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hoeffding.cpp
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hoeffding.cpp
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#include "hoeffding.h"
namespace TDatastream {
///////////////////////////////
// constant-definitions
// const int BinsN;
///////////////////////////////
// Helper-functions
void TMisc::AddVec(const int& Scalar, TIntV& FstV, TIntV& SndV) {
while (FstV.Len() < SndV.Len()) { FstV.Add(0); }
while (FstV.Len() > SndV.Len()) { SndV.Add(0); }
for (int ElN = 0; ElN < FstV.Len(); ++ElN) {
SndV[ElN] += Scalar*FstV[ElN];
}
}
double TMisc::Entropy(const TIntV& FreqV, const int& N) {
double h = 0.0, p = 0.0;
for (auto It = FreqV.BegI(); It != FreqV.EndI(); ++It) {
p = N > 0 ? 1.0*It->Val/N : 0.0;
if (p > 0) { h -= p*TMath::Log2(p); }
}
return h;
}
///////////////////////////////
// Bin
bool operator<=(const TBin& Bin1, const TBin& Bin2) {
return Bin1.Value <= Bin2.Value;
}
bool operator>=(const TBin& Bin1, const TBin& Bin2) {
return Bin1.Value >= Bin2.Value;
}
bool operator<(const TBin& Bin1, const TBin& Bin2) {
return Bin1.Value < Bin2.Value;
}
bool operator>(const TBin& Bin1, const TBin& Bin2) {
return Bin1.Value > Bin2.Value;
}
bool operator==(const TBin& Bin1, const TBin& Bin2) {
return Bin1.Value == Bin2.Value;
}
bool operator!=(const TBin& Bin1, const TBin& Bin2) {
return !(Bin1 == Bin2);
}
double TBin::Entropy() const {
return TMisc::Entropy(PartitionV, Count);
}
///////////////////////////////
// Histogram
// Per-class distribution for examples with attribute
// NOTE: This function must ensure the Example->BinId is set to the maximum ID of the bins containing the example
void THist::IncCls(PExample Example, const int& AttrIdx, PIdGen IdGen) {
int Idx = 0, BinN = 0;
double CurrDist = 0.0, PrevDist = 0.0;
const double Val = Example->AttributesV.GetVal(AttrIdx).Num;
const int Label = Example->Label;
// Add new bin, initialized with Val, if the number of bins didn't reach the treshold
if ((Idx = BinsV.SearchBin(Val)) == -1 && BinsV.Len() < BinsN) {
const int CrrBinId = IdGen->GetNextBinId();
const int CrrIdx = BinsV.AddSorted(TBin(Val, CrrBinId), true);
BinsV.GetVal(CrrIdx).Inc(Label);
Example->SetBinId(TMath::Mx<int>(Example->BinId, CrrBinId));
} else { // Find the closest bin
if (Idx != -1) { // Bin initialized with this very value
BinsV.GetVal(Idx).Inc(Label);
Example->SetBinId(TMath::Mx<int>(Example->BinId, BinsV.GetVal(Idx).Id));
} else { // Otherwise, increment the closest bin
Idx = 0;
PrevDist = CurrDist = abs(Val - BinsV.GetVal(0).GetVal());
// NOTE: We could use binary search because of the ordering invariant; but the number of bins rarely exeecds 100 (hardcoded constant)
// While distance starts increasing, stop --- our bin is the one before the current one
for (BinN = 1; BinN < BinsV.Len(); ++BinN) {
PrevDist = CurrDist;
if ((CurrDist = abs(Val - BinsV.GetVal(BinN).GetVal())) > PrevDist) {
Idx = BinN-1; break;
}
}
if (BinN == BinsV.Len()) { Idx = BinN-1; }
BinsV.GetVal(Idx).Inc(Label);
Example->SetBinId(TMath::Mx<int>(Example->BinId, BinsV.GetVal(Idx).Id));
}
}
}
// NOTE: This function must ensure the example is removed from the bins that existed at the time of its arrival
void THist::DecCls(PExample Example, const int& AttrIdx) {
int Idx = 0, BinN = 0, PrevIdx = 0;
double CurrDist = 0.0, PrevDist = 0.0;
const double Val = Example->AttributesV.GetVal(AttrIdx).Num;
const int Label = Example->Label;
// Idx = BinsV.SearchBin(Val); // Binary search for Val
if ((Idx = BinsV.SearchBin(Val)) == -1 && BinsV.Len() < BinsN) {
printf("Searching for value: %f\n", Val);
Print();
FailR("By construction, the value cannot be missing."); // NOTE: For deubgging purposes
} else { // Find the closest bin
