# Aligned Induction

## Lenter

### Sections

Conditional entropy tuple set builder

Conditional entropy fud decomper

### Conditional entropy tuple set builder

The application of the conditional entropy tuple set builder is described in Haskell.

The conditional entropy tuple set builder parametersBuilderConditionalVars is defined in module AlignmentPracticable.

parametersBuilderConditionalVars ::
Integer -> Integer -> Integer -> Set.Set Variable -> Histogram ->
Maybe (Map.Map (Set.Set Variable) Double)

parametersBuilderConditionalVars kmax omax qmax ll aa
| kmax < 0 || omax < 0 || qmax < 0 = Nothing
| otherwise = Just $bot qmax$ buildc rr rr
where
vvk = vars aa minus ll
rr = bot omax $llmm [(sgl w, ent (aa red (ll add w)) - ent (aa red (sgl w))) | w <- qqll vvk] buildc qq nn = if mm /= Map.empty then buildc mm (nn Map.union mm) else nn where pp = llqq [jj | (kk,e) <- mmll qq, e > 0, w <- qqll (vvk minus kk), let jj = kk add w] mm = bot omax$ llmm [(jj, ent (aa red (ll union jj)) - ent (aa red jj)) |
jj <- qqll pp, card jj <= kmax]
...


The repa builder is defined in module AlignmentPracticableRepa,

parametersBuilderConditionalVarsRepa ::
Integer -> Integer -> Integer -> Set.Set Variable -> HistoryRepa ->
Maybe (Map.Map (Set.Set Variable) Double)

parametersBuilderConditionalVarsRepa kmax omax qmax ll aa
| kmax < 0 || omax < 0 || qmax < 0 = Nothing
| otherwise = Just $bot qmax$ buildc rr rr
where
!z = fromIntegral $historyRepasSize aa vvk = vars aa minus ll rr = bot omax$ llmm [(sgl w, ent (aa red (ll add w)) - ent (aa red (sgl w))) | w <- qqll vvk]
buildc qq nn = if mm /= Map.empty then buildc mm (nn Map.union mm) else nn
where
pp = llqq [jj | (kk,e) <- mmll qq, e > 0, w <- qqll (vvk minus kk), let jj = kk add w]
mm = bot omax $llmm [(jj, ent (aa red (ll union jj)) - ent (aa red jj)) | jj <- qqll pp, card jj <= kmax] ...  An example of substrate analysis using the conditional entropy tuple set builder is described in Analysis of the UCI Machine Learning Repository Mushroom Data Set - Predicting edibility without modelling and Induced modelling of edibility. ### Conditional entropy fud decomper The application of the conditional entropy fud decomper is described in Haskell. The conditional entropy fud decomper parametersSystemsDecomperConditional is defined in module AlignmentPracticable. parametersSystemsDecomperConditional :: Integer -> Integer -> System -> Set.Set Variable -> Histogram -> Maybe (System, DecompFud)  as parametersSystemsDecomperConditional kmax omax uu ll aa ... | otherwise = Just$ decomp uu emptyTree 1
where
decomp uu zz f s
| zz == emptyTree && nnr == [] = (uu, decompFudEmpty)
| zz == emptyTree = decomp uur zzr (f+1)
| mm == [] = (uu, zzdf (zztrim zz))
| otherwise = decomp uuc zzc (f+1)
where
nnr = lenter kmax omax 1 ll aa
[(kkr,_)] = nnr
ffr = if nnr /= [] then vvff uu kkr f else fudEmpty
uur = uu uunion fsys ffr
zzr = tsgl (stateEmpty,ffr)
mm = [(e,nn,ss,bb) | (nn,yy) <- qqll (treesPlaces zz),
let rrc = llsthis nn, let hhc = llfhis nn, let (_,ff) = last nn, ff /= fudEmpty,
ss <- qqll (cart uu (fder ff) minus dom (treesRoots yy)),
let xx = hhc union rrc add unit (sgl ss),
let bb = apply vv vv xx aa,
let e = fromRational (size bb) * ent (bb red ll)
e > 0]
(_,nn,ss,bb) = last $sort mm nnc = lenter kmax omax 1 ll bb [(kkc,_)] = nnc ffc = if nnr /= [] then vvff uu kkc f else fudEmpty uuc = uu uunion fsys ffc zzc = pathsTree$ treesPaths zz add (nn ++ [(ss,ffc)])
lenter kmax omax qmax ll aa = mmll $fromJust$ parametersBuilderConditionalVars kmax omax qmax ll aa
...


The repa decomper is defined in module AlignmentPracticableRepa,

parametersSystemsHistoryRepasDecomperConditionalFmaxRepa ::
Integer -> Integer -> Integer -> System -> Set.Set Variable -> HistoryRepa ->
Maybe (System, DecompFud)
parametersSystemsHistoryRepasDecomperConditionalFmaxRepa kmax omax fmax uu ll aa
...
| otherwise = Just $decomp uu emptyTree 1 where vv = vars aa decomp uu zz f | zz == emptyTree && nnr == [] = (uu, decompFudEmpty) | zz == emptyTree = decomp uur zzr (f+1) | (fmax > 0 && f > fmax) || V.null mm || nnc == [] = (uu, zzdf zz) | otherwise = decomp uuc zzc (f+1) where nnr = lenter kmax omax ll aa [(kkr,_)] = nnr ffr = vvff uu kkr f uur = uu uunion fsys ffr aar = apply uur ffr aa aa' = trim$ reduce uur (fder ffr union ll) aar
zzr = tsgl ((stateEmpty,ffr),(aar, aa'))
mm = V.fromList [(e,(nn,ss,bb)) | (nn,yy) <- qqll (treesPlaces zz),
let ((_,ff),(bb,bb')) = last nn,
let tt = dom (dom (treesRoots yy)),
(ss,a) <- aall (bb' red fder ff), a > 0, ss notin tt,
let e = fromRational a * ent (bb' mul unit (sgl ss) red ll), e > rounding]
(_,(nn,ss,bb)) = V.head $vectorPairsTop 1 mm cc = select uu ss bb hrred vv nnc = lenter kmax omax ll cc [(kkc,_)] = nnc ffc = vvff uu kkc f uuc = uu uunion fsys ffc ccc = apply uuc ffc cc cc' = trim$ reduce uuc (fder ffc union ll) ccc
zzc = pathsTree $treesPaths zz add (nn List.++ [((ss,ffc),(ccc, cc'))]) lenter kmax omax ll aa = mmll$ fromJust \$ parametersBuilderConditionalVarsRepa kmax omax 1 ll aa
...


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