void PhonetisaurusE2F::entry_to_fsa_w( vector<string>* tokens ){
/*
Convert an input grapheme sequence to an equivalent
Finite-State Machine.
*/
//Build a linear FSA representing the input
_entry_to_skip_fsa( tokens );
//Add any multi-grapheme arcs
word = VectorFst<StdArc>(ComposeFst<StdArc>(word,ifilter));
Project(&word, PROJECT_OUTPUT);
//Now optimize the result
RmEpsilon(&word);
ArcSort(&word,OLabelCompare<StdArc>());
return;
}
void M2MFstAligner::_conditional_max( bool y_given_x ){
/*
Compute the conditional distribution, P(Y|X) using the WFST paradigm.
This is bassed on the approach from Shu and Hetherington 2002.
It is assumed that all WFSTs and operations use the Log semiring.
Given:
FST1 = P(X,Y)
Compute:
FST2 = P(X)
:= Map_inv(Det(RmEps(Proj_i(FST1))))
FST3 = P(Y|X)
:= Compose(FST2,FST1)
Proj_i: project on input labels
RmEps: epsilon removal
Det: determinize
Map_inv: invert weights
Notes: An analogous process may be used to compute P(X|Y). In this
case one would project on OUTPUT labels - Proj_o, and reverse the
composition order to Compose(FST1,FST2).
Future work:
What we are doing here in terms of *generating* the JOINT fst each
time is really just a dumb hack. We *should* encode the model in an
FST and encode the individual lattices, rather than doing the hacky
manual label encoding that we currently rely on.
*/
//Joint distribution that we start with
VectorFst<LogArc>* joint = new VectorFst<LogArc>();
SymbolTable* misyms = new SymbolTable("misyms");
SymbolTable* mosyms = new SymbolTable("mosyms");
joint->AddState();
joint->AddState();
joint->SetStart(0);
joint->SetFinal(1,LogArc::Weight::One());
map<LogArc::Label,LogWeight>::iterator it;
for( it=prev_alignment_model.begin(); it != prev_alignment_model.end(); it++ ){
string isym = isyms->Find((*it).first);
vector<string> io = tokenize_utf8_string( &isym, &s1s2_sep );
LogArc arc( misyms->AddSymbol(io[0]), mosyms->AddSymbol(io[1]), (*it).second, 1 );
joint->AddArc( 0, arc );
}
//VectorFst<LogArc>* joint = new VectorFst<LogArc>();
//Push<LogArc,REWEIGHT_TO_FINAL>(*_joint, joint, kPushWeights);
//joint->SetFinal(1,LogWeight::One());
joint->Write("m2mjoint.fst");
//BEGIN COMPUTE MARGINAL P(X)
VectorFst<LogArc>* dmarg;
if( y_given_x )
dmarg = new VectorFst<LogArc>(ProjectFst<LogArc>(*joint, PROJECT_INPUT));
else
dmarg = new VectorFst<LogArc>(ProjectFst<LogArc>(*joint, PROJECT_OUTPUT));
RmEpsilon(dmarg);
VectorFst<LogArc>* marg = new VectorFst<LogArc>();
Determinize(*dmarg, marg);
ArcMap(marg, InvertWeightMapper<LogArc>());
if( y_given_x )
ArcSort(marg, OLabelCompare<LogArc>());
else
ArcSort(marg, ILabelCompare<LogArc>());
//END COMPUTE MARGINAL P(X)
marg->Write("marg.fst");
//CONDITIONAL P(Y|X)
VectorFst<LogArc>* cond = new VectorFst<LogArc>();
if( y_given_x )
Compose(*marg, *joint, cond);
else
Compose(*joint, *marg, cond);
//cond now contains the conditional distribution P(Y|X)
cond->Write("cond.fst");
//Now update the model with the new values
for( MutableArcIterator<VectorFst<LogArc> > aiter(cond, 0); !aiter.Done(); aiter.Next() ){
LogArc arc = aiter.Value();
string lab = misyms->Find(arc.ilabel)+"}"+mosyms->Find(arc.olabel);
int labi = isyms->Find(lab);
alignment_model[labi] = arc.weight;
prev_alignment_model[labi] = LogWeight::Zero();
}
delete joint, marg, cond, dmarg;
delete misyms, mosyms;
return;
}
vector<PathData> M2MFstAligner::write_alignment(const VectorFst<LogArc> &ifst,
int nbest)
{
//Generic alignment generator
VectorFst<StdArc> fst;
Map(ifst, &fst, LogToStdMapper());
for (StateIterator<VectorFst<StdArc> > siter(fst); !siter.Done();
siter.Next()) {
StdArc::StateId q = siter.Value();
for (MutableArcIterator<VectorFst<StdArc> > aiter(&fst, q);
!aiter.Done(); aiter.Next()) {
//Prior to decoding we make several 'heuristic' modifications to the weights:
// 1. A multiplier is applied to any multi-token substrings
// 2. Any LogWeight::Zero() arc weights are reset to '99'.