if (Idx != -1 && BinsV.GetVal(Idx).Id <= Example->BinId) { // Bin initialized with this very value
BinsV.GetVal(Idx).Dec(Label);
} else { // Otherwise, decrement the closest bin that WAS NOT created after the example was accumulated
Idx = 0;
// NOTE: We can't take the first bin as it may have been created AFTER the example was accumulated; instead we find the first suitable bin
for (BinN = 0; BinN < BinsV.Len() && BinsV.GetVal(BinN).Id > Example->BinId; ++BinN);
AssertR(BinN < BinsV.Len(), "No suitable bin --- impossible."); // NOTE: For debugging purposes
PrevIdx = Idx = BinN; // First suitable bin
PrevDist = CurrDist = abs(Val - BinsV.GetVal(BinN).GetVal());
// The order is preserved even though new bins might have been created between the old ones
for (; BinN < BinsV.Len(); ++BinN) {
if (BinsV.GetVal(BinN).Id <= Example->BinId) {
PrevDist = CurrDist;
if ((CurrDist = abs(Val - BinsV.GetVal(BinN).GetVal())) > PrevDist) {
Idx = PrevIdx; break;
} else { PrevIdx = BinN; }
}
}
if (BinN == BinsV.Len() && Idx != PrevIdx) { Idx = PrevIdx; }
BinsV.GetVal(Idx).Dec(Label);
}
}
}
void THist::IncReg(const PExample Example, const int& AttrIdx) {
int Idx = 0, BinN = 0;
double CurrDist = 0.0, PrevDist = 0.0;
const double Val = Example->AttributesV.GetVal(AttrIdx).Num; // Numeric attribute value
const double RegValue = Example->Value; // Value of the target variable
if (BinsV.Len() < BinsN && (Idx = BinsV.SearchForw(Val, 0)) == -1) { // BinsV.SearchBin(Val)) == -1) {
const int TmpIdx = BinsV.AddSorted(TBin(Val), true);
BinsV.GetVal(TmpIdx).Inc(RegValue);
} else { // Find the closest bin
if (Idx != -1) { // Bin initialized with this very value
BinsV.GetVal(Idx).Inc(RegValue);
} else { // Otherwise, increment the closest bin
Idx = 0;
CurrDist = PrevDist = abs(Val - BinsV.GetVal(0).GetVal());
for (BinN = 1; BinN < BinsV.Len(); ++BinN) {
PrevDist = CurrDist;
// We are fine, because bins are ordered inside the vector by the initialization values
if ((CurrDist = abs(Val - BinsV.GetVal(BinN).GetVal())) > PrevDist) {
Idx = BinN - 1;
break;
}
}
if(BinN == BinsV.Len()) { Idx = BinN-1; }
BinsV.GetVal(Idx).Inc(RegValue);
}
}
}
// Find best split
double THist::InfoGain(double& SplitVal) const {
int HiCount = 0, LoCount = 0, CurrCount = 0, MxIdx = 0;
double Val = 0.0, MxGain = 0.0, CurrGain = 0.0;
double LoImp = 0.0, HiImp = 0.0;
TIntV LoV, HiV;
double* GArr = new double[sizeof(double)*BinsV.Len()]();
int* NArr = new int[sizeof(int)*BinsV.Len()]();
// Compute initial split
LoCount = 0; // BinsV.GetVal(0).Count;
// LoV = BinsV.GetVal(0).PartitionV;
HiCount = 0;
for (int BinN = 0; BinN < BinsV.Len(); ++BinN) {
TIntV TmpV = BinsV.GetVal(BinN).PartitionV;
TMisc::AddVec(1, TmpV, HiV); // HiV = HiV+TmpV
HiCount += BinsV.GetVal(BinN).Count;
GArr[BinN] = TMisc::Entropy(HiV, HiCount); // h_i := H(B_1\cup B_2\cup \ldots\cup B_i)
NArr[BinN] = HiCount; // n_i := |B_1|+\ldots+|B_i|
}
const int AllN = HiCount;
const double H = TMisc::Entropy(HiV, AllN);
// printf("H = %f\n", H);
// Now find the best split
CurrGain = MxGain = 0.0;
MxIdx = 0;
for (int BinN = BinsV.Len()-2; BinN >= 0; --BinN) {
CurrCount = BinsV.GetVal(BinN+1).Count;
Val = BinsV.GetVal(BinN+1).Value;
LoCount += CurrCount;
HiCount = NArr[BinN];
HiImp = GArr[BinN];
TIntV TmpV = BinsV.GetVal(BinN+1).PartitionV;
TMisc::AddVec(1, TmpV, LoV);
LoImp = TMisc::Entropy(LoV, LoCount);
if ((CurrGain = H - LoCount*LoImp/AllN - HiCount*HiImp/AllN) > MxGain) {
MxGain = CurrGain;
MxIdx = BinN;
}
}
delete GArr;
delete NArr;
if (MxIdx > 0) {
SplitVal = BinsV.GetVal(MxIdx).GetVal();
return MxGain;
} else {
return 0;
}
}
double THist::GiniGain(double& SpltVal) const {
EFailR("Implementation in progress.");
return 0.0;
}
// See [Knuth, 1997] and [Chan et al., 1979] for details regarding updating formulas for variance
