Automated Differentiation Type Question
Can anyone tell me why I get a type error with testGrad2? What are my options? Clearly I would like to be able find the gradient of my cost function for different sets of observations. Thanks, Dominic.
{-# LANGUAGE NoMonomorphismRestriction #-}
import Numeric.AD
default()
costFn :: Floating a => [a] -> [[a]] -> [a] -> a costFn ys xss thetas = (/ (2*m)) $ sum $ map (^ (2 :: Int)) $ zipWith (\y xs -> costFnAux y xs thetas) ys xss where m = fromIntegral $ length xss costFnAux :: Floating a => a -> [a] -> [a] -> a costFnAux y xs thetas = y - head thetas - sum (zipWith (*) xs (tail thetas))
ys :: Floating a => [a] ys = [1.0, 2.0, 3.0]
xss :: Floating a => [[a]] xss = [[1.0], [2.0], [3.0]]
thetas :: Floating a => [a] thetas = [0.0, 1.0]
test :: Floating a => a test = costFn ys xss thetas
testGrad0 = grad (costFn ys xss)
testGrad1 :: Floating a => [a] -> [[a]] -> [a] -> [a] testGrad1 ys xss = grad (costFn (undefined :: Floating a => [a]) (undefined :: Floating a => [[a]]))
testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a] testGrad2 ys xss = grad (costFn ys xss)
[1 of 1] Compiling Main ( /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs, interpreted )
/Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:33: Could not deduce (a ~ ad-3.4:Numeric.AD.Internal.Types.AD s a) from the context (Floating a) bound by the type signature for testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a] at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14-53 or from (Numeric.AD.Internal.Classes.Mode s) bound by a type expected by the context: Numeric.AD.Internal.Classes.Mode s => [ad-3.4:Numeric.AD.Internal.Types.AD s a] -> ad-3.4:Numeric.AD.Internal.Types.AD s a at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:20-39 `a' is a rigid type variable bound by the type signature for testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a] at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14 Expected type: [ad-3.4:Numeric.AD.Internal.Types.AD s a] Actual type: [a] In the first argument of `costFn', namely `ys' In the first argument of `grad', namely `(costFn ys xss)' In the expression: grad (costFn ys xss)
/Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:36: Could not deduce (a ~ ad-3.4:Numeric.AD.Internal.Types.AD s a) from the context (Floating a) bound by the type signature for testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a] at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14-53 or from (Numeric.AD.Internal.Classes.Mode s) bound by a type expected by the context: Numeric.AD.Internal.Classes.Mode s => [ad-3.4:Numeric.AD.Internal.Types.AD s a] -> ad-3.4:Numeric.AD.Internal.Types.AD s a at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:20-39 `a' is a rigid type variable bound by the type signature for testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a] at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14 Expected type: [[ad-3.4:Numeric.AD.Internal.Types.AD s a]] Actual type: [[a]] In the second argument of `costFn', namely `xss' In the first argument of `grad', namely `(costFn ys xss)' In the expression: grad (costFn ys xss) Failed, modules loaded: none.
Answering my own question, what I needed was:
testGrad2 :: (Fractional a, Num a) =>
(forall s . Mode s => [AD s a]) ->
(forall s . Mode s => [[AD s a]]) ->
[a] -> [a]
testGrad2 ys xss = grad (costFn ys xss)
On 23 Apr 2013, at 10:44, Dominic Steinitz
Can anyone tell me why I get a type error with testGrad2? What are my options? Clearly I would like to be able find the gradient of my cost function for different sets of observations.
Thanks, Dominic.
{-# LANGUAGE NoMonomorphismRestriction #-}
import Numeric.AD
default()
costFn :: Floating a => [a] -> [[a]] -> [a] -> a costFn ys xss thetas = (/ (2*m)) $ sum $ map (^ (2 :: Int)) $ zipWith (\y xs -> costFnAux y xs thetas) ys xss where m = fromIntegral $ length xss costFnAux :: Floating a => a -> [a] -> [a] -> a costFnAux y xs thetas = y - head thetas - sum (zipWith (*) xs (tail thetas))
ys :: Floating a => [a] ys = [1.0, 2.0, 3.0]
xss :: Floating a => [[a]] xss = [[1.0], [2.0], [3.0]]
thetas :: Floating a => [a] thetas = [0.0, 1.0]
test :: Floating a => a test = costFn ys xss thetas
testGrad0 = grad (costFn ys xss)
testGrad1 :: Floating a => [a] -> [[a]] -> [a] -> [a] testGrad1 ys xss = grad (costFn (undefined :: Floating a => [a]) (undefined :: Floating a => [[a]]))
testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a] testGrad2 ys xss = grad (costFn ys xss)
[1 of 1] Compiling Main ( /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs, interpreted )
/Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:33: Could not deduce (a ~ ad-3.4:Numeric.AD.Internal.Types.AD s a) from the context (Floating a) bound by the type signature for testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a] at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14-53 or from (Numeric.AD.Internal.Classes.Mode s) bound by a type expected by the context: Numeric.AD.Internal.Classes.Mode s => [ad-3.4:Numeric.AD.Internal.Types.AD s a] -> ad-3.4:Numeric.AD.Internal.Types.AD s a at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:20-39 `a' is a rigid type variable bound by the type signature for testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a] at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14 Expected type: [ad-3.4:Numeric.AD.Internal.Types.AD s a] Actual type: [a] In the first argument of `costFn', namely `ys' In the first argument of `grad', namely `(costFn ys xss)' In the expression: grad (costFn ys xss)
/Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:36: Could not deduce (a ~ ad-3.4:Numeric.AD.Internal.Types.AD s a) from the context (Floating a) bound by the type signature for testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a] at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14-53 or from (Numeric.AD.Internal.Classes.Mode s) bound by a type expected by the context: Numeric.AD.Internal.Classes.Mode s => [ad-3.4:Numeric.AD.Internal.Types.AD s a] -> ad-3.4:Numeric.AD.Internal.Types.AD s a at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:33:20-39 `a' is a rigid type variable bound by the type signature for testGrad2 :: Floating a => [a] -> [[a]] -> [a] -> [a] at /Users/dom/Dropbox/Private/Whales/ADTypePuzzle.hs:32:14 Expected type: [[ad-3.4:Numeric.AD.Internal.Types.AD s a]] Actual type: [[a]] In the second argument of `costFn', namely `xss' In the first argument of `grad', namely `(costFn ys xss)' In the expression: grad (costFn ys xss) Failed, modules loaded: none.
participants (1)
-
Dominic Steinitz