covariance 0.1.0.1 → 0.1.0.2

raw patch · 5 files changed

+93/−6 lines, 5 filesdep +statistics

Dependencies added: statistics

Files

• CHANGELOG.md +6/−0
• covariance.cabal +3/−1
• src/Statistics/Covariance.hs +54/−3
• src/Statistics/Covariance/LedoitWolf.hs +6/−2
• src/Statistics/Covariance/Types.hs +24/−0

@@ -5,6 +5,12 @@ ## Unreleased changes  +## 0.1.0.2++-   `scale`, `rescaleWith` functions.+-   Avoid duplicate centering.++ ## 0.1.0.1  -   Fix tests, remove debug output.

@@ -1,6 +1,6 @@ cabal-version:      2.4 name:               covariance-version:            0.1.0.1+version:            0.1.0.2 synopsis:     Well-conditioned estimation of large-dimensional covariance matrices @@ -26,6 +26,7 @@     exposed-modules:       Statistics.Covariance     other-modules:+      Statistics.Covariance.Types       Statistics.Covariance.LedoitWolf       Statistics.Covariance.RaoBlackwellLedoitWolf       Statistics.Covariance.OracleApproximatingShrinkage@@ -33,6 +34,7 @@     ghc-options: -Wall -Wunused-packages     build-depends:    base ^>=4.14.3.0                     , hmatrix+                    , statistics                     , vector     hs-source-dirs:   src     default-language: Haskell2010

@@ -10,22 +10,30 @@ -- -- Creation date: Tue Sep 14 13:02:15 2021. module Statistics.Covariance-  ( empiricalCovariance,+  ( -- * Empirical estimator+    empiricalCovariance,      -- * Shrinkage based estimators-    --+     -- | See the overview on shrinkage estimators provided by     -- [scikit-learn](https://scikit-learn.org/dev/modules/covariance.html#shrunk-covariance).     module Statistics.Covariance.LedoitWolf,     module Statistics.Covariance.RaoBlackwellLedoitWolf,     module Statistics.Covariance.OracleApproximatingShrinkage,++    -- * Helper functions+    scale,+    rescaleWith,   ) where +import qualified Data.Vector.Storable as VS import qualified Numeric.LinearAlgebra as L+import qualified Numeric.LinearAlgebra.Devel as L import Statistics.Covariance.LedoitWolf import Statistics.Covariance.OracleApproximatingShrinkage import Statistics.Covariance.RaoBlackwellLedoitWolf+import qualified Statistics.Sample as S  -- | Empirical or sample covariance. --@@ -36,5 +44,48 @@ -- [hmatrix](https://hackage.haskell.org/package/hmatrix). -- -- NOTE: This function may call 'error'.-empiricalCovariance :: L.Matrix Double -> L.Herm Double+empiricalCovariance ::+  -- | Data matrix of dimension NxP, where N is the number of observations, and+  -- P is the number of parameters.+  L.Matrix Double ->+  L.Herm Double empiricalCovariance = snd . L.meanCov++scaleWith ::+  -- Vector of means (length P).+  L.Vector Double ->+  -- Vector of standard deviations (length P)+  L.Vector Double ->+  -- Data matrix of dimension N x P.+  L.Matrix Double ->+  -- Data matrix with means 0 and variance 1.0.+  L.Matrix Double+scaleWith ms ss = L.mapMatrixWithIndex (\(_, j) x -> (x - ms VS.! j) / (ss VS.! j))++-- | Center and scales columns.+--+-- Normalize a data matrix to have means 0 and standard deviations/variances+-- 1.0. The estimated covariance matrix of a scaled data matrix is a correlation+-- matrix, which is easier to estimate.+scale ::+  -- | Data matrix of dimension NxP, where N is the number of observations, and+  -- P is the number of parameters.+  L.Matrix Double ->+  -- | (Means, Standard deviations, Centered and scaled matrix)+  (L.Vector Double, L.Vector Double, L.Matrix Double)+scale xs = (ms, ss, scaleWith ms ss xs)+  where+    msVs = map S.meanVariance $ L.toColumns xs+    ms = L.fromList $ map fst msVs+    ss = L.fromList $ map (sqrt . snd) msVs++-- | Convert a correlation matrix with given standard deviations to original+-- scale.+rescaleWith ::+  -- | Vector of standard deviations (length P)+  L.Vector Double ->+  -- | Correlation matrix.+  L.Matrix Double ->+  -- | Covariance matrix.+  L.Matrix Double+rescaleWith ss = L.mapMatrixWithIndex (\(i, j) x -> x * (ss VS.! i) * (ss VS.! j))

@@ -17,6 +17,7 @@ import Data.Foldable import qualified Numeric.LinearAlgebra as L import Statistics.Covariance.Internal.Tools+import Statistics.Covariance.Types  -- | Shrinkage based covariance estimator by Ledoit and Wolf. --@@ -32,11 +33,12 @@ -- -- NOTE: This function may call 'error' due to partial library functions. ledoitWolf ::+  DoCenter ->   -- | Sample data matrix of dimension \(n \times p\), where \(n\) is the number   -- of samples (rows), and \(p\) is the number of parameters (columns).   L.Matrix Double ->   Either String (L.Herm Double)-ledoitWolf xs+ledoitWolf c xs   | n < 2 = Left "ledoitWolf: Need more than one sample."   | p < 1 = Left "ledoitWolf: Need at least one parameter."   -- The Ledoit and Wolf shrinkage estimator of the covariance matrix@@ -47,7 +49,9 @@     n = L.rows xs     p = L.cols xs     (means, sigma) = L.meanCov xs-    xsCentered = centerWith means xs+    xsCentered = case c of+      DoCenter -> centerWith means xs+      AssumeCentered -> xs     im = L.trustSym $ L.ident p     mu = muE sigma     d2 = d2E im sigma mu

@@ -0,0 +1,24 @@+-- |+-- Module      :  Statistics.Covariance.Types+-- Description :  Common types+-- Copyright   :  (c) 2021 Dominik Schrempf+-- License     :  GPL-3.0-or-later+--+-- Maintainer  :  dominik.schrempf@gmail.com+-- Stability   :  experimental+-- Portability :  portable+--+-- Creation date: Wed Sep 15 09:03:01 2021.+module Statistics.Covariance.Types+  ( DoCenter (..),+  )+where++-- | For some methods, data matrices have to be centered before estimation of+-- the covariance matrix. Sometimes, data matrices are already centered, and in+-- this case, duplicate centering can be avoided.+data DoCenter+  = -- | Perform centering.+    DoCenter+  | -- | Do not perform centering; assume the data matrix is already centered.+    AssumeCentered