// (Wikipedia link: http://en.wikipedia.org/wiki/Algorithms_for_calculating_variance, accessed on 7 Jun 2013)
double THist::StdGain(double& SpltVal) const { // for regression
int HiCnt, LoCnt, CrrCnt;
int MxIdx;
double MxGain, CrrGain;
double LoS, HiS, LoT, HiT;
double* SArr = new double[BinsN](); // Define VarArr[i] := n*Var(B_1\cup B_2\cup ...\cup B_i)
double* TArr = new double[BinsN](); // Define AvgArr[i] := x_1+x_2+...+x_i
// Compute initial split
LoCnt = HiCnt = 0; // BinsV.GetVal(0).Count;
SArr[0] = TArr[0] = 0;
for (int BinN = 0; BinN < BinsV.Len(); ++BinN) {
const TBin CrrBin = BinsV.GetVal(BinN);
const double PrevS = BinN > 0 ? SArr[BinN-1] : 0;
const double PrevT = BinN > 0 ? TArr[BinN-1] : 0;
TArr[BinN] = PrevT + CrrBin.T;
CrrCnt = BinsV.GetVal(BinN).Count;
SArr[BinN] = PrevS+CrrBin.S;
if (CrrCnt > 0 && HiCnt > 0) {
SArr[BinN] += TMath::Sqr(CrrCnt*PrevT/HiCnt-CrrBin.T)*HiCnt/(CrrCnt*(CrrCnt+HiCnt));
}
HiCnt += CrrCnt;
}
const int AllN = HiCnt;
const double S = SArr[BinsV.Len()-1];
// printf("AllN = %d; S = %f\n", AllN, S);
HiS = CrrGain = MxGain = 0.0;
MxIdx = 0;
LoS = BinsV.Last().S;
LoT = BinsV.Last().T;
LoCnt = BinsV.Last().Count;
HiCnt -= LoCnt;
// Compute expected variance reduction, as defined by [Ikonomovska, 2012] and [Ikonomovska et al., 2011]
for (int BinN = BinsV.Len()-2; BinN >= 0; --BinN) {
HiS = SArr[BinN];
HiT = TArr[BinN];
const double SigmaS = TMath::Sqrt(S/(AllN));
const double SigmaS1 = TMath::Sqrt(LoS/(LoCnt));
const double SigmaS2 = TMath::Sqrt(HiS/(HiCnt));
// printf("S = %f ;; S1 = %f ;; S2 = %f\n", SigmaS, LoCnt*SigmaS1/AllN, HiCnt*SigmaS2/AllN);
if ((CrrGain = SigmaS - LoCnt*SigmaS1/AllN - HiCnt*SigmaS2/AllN) > MxGain) {
MxGain = CrrGain;
MxIdx = BinN;
}
// printf("CurrGain = %f\n", CrrGain); getchar();
// Update variance
const double CrrS = BinsV.GetVal(BinN).S; // S_2
const double CrrT = BinsV.GetVal(BinN).T;
CrrCnt = BinsV.GetVal(BinN).Count; // n
LoS += CrrS;
if (LoCnt > 0 && CrrCnt > 0) {
LoS += TMath::Sqr(CrrCnt*LoT/LoCnt-CrrT)*LoCnt/(CrrCnt*(CrrCnt+LoCnt));
}
LoT += BinsV.GetVal(BinN).T;
LoCnt += CrrCnt;
HiCnt -= CrrCnt;
}
delete [] TArr;
delete [] SArr;
if (MxIdx > 0) {
SpltVal = BinsV.GetVal(MxIdx).GetVal();
// printf("MxGain = %f\n", MxGain);
return MxGain;
} else {
return 0;
}
}
void THist::Print() const {
for (auto It = BinsV.BegI(); It != BinsV.EndI(); ++It) {
printf("%f (%d)\t", It->GetVal(), It->Count);
}
putchar('\n');
}
///////////////////////////////
// Attribute
///////////////////////////////
// Attribute-Managment
TAttrMan::TAttrMan(const THash<TStr, TInt>& AttrH_, const THash<TInt, TStr>& InvAttrH_,
const int& Id_, const TStr& Nm_, const TAttrType& Type_)
: AttrH(AttrH_), InvAttrH(InvAttrH_), Id(Id_), Nm(Nm_), Type(Type_) {
AttrH.GetDatV(ValueV); // Possible values; there is a single value for numeric attributes
}
///////////////////////////////
// Example
TExample& TExample::operator=(const TExample& Example) {
if(*this != Example) {
AttributesV = Example.AttributesV; BinId = Example.BinId;
Label = Example.Label; LeafId = Example.LeafId; Value = Example.Value;
}
return *this;
}
/////////////////////////////////
// Node
// Copy constructor
TNode::TNode(const TNode& Node)
: CndAttrIdx(Node.CndAttrIdx), ExamplesN(Node.ExamplesN), UsedAttrs(Node.UsedAttrs),
Avg(Node.Avg), VarSum(Node.VarSum), Err(Node.Err), TestModeN(Node.TestModeN), Id(Node.Id),
Correct(Node.Correct), All(Node.All), PartitionV(Node.PartitionV), HistH(Node.HistH),
Type(Node.Type), Val(Node.Val), ExamplesV(Node.ExamplesV) { }
// Assignment operator
TNode& TNode::operator=(const TNode& Node) {
if (*this != Node) {
//Clr(); // Delete old elements
All = Node.All; AltTreesV = Node.AltTreesV;
Avg = Node.Avg; ChildrenV = Node.ChildrenV;
CndAttrIdx = Node.CndAttrIdx; Correct = Node.Correct;
