regress (empty) → 0.1
raw patch · 7 files changed
+265/−0 lines, 7 filesdep +addep +basedep +vectorsetup-changed
Dependencies added: ad, base, vector
Files
- LICENSE +30/−0
- README.md +8/−0
- Setup.hs +2/−0
- regress.cabal +33/−0
- src/Numeric/Regression/Internal.hs +21/−0
- src/Numeric/Regression/Linear.hs +88/−0
- src/Numeric/Regression/Logistic.hs +83/−0
+ LICENSE view
@@ -0,0 +1,30 @@+Copyright (c) 2015, Alp Mestanogullari++All rights reserved.++Redistribution and use in source and binary forms, with or without+modification, are permitted provided that the following conditions are met:++ * Redistributions of source code must retain the above copyright+ notice, this list of conditions and the following disclaimer.++ * 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.++ * Neither the name of Alp Mestanogullari nor the names of other+ contributors may be used to endorse or promote products derived+ from this software without specific prior written permission.++THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS+"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 COPYRIGHT+OWNER OR CONTRIBUTORS 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.
+ README.md view
@@ -0,0 +1,8 @@+regress+=======++[](http://travis-ci.org/alpmestan/regress)++Perform a linear or logistic regression using automatic differentiation ([ad](http://hackage.haskell.org/package/ad)).++See the haddocks for `Numeric.Regression.Linear` and `Numeric.Regression.Logistic` for documentation and examples.
+ Setup.hs view
@@ -0,0 +1,2 @@+import Distribution.Simple+main = defaultMain
+ regress.cabal view
@@ -0,0 +1,33 @@+name: regress+version: 0.1+synopsis: Linear and logistic regression through automatic differentiation+description:+ Linear and logistic regression through automatic differentiation+ .+ See "Numeric.Regression.Linear" and "Numeric.Regression.Logistic" for+ docs and examples.++homepage: https://github.com/alpmestan/regress+license: BSD3+license-file: LICENSE+author: Alp Mestanogullari+maintainer: alpmestan@gmail.com+copyright: Alp Mestanogullari+category: Math+build-type: Simple+cabal-version: >=1.10+extra-source-files: README.md++library+ exposed-modules:+ Numeric.Regression.Linear+ , Numeric.Regression.Logistic+ other-modules:+ Numeric.Regression.Internal++ build-depends: base >=4.7 && <5,+ ad >= 4.2 && <4.3,+ vector >= 0.10 && <0.11+ hs-source-dirs: src+ default-language: Haskell2010+ ghc-options: -O2 -Wall
+ src/Numeric/Regression/Internal.hs view
@@ -0,0 +1,21 @@+module Numeric.Regression.Internal where++import Control.Applicative+import Data.Foldable+import Data.Monoid++data Acc a = Acc {-# UNPACK #-} !Int !a++instance Monoid a => Monoid (Acc a) where+ mempty = Acc 0 mempty++ Acc m a `mappend` Acc n b = Acc (m + n) (a <> b)++acc :: a -> Acc (Sum a)+acc = Acc 1 . Sum++dot :: (Applicative v, Foldable v, Num a)+ => v a+ -> v a+ -> a+dot x y = getSum . foldMap Sum $ liftA2 (*) x y
+ src/Numeric/Regression/Linear.hs view
@@ -0,0 +1,88 @@+module Numeric.Regression.Linear+ (Model, compute, regress) where++import Control.Applicative+import Data.Foldable+import Data.Monoid+import Data.Traversable+import Numeric.AD+import Numeric.Regression.Internal++-- | A model using the given @f@ to store parameters of type @a@.+-- Can be thought of as some kind of vector throughough this+-- package.+type Model f a = f a++-- | Compute the predicted value for+-- the given model on the given observation+compute :: (Applicative v, Foldable v, Num a)+ => Model v a -- ^ theta vector, the model's parameters+ -> v a -- ^ @x@ vector, with the observed numbers+ -> a -- ^ predicted @y@ for this observation+compute theta x = theta `dot` x+{-# INLINE compute #-}++-- | Cost function for a linear regression on a single observation+cost :: (Applicative v, Foldable v, Floating a)+ => Model v a -- ^ theta vector, the model's parameters+ -> v a -- ^ @x@ vector+ -> a -- ^ expected @y@ for the observation+ -> a -- ^ cost+cost theta x y = 0.5 * (y - compute theta x) ^ (2 :: Int)+{-# INLINE compute #-}++-- | Cost function for a linear regression on a set of observations+totalCost :: (Applicative v, Foldable v, Applicative f, Foldable f, Floating a)+ => Model v a -- ^ theta vector, the model's parameters+ -> f a -- ^ expected @y@ value for each observation+ -> f (v a) -- ^ input data for each observation+ -> a -- ^ total cost over all observations+totalCost theta ys xs =+ let Acc n (Sum s) = foldMap acc $ liftA2 (cost theta) xs ys+ in s / fromIntegral n+{-# INLINE totalCost #-}++-- | Given some observed \"predictions\" @ys@, the corresponding+-- input values @xs@ and initial values for the model's parameters @theta0@,+--+-- > regress ys xs theta0+--+-- returns a stream of values for the parameters that'll fit the data better+-- and better.