Conditional entropy optimisation
Code commentary on the implementation of Tractable and Practicable Inducers/Python Implementation/Conditional entropy optimisation
Sections
Conditional entropy tuple set builder
Conditional entropy tuple set builder
Define the limited-dimension conditional entropy tuple set list minimiser
\[
Z_{P,A,\mathrm{L}} = \mathrm{maximiseLister}(X_{P,A,\mathrm{L}},P_{P,A,\mathrm{L}},\mathrm{top}(\mathrm{omax}),R_{P,A,\mathrm{L}})
\]
where (i) the optimiser function is
\[
\begin{eqnarray}
X_{P,A,\mathrm{L}} &=& \{(K,-(\mathrm{entropy}(A~\%~(K \cup L))-\mathrm{entropy}(A~\%~K))) : K \subseteq V \setminus L\}
\end{eqnarray}
\]
and (ii) the neighbourhood function is
\[
\begin{eqnarray}
&&P_{P,A,\mathrm{L}}(M) = \{(J,X_{P,A,\mathrm{L}}(J)) : \\
&&\hspace{2em}(K,\cdot) \in M,~w \in V \setminus L \setminus K,~J = K \cup \{w\},~|J| \leq \mathrm{kmax}\}
\end{eqnarray}
\]
and (iii) the initial subset is
\[
\begin{eqnarray}
R_{P,A,\mathrm{L}} &=& \{(\{w\},X_{P,A,\mathrm{L}}(\{w\})) : w \in V \setminus L\}
\end{eqnarray}
\]
Then the conditional entropy optimised limited-dimension conditional entropy tuple set list, $M$, is (Text)
\[
\begin{eqnarray}
M &=& \mathrm{topd}(\mathrm{qmax})(\mathrm{elements}(Z_{P,A,\mathrm{L}})) \subset \mathrm{P}(V \setminus L)
\end{eqnarray}
\]
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)
def parametersBuilderConditionalVars(kmax,omax,qmax,ll,aa):
...
def buildc(qq,nn):
pp = sset([kk|sgl(w) for (kk,e) in qq.items() if e > 0 for w in vvk-kk])
mm = bot(omax,sdict([(jj,ent(red(aa,ll|jj))-ent(red(aa,jj))) for jj in pp if len(jj) <= kmax]))
if len(mm) > 0:
nn1 = nn.copy()
nn1.update(mm)
return buildc(mm,nn1)
return nn
if kmax < 0 or omax < 0 or qmax < 0:
return None
vvk = vars(aa) - ll
rr = bot(omax,sdict([(sgl(w),ent(red(aa,ll|sgl(w)))-ent(red(aa,sgl(w)))) for w in vvk]))
return bot(qmax,buildc(rr,rr))