Counts = Node.Counts; Err = Node.Err; ExamplesN = Node.ExamplesN;
ExamplesV = Node.ExamplesV; HistH = Node.HistH; Id = Node.Id;
PartitionV = Node.PartitionV;
#ifdef GLIB_OK
SeenH = Node.SeenH;
#else
seen_h = Node.seen_h;
#endif
TestModeN = Node.TestModeN; Type = Node.Type;
Val = Node.Val; VarSum = Node.VarSum;
}
return *this;
}
bool TNode::operator==(const TNode& Node) const {
return CndAttrIdx == Node.CndAttrIdx && Type == Node.Type && ExamplesV == Node.ExamplesV &&
Counts == Node.Counts && PartitionV == Node.PartitionV && Id == Node.Id &&
ChildrenV == Node.ChildrenV && UsedAttrs == Node.UsedAttrs;
}
// Training set entropy
double TNode::ComputeEntropy() const {
return TMisc::Entropy(PartitionV, ExamplesN);
}
double TNode::ComputeGini() const {
double g = 1.0, p = 0.0;
for(auto It = PartitionV.BegI(); It != PartitionV.EndI(); It++) {
p = 1.0*(*It)/ExamplesN;
g -= p*p;
}
return g;
}
// Compute inforation gain from sufficient statistics
double TNode::InfoGain(const int& AttrIndex, const TAttrManV& AttrManV) const {
double h = 0, hj = 0, p = 0, pj = 0;
int SubExamplesN = 0; // Number of examples x with A(x)=a_j for j=1,2,...,ValsN
const int LabelsN = AttrManV.GetVal(AttrManV.Len()-1).ValueV.Len();
TAttrMan AttrMan(AttrManV.GetVal(AttrIndex));
const int ValsN = AttrMan.ValueV.Len();
// Compute entropy H(E)
h = TMisc::Entropy(PartitionV, ExamplesN);
// Compute information gain
for (int j = 0; j < ValsN; ++j) {
SubExamplesN = 0;
// Compute |E_j|
for (int i = 0; i < LabelsN; ++i) {
TTriple<TInt, TInt, TInt> TmpTriple(AttrIndex, j, i);
if(Counts.IsKey(TmpTriple)) {
SubExamplesN += Counts.GetDat(TmpTriple);
}
}
hj = 0;
// Compute H(E_j)
for (int i = 0; i < LabelsN; ++i) {
TTriple<TInt, TInt, TInt> TmpTriple(AttrIndex, j, i);
if (Counts.IsKey(TmpTriple)) {
pj = SubExamplesN > 0 ? 1.0*Counts.GetDat(TmpTriple)/SubExamplesN : 0; // Prevent divison by zero
if (pj > 0) { // Ensure Log2(pj) exists
hj -= pj*TMath::Log2(pj);
}
}
}
p = ExamplesN > 0 ? 1.0*SubExamplesN/ExamplesN : 0;
h -= p*hj;
}
// Return information gain G(A)
return h;
}
// Compute Gini index from sufficient statistics
double TNode::GiniGain(const int& AttrIndex, const TVec<TAttrMan>& AttrManV) const {
double g = 1.0, gj = 0.0, p = 0, pj = 0;
int SubExamplesN = 0; // Number of examples x with A(x)=a_j for j=1,2,...,ValsN
const int LabelsN = AttrManV.GetVal(AttrManV.Len()-1).ValueV.Len();
TAttrMan AttrMan(AttrManV.GetVal(AttrIndex));
const int ValsN = AttrMan.ValueV.Len();
for (auto It = PartitionV.BegI(); It != PartitionV.EndI(); ++It) {
p = ExamplesN > 0 ? 1.0*(*It)/ExamplesN : 0; // Prevent division by zero
g -= p*p;
}
for (int j = 0; j < ValsN; ++j) {
SubExamplesN = 0;
// Compute |E_j|
for (int i = 0; i < LabelsN; ++i) {
TTriple<TInt, TInt, TInt> TmpTriple(AttrIndex, j, i);
if (Counts.IsKey(TmpTriple)) {
SubExamplesN += Counts.GetDat(TmpTriple);
}
}
gj = 1.0;
for (int i = 0; i < LabelsN; ++i) {
TTriple<TInt, TInt, TInt> TmpTriple(AttrIndex, j, i);
if (Counts.IsKey(TmpTriple)) {
pj = SubExamplesN > 0 ? 1.0*Counts.GetDat(TmpTriple)/SubExamplesN : 0; // Prevent divison by zero
gj -= pj*pj;
}
}
p = ExamplesN > 0 ? 1.0*SubExamplesN/ExamplesN : 0;
g -= p*gj;
}
// Return information gain GiniGain(A)
return g;
}
double TNode::StdGain(const int& AttrIdx, const TAttrManV& AttrManV) const {
// NOTE: Compute variances Var(S_i) for all possible values attribute A_i can take
const TAttrType AttrType = AttrManV.GetVal(AttrIdx).Type;
EAssertR(AttrType == TAttrType::DISCRETE, "This function works with nominal attributes.");
const int ValsN = AttrManV.GetVal(AttrIdx).ValueV.Len();
TVec<TTriple<TFlt, TFlt, TInt> > VarV; // Vector of (mean, variance, n) pairs
// TODO: Avoid iterating over the vector twice --- is there a faster way to initialize the thing?