+--+-- Example:+--+-- @+-- -- the theta we're approximating+-- realtheta :: Model V.Vector Double+-- realtheta = V.fromList [1.0, 2.0, 3.0]+--+-- -- let's start there and make 'regress'+-- -- get values that better fit the input data+-- theta0 :: Model V.Vector Double+-- theta0 = V.fromList [0.2, 3.0, 2.23]+--+-- -- input data. (output value, vector of values for each input)+-- ys_ex :: V.Vector Double+-- xs_ex :: V.Vector (V.Vector Double)+-- (ys_ex, xs_ex) = V.unzip . V.fromList $+-- [ (3, V.fromList [0, 0, 1])+-- , (1, V.fromList [1, 0, 0])+-- , (2, V.fromList [0, 1, 0])+-- , (6, V.fromList [1, 1, 1])+-- ]+--+-- -- stream of increasingly accurate parameters+-- thetaApproxs :: [Model V.Vector Double]+-- thetaApproxs = learnAll ys_ex xs_ex theta0+-- @+regress :: (Traversable v, Applicative v, Foldable v, Applicative f, Foldable f, Ord a, Floating a)+ => f a -- ^ expected @y@ value for each observation+ -> f (v a) -- ^ input data for each observation+ -> Model v a -- ^ initial parameters for the model, from which we'll improve+ -> [Model v a] -- ^ a stream of increasingly accurate values+ -- for the model's parameter to better fit the observations.+regress ys xs t0 =+ gradientDescent (\theta -> totalCost theta (fmap auto ys) (fmap (fmap auto) xs))+ t0+{-# INLINE regress #-}
+ src/Numeric/Regression/Logistic.hs view
@@ -0,0 +1,83 @@+module Numeric.Regression.Logistic+ (Model, regress) where++import Control.Applicative+import Data.Foldable+import Data.Monoid+import Data.Traversable+import Numeric.AD+import Numeric.Regression.Internal++-- | A model using the given @f@ to store parameters of type @a@.+-- Can be thought of as some kind of vector throughough this+-- package.+type Model f a = f a++logit :: Floating a => a -> a+logit x = 1 / (1 + exp (negate x))+{-# INLINE logit #-}++logLikelihood :: (Applicative v, Foldable v, Floating a)+ => Model v a -- theta vector+ -> a -- y+ -> v a -- x vector (observation)+ -> a+logLikelihood theta y x =+ y * log (logit z) + (1 - y) * log (1 - logit z)++ where z = theta `dot` x+{-# INLINE logLikelihood #-}++totalLogLikelihood :: (Applicative v, Foldable v, Applicative f, Foldable f, Floating a)+ => a -- delta+ -> Model v a+ -> f a+ -> f (v a)+ -> a+totalLogLikelihood delta theta ys xs =+ (a - delta * b) / fromIntegral n++ where Acc n (Sum a) = foldMap acc $ liftA2 (logLikelihood theta) ys xs+ b = (/2) . getSum $ foldMap (\x -> Sum (x^(2::Int))) theta+{-# INLINE totalLogLikelihood #-}++-- | Given some observed \"predictions\" @ys@, the corresponding+-- input values @xs@ and initial values for the model's parameters @theta0@,+--+-- > regress ys xs theta0+--+-- returns a stream of values for the parameters that'll fit the data better+-- and better.+--+-- Example:+--+-- @+-- ys_ex :: [Double]+-- xs_ex :: [[Double]]+-- (ys_ex, xs_ex) = unzip $+-- [ (1, [1, 1])+-- , (0, [-1, -2])+-- , (1, [2, 5])+-- , (0, [-1, 1])+-- , (1, [2, -1])+-- , (1, [1, -10])+-- , (0, [-0.1, 30])+-- ]+--+-- t0 :: [Double]+-- t0 = [1, 0.1]+--+-- approxs' :: [Model [] Double]+-- approxs' = learn 0.1 ys_ex xs_ex t0+-- @+regress :: (Traversable v, Applicative v, Foldable f, Applicative f, Ord a, Floating a)+ => a -- ^ learning rate+ -> f a -- ^ expect prediction for each observation+ -> f (v a) -- ^ input data for each observation+ -> Model v a -- ^ initial values for the model's parameters+ -> [Model v a] -- ^ stream of increasingly accurate values for+ -- the model's parameters+regress delta ys xs =+ gradientAscent $ \theta ->+ totalLogLikelihood (auto delta) theta (fmap auto ys) (fmap (fmap auto) xs)+{-# INLINE regress #-}