (sSoFar, b, (pi, mi), (pj, mj))) False = undefined
+ | pi <= b && b < pj = (sTrapezoid pi mi pj mj) + sSoFar + (fromIntegral mi) / 2.0
+ | otherwise = discover (sSoFar + fromIntegral mi) ((pj, mj):xs)
+
+ -- Initial value for S (trapezoid rule)
+ sTrapezoid pi mi pj mj =
+ let
+ mb = (fromIntegral mi) + (fromIntegral (mj - mi)) / (pj - pi) * (b - pi)
+ in
+ ((fromIntegral mi) + mb) / 2.0 * (b - pi) / (pj - pi)
+
+-- TODO implement 'uniform' but I don't need it just now
diff --git a/src/Numeric/StreamingHistogram/Internal.hs b/src/Numeric/StreamingHistogram/Internal.hs
new file mode 100644
index 0000000..e19a40b
--- /dev/null
+++ b/src/Numeric/StreamingHistogram/Internal.hs
@@ -0,0 +1,23 @@
+module Numeric.StreamingHistogram.Internal
+ ( shrink
+ ) where
+
+import qualified Data.List as L
+
+-- Internal: Lossy compression of histogram by finding the pair of
+-- values that would introduce minimum error when merged and then do a
+-- weighted merge.
+shrink :: [(Double, Int)] -> [(Double, Int)]
+shrink m
+ | length m == 0 = m
+ | otherwise = shrunk'
+ where
+ deltas = L.zipWith (\(x, _) (y, _)-> y - x) (init m) (L.tail m)
+ minDelta = L.minimum deltas
+ shrunk' = shrunk (init m) (L.tail m)
+
+ shrunk :: [(Double, Int)] -> [(Double, Int)] -> [(Double, Int)]
+ shrunk [] [] = []
+ shrunk ((lq, lk):ls) ((rq, rk):rs)
+ | rq - lq == minDelta = ((lq * (fromIntegral lk) + rq * (fromIntegral rk)) / (fromIntegral (lk + rk)), lk + rk) : rs
+ | otherwise = (lq, lk) : (shrunk ls rs)
diff --git a/streaming-histogram.cabal b/streaming-histogram.cabal
new file mode 100644
index 0000000..c0f3a35
--- /dev/null
+++ b/streaming-histogram.cabal
@@ -0,0 +1,58 @@
+-- Initial streaming-histogram.cabal generated by cabal init. For further
+-- documentation, see http://haskell.org/cabal/users-guide/
+
+name: streaming-histogram
+version: 0.1.0.0
+-- synopsis:
+description: Inefficient implementation of a lossy online histogram
+ algorithm. See "Numeric.StreamingHistogram" for more.
+
+license: Apache-2.0
+license-file: LICENSE
+author: Tom Hunger
+maintainer: tehunger@gmail.com
+-- copyright:
+-- category:
+build-type: Simple
+-- extra-source-files:
+cabal-version: >=1.10
+
+
+source-repository head
+ type: git
+ location: https://github.com/teh/streaming-histogram
+
+
+library
+ exposed-modules: Numeric.StreamingHistogram
+ , Numeric.StreamingHistogram.Internal
+ -- other-modules:
+ -- other-extensions:
+ build-depends: base >= 4.0 && < 5
+ , containers
+ , criterion >= 1.0
+
+ hs-source-dirs: src
+ ghc-options: -Wall
+ default-language: Haskell2010
+
+
+test-suite streaminghist-tests
+ type: exitcode-stdio-1.0
+ main-is: TestStreamingHist.hs
+ hs-source-dirs: tests
+ build-depends: base >= 4.0 && < 5
+ , streaming-histogram
+ , tasty
+ , tasty-hunit
+ , tasty-quickcheck
+ , containers
+
+
+benchmark streaminghist-bench
+ type: exitcode-stdio-1.0
+ main-is: BenchStreamingHist.hs
+ build-depends: base >= 4.0 && < 5
+ , streaming-histogram
+ , criterion >= 0.8
+ hs-source-dirs: tests
diff --git a/tests/BenchStreamingHist.hs b/tests/BenchStreamingHist.hs
new file mode 100644
index 0000000..e8f386d
--- /dev/null
+++ b/tests/BenchStreamingHist.hs
@@ -0,0 +1,21 @@
+import Criterion.Main
+import qualified Numeric.StreamingHistogram as H
+
+
+loop [] hist = hist
+loop (x:xs) hist = loop xs (H.update x hist)
+
+a = loop [1.0..1e5] (H.empty 10)
+b = loop [1.0..1e5] (H.empty 10)
+
+main :: IO ()
+main = defaultMain
+ [ bgroup "update"
+ [ bench "10" $ whnf (loop [1.0..1e4]) (H.empty 10)
+ , bench "100" $ whnf (loop [1.0..1e4]) (H.empty 100)
+ , bench "1000" $ whnf (loop [1.0..1e4]) (H.empty 1000)
+ ]
+ , bgroup "merge"
+ [ bench "1" $ whnf (H.merge a) b
+ ]
+ ]
diff --git a/tests/TestStreamingHist.hs b/tests/TestStreamingHist.hs
new file mode 100644
index 0000000..0c9fe14
--- /dev/null
+++ b/tests/TestStreamingHist.hs
@@ -0,0 +1,92 @@
+module Main where
+
+import qualified Data.List as L
+import qualified Data.Map as M
+import Data.Maybe (fromJust)
+import qualified Numeric.StreamingHistogram as H
+import qualified Numeric.StreamingHistogram.Internal as H
+import Test.Tasty
+import Test.Tasty.HUnit
+import Test.Tasty.QuickCheck as QC
+
+main :: IO ()
+main = defaultMain tests
+
+
+tests :: TestTree
+tests = testGroup "All Tests"
+ [ shrinkTests
+ , updateTests
+ , updateQuickCheck
+ , mergeTests
+ , sumTests
+ ]
+
+
+-- Need a small list because we're using it as input to the fold
+-- function.