for (int ValN = 0; ValN < ValsN; ++ValN) {
VarV.Add(TTriple<TFlt, TFlt, TInt>(0.0, 0.0, 0));
}
// Incrementally compute variances
for (int ValN = 0; ValN < ExamplesV.Len(); ++ValN) {
const int CrrIdx = ExamplesV.GetVal(ValN)->AttributesV.GetVal(AttrIdx).Value;
const double CrrVal = ExamplesV.GetVal(ValN)->Value;
TTriple<TFlt, TFlt, TInt>& CrrTriple = VarV.GetVal(CrrIdx);
// See [Knuth, 1997] for details regarding incremental algorithms for variance
const int N = CrrTriple.Val3++;
const double Delta = CrrVal - CrrTriple.Val1;
CrrTriple.Val1 += Delta/N;
CrrTriple.Val2 += Delta*(CrrVal - CrrTriple.Val1);
}
double CrrStd = Std();
for (int ValN = 0; ValN < ValsN; ++ValN) {
const int CrrN = VarV.GetVal(ValN).Val3;
if (CrrN > 0) {
const double TmpStd = TMath::Sqrt(VarV.GetVal(ValN).Val2/CrrN);
CrrStd -= CrrN*TmpStd/ExamplesN;
}
}
return CrrStd;
}
TBstAttr TNode::BestAttr(const TAttrManV& AttrManV, const TTaskType& TaskType) {
if (TaskType == TTaskType::CLASSIFICATION) {
return BestClsAttr(AttrManV);
} else {
return BestRegAttr(AttrManV);
}
}
TBstAttr TNode::BestRegAttr(const TAttrManV& AttrManV) { // Regression
const int AttrsN = AttrManV.Len()-1; // AttrsManV includes attribute manager for the label
double CrrSdr, Mx1, Mx2;
int Idx1, Idx2;
CrrSdr = Mx1 = Mx2 = 0;
Idx1 = Idx2 = 0;
for (int AttrN = 0; AttrN < AttrsN; ++AttrN) {
const TAttrType AttrType = AttrManV.GetVal(AttrN).Type;
if (AttrType == TAttrType::DISCRETE) { // Discrete
if (UsedAttrs.SearchForw(AttrN, 0) < 0) {
// Compute standard deviation reduction
CrrSdr = StdGain(AttrN, AttrManV);
}
} else { // Continuous
CrrSdr = HistH.GetDat(AttrN).StdGain(Val);
// printf("SplitVal = %f\n", CrrSdr);
}
if (CrrSdr > Mx1) {
Idx2 = Idx1; Idx1 = AttrN; Mx2 = Mx1; Mx1 = CrrSdr;
} else if (CrrSdr >= Mx2) {
Idx2 = AttrN; Mx2 = CrrSdr;
}
}
const double Ratio = Mx2/Mx1;
return TBstAttr(TPair<TInt, TFlt>(Idx1, Mx1), TPair<TInt, TFlt>(Idx2, Mx2), Ratio);
}
TBstAttr TNode::BestClsAttr(const TAttrManV& AttrManV, const TIntV& BannedAttrV) { // Classification
int Idx1, Idx2;
double Mx1, Mx2, Crr, SplitVal;
const int AttrsN = AttrManV.Len()-1;
Crr = Mx1 = Mx2 = 0;
Idx1 = Idx2 = -1;
for (int AttrN = 0; AttrN < AttrsN; ++AttrN) {
// NOTE: BannedAttrV almost never contains more than two indices
if (BannedAttrV.IsIn(AttrN)) { continue; }
if (AttrManV.GetVal(AttrN).Type == TAttrType::DISCRETE) {
if (UsedAttrs.SearchForw(AttrN, 0) < 0) {
Crr = InfoGain(AttrN, AttrManV);
}
} else { // Numeric attribute
Crr = HistH.GetDat(AttrN).InfoGain(SplitVal);
// HistH.GetDat(AttrN).Print();
// getchar();
Val = SplitVal;
}
if (Crr > Mx1) {
Idx2 = Idx1; Idx1 = AttrN; Mx2 = Mx1; Mx1 = Crr;
} else if (Crr > Mx2) {
Idx2 = AttrN; Mx2 = Crr;
}
}
const double Diff = Mx1 - Mx2;
return TBstAttr(TPair<TInt, TFlt>(Idx1, Mx1), TPair<TInt, TFlt>(Idx2, Mx2), Diff);
}
// See [Domingos and Hulten, 2000] and [Hulten et al., 2001] for explanation
double TNode::ComputeTreshold(const double& Delta, const int& LabelsN) const {
const double R = TMath::Log2(LabelsN); // Range of the random variable for information gain
// EAssertR(!ExamplesN > 0, "This node has no examples.\n");
return TMath::Sqrt(R*R*TMath::Log(1.0/Delta)/(2.0*ExamplesN)); // t = \sqrt{ \frac{R^2 * log(1/delta)}{2n} }