// We are basically resetting 'Infinity' values to a 'smallest non-Infinity'
// so that the ShortestPath algorithm actually produces something no matter what.
// 3. Any arcs that consist of subseq1:subseq2 being the same length and subseq1>1
// are set to '99' this forces shortestpath to choose arcs where one of the
// following conditions holds true
// * len(subseq1)>1 && len(subseq2)!=len(subseq1)
// * len(subseq2)>1 && len(subseq1)!=len(subseq2)
// * len(subseq1)==len(subseq2)==1
//I suspect these heuristics can be eliminated with a better choice of the initialization
// function and maximization function, but this is the way that m2m-aligner works, so
// it makes sense for our first cut implementation.
//In any case, this guarantees that M2MFstAligner produces results identical to those
// produced by m2m-aligner - but with a bit more reliability.
//UPDATE: this now produces a better alignment than m2m-aligner.
// The maxl heuristic is still in place. The aligner will produce *better* 1-best alignments
// *without* the maxl heuristic below, BUT this comes at the cost of producing a less
// flexible corpus. That is, for a small training corpus like nettalk, if we use the
// best alignment we wind up with more 'chunks' and thus get a worse coverage for unseen
// data. Using the aignment lattices to train the joint ngram model solves this problem.
// Oh baby. Can't wait to for everyone to see the paper!
//NOTE: this is going to fail if we encounter any alignments in a new test item that never
// occurred in the original model.
StdArc
arc = aiter.Value();
int
maxl = get_max_length(isyms->Find(arc.ilabel));
if (maxl == -1) {
arc.weight = 999;
}
else {
//Optionally penalize m-to-1 / 1-to-m links. This produces
// WORSE 1-best alignments, but results in better joint n-gram
// models for small training corpora when using only the 1-best
// alignment. By further favoring 1-to-1 alignments the 1-best
// alignment corpus results in a more flexible joint n-gram model
// with regard to previously unseen data.
//if( penalize==true ){
arc.weight = alignment_model[arc.ilabel].Value() * maxl;
//}else{
//For larger corpora this is probably unnecessary.
//arc.weight = alignment_model[arc.ilabel].Value();
//}
}
if (arc.weight == LogWeight::Zero())
arc.weight = 999;
if (arc.weight != arc.weight)
arc.weight = 999;
aiter.SetValue(arc);
}
}
VectorFst<StdArc> shortest;
ShortestPath(fst, &shortest, nbest);
RmEpsilon(&shortest);
//Skip empty results. This should only happen
// in the following situations:
// 1. seq1_del=false && len(seq1)<len(seq2)
// 2. seq2_del=false && len(seq1)>len(seq2)
//In both 1.and 2. the issue is that we need to
// insert a 'skip' in order to guarantee at least
// one valid alignment path through seq1*seq2, but
// user params didn't allow us to.
//Probably better to insert these where necessary
// during initialization, regardless of user prefs.
if (shortest.NumStates() == 0) {
vector<PathData> dummy;
return dummy;
}
FstPathFinder
pathfinder(skipSeqs);
pathfinder.isyms = isyms;
pathfinder.findAllStrings(shortest);
return pathfinder.paths;
}