+newtype SmallDoubleList = SmallDoubleList [Double] deriving (Eq,Show)
+
+instance Arbitrary SmallDoubleList where
+ arbitrary = sized $ \s -> do
+ n <- choose (20,s `min` 1000)
+ xs <- vectorOf n (choose (-10000.0, 10000.0))
+ return (SmallDoubleList xs)
+ shrink (SmallDoubleList xs) = map SmallDoubleList (shrink xs)
+
+
+updateQuickCheck = testGroup "quickcheck update"
+ [ QC.testProperty "always bounded to 10" $ testOne
+ ]
+ where
+ testOne (SmallDoubleList list) =
+ let e = H.empty 10
+ loop [] hist = hist
+ loop (x:xs) hist = loop xs (H.update x hist)
+ result = (M.size . H.histData) (loop list e)
+ in
+ result <= 10
+
+
+shrinkTests = testGroup "shrink"
+ [ testCase "unmodified" $ H.shrink [(0.0, 1)] @?= [] -- always shrink by exactly one
+ , testCase "empty" $ H.shrink [] @?= []
+ , testCase "actual" $ H.shrink [(0.0, 1), (1.0, 1)] @?= [(0.5, 2)]
+ , testCase "leftmost" $ H.shrink [(0.0, 1), (1.0, 1), (5.0, 1)] @?= [(0.5, 2), (5.0, 1)]
+ , testCase "rightmost" $ H.shrink [(0.0, 1), (4.0, 1), (5.0, 1)] @?= [(0.0, 1), (4.5, 2)]
+ , testCase "middle" $ H.shrink [(0.0, 1), (1.0, 1), (3.0, 1), (3.2, 1), (4.0, 1)] @?= [(0.0,1), (1.0,1), (3.1,2), (4.0,1)]
+ ]
+
+updateTests = testGroup "update"
+ [ testCase "empty" $ H.histData (H.empty 5) @?= M.empty
+ , testCase "two updates" $ (M.assocs . H.histData) (H.update 1.0 (H.update 0.0 (H.empty 2))) @?= [(0.0, 1), (1.0, 1)]
+ ]
+
+mergeTests = testGroup "merge"
+ [ testCase "mergeEmpty" $ H.merge (H.empty 5) (H.empty 5) @?= Just (H.empty 5)
+ , testCase "mergeOnes" $ (M.assocs . H.histData . fromJust) (H.merge a b) @?= [(0.5, 2)]
+ ]
+ where
+ a = H.update 0.0 (H.empty 1)
+ b = H.update 1.0 (H.empty 1)
+
+sumTests = testGroup "sum"
+ [ testCase "sumLeft" $ H.sum (-1.0) x3 @?= 0.5
+ , testCase "sumRight" $ H.sum (3.0) x3 @?= 2.5
+ ]
+ where
+ x3 = L.foldr H.update (H.empty 3) [0.0, 1.0, 2.0]
+
+-- | Tests from Appendix A from the Ben-Haim paper.
+paperTests = testGroup "paper"
+ [ testCase "update6" $ run 5 (L.take 6 testSequence) @?= [(2,1),(10,1),(17.5,2),(23,1),(36,1)]
+ , testCase "update7" $ run 5 (L.take 7 testSequence) @?= [(2,1),(9.5,2),(17.5,2),(23,1),(36,1)]
+ , testCase "merge3" $ (M.assocs . H.histData . fromJust) (H.merge lhist rhist) @?= [(2,1),(9.5,2),(19.33,3),(32.67,3),(45,1)]
+ , testCase "sum15" $ H.sum 15 (fromJust (H.merge lhist rhist)) @?= 3.28
+ ]
+ where
+ run nBins s = (M.assocs . H.histData) (L.foldr H.update (H.empty nBins) s)
+ testSequence = [23,19,10,16,36,2,9,32,30,4] :: [Double]
+ (ls, rs) = L.splitAt 7 testSequence
+ lhist = L.foldr H.update (H.empty 5) ls
+ rhist = L.foldr H.update (H.empty 5) rs