}
void TNode::Split(const int& AttrIdx, const TAttrManV& AttrManV, PIdGen IdGen) {
// (i) Mark attribute, if discrete, as used
// New child for each value of AttrIdx attribute
CndAttrIdx = AttrIdx;
const TAttrType AttrType = AttrManV.GetVal(AttrIdx).Type;
int ValsN = AttrManV.GetVal(AttrIdx).ValueV.Len();
if (AttrType == TAttrType::DISCRETE) { // Categorial attributes can only be used once
UsedAttrs.Add(AttrIdx);
} else {
ValsN = 2;
printf("[DEBUG] Splitting on continuous value %f\n", Val);
}
// UsedAttrs.Add(CondAttrIndex);
const int LabelsN = AttrManV.GetVal(AttrManV.Len()-1).ValueV.Len();
for (int ValN = 0; ValN < ValsN; ++ValN) {
ChildrenV.Add(TNode::New(LabelsN, UsedAttrs, AttrManV, IdGen->GetNextLeafId())); // Leaf node
}
if(Type != TNodeType::ROOT) { Type = TNodeType::INTERNAL; }
}
void TNode::Clr() { // Forget training examples
ExamplesV.Clr(); PartitionV.Clr(); Counts.Clr();
HistH.Clr(true); AltTreesV.Clr(); UsedAttrs.Clr();
#ifdef GLIB_OK
SeenH.Clr(true);
#endif
}
// See page 232 of Knuth's TAOCP, Vol. 2: Seminumeric Algorithms [Knuth, 1997] for details
void TNode::UpdateStats(PExample Example) {
++ExamplesN;
const double CrrValue = Example->Value;
const double Delta = CrrValue - Avg;
Avg += Delta/ExamplesN;
VarSum += Delta*(CrrValue - Avg);
// Variance := VarSum/(ExamplesN - 1)
}
void TNode::UpdateErr(const double& Loss, const double& Alpha) {
Err = Loss+Alpha*Err;
if (++TestModeN > 500) { TestModeN = 0; }
}
void TNode::Init(const TAttrManV& AttrManV) {
for (int AttrN = 0; AttrN < AttrManV.Len(); ++AttrN) {
if (AttrManV.GetVal(AttrN).Type == TAttrType::CONTINUOUS) {
// const int LabelsN = AttrManV.GetVal(AttrN).ValueV.Last();
HistH.AddDat(AttrN, THist());
}
}
}
/////////////////////////////////
// Hoeffding-Tree
double THoeffdingTree::Predict(PExample Example) const { // Regression
PNode CrrNode = Root;
while (CrrNode->CndAttrIdx != -1) {
const TAttrType AttrType = AttrManV.GetVal(CrrNode->CndAttrIdx).Type;
if (AttrType == TAttrType::DISCRETE) {
CrrNode = CrrNode->ChildrenV.GetVal(Example->AttributesV.GetVal(CrrNode->CndAttrIdx).Value);
} else { // Numeric attribute
const double Val = Example->AttributesV.GetVal(CrrNode->CndAttrIdx).Num;
const int Idx = Val <= CrrNode->Val;
CrrNode = CrrNode->ChildrenV.GetVal(Idx);
}
}
// Ikonomovska [Ikonomovska, 2012] trains perceptron in the leaves
return CrrNode->Avg;
}
TLabel THoeffdingTree::Classify(PNode Node, PExample Example) const {
PNode CrrNode = Node;
while (!IsLeaf(CrrNode)) { CrrNode = GetNextNodeCls(CrrNode, Example); }
return Majority(CrrNode);
}
TLabel THoeffdingTree::Classify(PExample Example) const { // Classification
PNode CrrNode = Root;
while (!IsLeaf(CrrNode)) { CrrNode = GetNextNodeCls(CrrNode, Example); }
// return Majority(CrrNode);
return NaiveBayes(CrrNode, Example);
}
void THoeffdingTree::IncCounts(PNode Node, PExample Example) const {
Node->PartitionV.GetVal(Example->Label)++;
Node->ExamplesN++;
int AttrN = 0;
for (auto It = Example->AttributesV.BegI(); It != Example->AttributesV.EndI(); ++It) {
switch (AttrManV.GetVal(It->Id).Type) {
case TAttrType::DISCRETE: {
TTriple<TInt, TInt, TInt> Idx(It->Id, It->Value, Example->Label);
if (Node->Counts.IsKey(Idx)) {
Node->Counts.GetDat(Idx)++;
} else {
Node->Counts.AddDat(Idx, 1);
}
break; }
case TAttrType::CONTINUOUS:
Node->HistH.GetDat(AttrN).IncCls(Example, AttrN, IdGen);
break;
default:
EFailR("Attribute type not supported.");
}
++AttrN;
}
}
void THoeffdingTree::DecCounts(PNode Node, PExample Example) const {
AssertR(Node->PartitionV.GetVal(Example->Label)-- >= 0, "Negative partition count.");
AssertR(--Node->ExamplesN >= 0, "Negative example count.");
int AttrN = 0;
for (auto It = Example->AttributesV.BegI(); It != Example->AttributesV.EndI(); ++It) {
switch (AttrManV.GetVal(It->Id).Type) {
case TAttrType::DISCRETE: {
TTriple<TInt, TInt, TInt> Idx(It->Id, It->Value, Example->Label);
if (Node->Counts.IsKey(Idx)) {
AssertR(Node->Counts.GetDat(Idx)-- >= 0, "Negative id-value-label triple count.");
} else {
Print(Example);
printf("Example ID: %d; Node ID: %d; Node examples: %d\n", Example->LeafId, Node->Id, Node->ExamplesN);
if(!IsLeaf(Node)) { printf("Node test attribute: %s\n", AttrManV.GetVal(Node->CndAttrIdx).Nm.CStr()); }
printf("Problematic attribute: %s = %s\n", AttrManV.GetVal(It->Id).Nm.CStr(), AttrManV.GetVal(It->Id).InvAttrH.GetDat(It->Value).CStr());
FailR("Corresponding id-value-label triple is missing in counts hashtable."); // NOTE: For dbugging purposes; this fail probably indicates serious problems
}
break; }
case TAttrType::CONTINUOUS:
Node->HistH.GetDat(AttrN).DecCls(Example, AttrN);
break;
default:
FailR("Attribute type not supported.");
}
++AttrN;
}
}
bool THoeffdingTree::IsAltSplitIdx(PNode Node, const int& AttrIdx) const {
for (auto It = Node->AltTreesV.BegI(); It != Node->AltTreesV.EndI(); ++It) {
if ((*It)->CndAttrIdx == AttrIdx) { // || IsAltSplitIdx((*It)->Root, AttrIdx)) {
return true;
}
}
return false;
}
void THoeffdingTree::CheckSplitValidityCls() { // Classification
PNode CrrNode = Root;
TSStack<PNode> NodeS;
const int AttrsN = AttrManV.Len()-1; // Need -1 because AttrManV also manages class labels
NodeS.Push(CrrNode);
// Depth-first tree traversal
while (!NodeS.Empty()) {
CrrNode = NodeS.Top(); NodeS.Pop();
// Check split validity in the alternate trees
for (auto It = CrrNode->AltTreesV.BegI(); It != CrrNode->AltTreesV.EndI(); ++It) {
if (!IsLeaf(*It)) { NodeS.Push(*It); }
}
// Push non-leaf children on the stack
for (auto It = CrrNode->ChildrenV.BegI(); It != CrrNode->ChildrenV.EndI(); ++It) {
if (!IsLeaf(*It)) { NodeS.Push(*It); }
}
// Find the best two attributes among the remaining attributes --- must not use CrrSplitAttrIdx
const int CrrSpltAttrIdx = CrrNode->CndAttrIdx;
TVec<TInt> CrrBannedAttrV; CrrBannedAttrV.Add(CrrSpltAttrIdx);
TBstAttr SpltAttr = CrrNode->BestClsAttr(AttrManV, CrrBannedAttrV);
CrrBannedAttrV.Clr(); CrrBannedAttrV.Add(SpltAttr.Val1.Val1);
TBstAttr AltAttr = CrrNode->BestClsAttr(AttrManV, CrrBannedAttrV);
const double EstG = SpltAttr.Val1.Val2 - AltAttr.Val1.Val2;
// Does it make sense to split on this one?
if (EstG >= 0 && SpltAttr.Val1.Val1 != -1 && SpltAttr.Val2.Val1 != -1 && !IsAltSplitIdx(CrrNode, SpltAttr.Val1.Val1)) {
// Hoeffding test
const double Eps = CrrNode->ComputeTreshold(SplitConfidence, AttrManV.GetVal(AttrsN).ValueV.Len());
if (EstG > Eps || (Eps < TieBreaking && EstG >= TieBreaking/2)) { // EstG >= TieBreaking/2 ?
// Grow alternate tree
Print('-');
printf("Starting alternate tree for node splitting on `%s' with `%s' at root ; tie = %d\n", AttrManV.GetVal(CrrNode->CndAttrIdx).Nm.CStr(), AttrManV.GetVal(SpltAttr.Val1.Val1).Nm.CStr(), EstG <= Eps);
// Export("exports/titanic-"+TInt(ExportN++).GetStr()+".gv", TExportType::DOT);
const int LabelsN = AttrManV.GetVal(AttrManV.Len()-1).ValueV.Len();
PNode AltHt = TNode::New(LabelsN, CrrNode->UsedAttrs, AttrManV, IdGen->GetNextLeafId());
AltHt->Split(SpltAttr.Val1.Val1, AttrManV, IdGen);
CrrNode->AltTreesV.Add(AltHt);
++AltTreesN;
}
}
}
}
void THoeffdingTree::ForgetCls(PExample Example) const { // Classification
PNode CrrNode = Root;
TSStack<PNode> NodeS;
NodeS.Push(CrrNode);
// EAssertR(!Sacrificed(CrrNode, Example), "Izgleda v redu.");
while (!NodeS.Empty()) {
CrrNode = NodeS.Top(); NodeS.Pop();
if (CrrNode->Id <= Example->LeafId && !Sacrificed(CrrNode, Example)) {
DecCounts(CrrNode, Example);
if (!IsLeaf(CrrNode)) {
NodeS.Push(GetNextNodeCls(CrrNode, Example));
for (auto It = CrrNode->AltTreesV.BegI(); It != CrrNode->AltTreesV.EndI(); ++It) {
if ((*It)->Id <= Example->LeafId) { NodeS.Push(*It); }
}
}
} else if (Sacrificed(CrrNode, Example)) { // Unmark
#ifdef GLIB_OK
CrrNode->SeenH.DelIfKey(*Example);
#else
CrrNode->seen_h.erase(*Example);
#endif
}
}
}
void THoeffdingTree::ProcessLeafReg(PNode Leaf, PExample Example) { // Regression
Leaf->UpdateStats(Example);
// Leaf->ExamplesV.Add(Example);
const int AttrsN = Example->AttributesV.Len();
for (int AttrN = 0; AttrN < AttrsN; AttrN++) {
if (AttrManV.GetVal(AttrN).Type == TAttrType::CONTINUOUS) {
// TODO: Find an efficient way to compute s(A) from s(A1) and s(A2) if A1 and A2 parition A
Leaf->HistH.GetDat(AttrN).IncReg(Example, AttrN);
// EFailR("Current regression discretization is deprecated.");
}
}
if (Leaf->ExamplesN % GracePeriod == 0 && Leaf->Std() > 0) { // Regression
// See if we can get variance reduction
TBstAttr SplitAttr = Leaf->BestAttr(AttrManV, TaskType);
// Pass 2, because TMath::Log2(2) = 1; since r lies in [0,1], we have R=1; see also PhD thesis [Ikonomovska, 2012] and [Ikonomovska et al., 2011]
const double Eps = Leaf->ComputeTreshold(SplitConfidence, 2);
const double EstG = SplitAttr.Val3;
printf("EstG = %f\n", EstG);
if ((EstG < 1.0-Eps /*|| Eps < TieBreaking*/) && Leaf->UsedAttrs.SearchForw(SplitAttr.Val1.Val1, 0) < 0) {
printf("[DEBUG] Selected split attribute: %d\n", SplitAttr.Val1.Val1);
Leaf->Split(SplitAttr.Val1.Val1, AttrManV, IdGen);
}
}
}
void THoeffdingTree::ProcessLeafCls(PNode Leaf, PExample Example) { // Classification
const int AttrsN = Example->AttributesV.Len();
IncCounts(Leaf, Example);
if (Leaf->ExamplesN % GracePeriod == 0 && Leaf->ComputeEntropy() > 0.65) {
TBstAttr SplitAttr = Leaf->BestAttr(AttrManV, TaskType);
const double EstG = SplitAttr.Val3;
const double Eps = Leaf->ComputeTreshold(SplitConfidence, AttrManV.GetVal(AttrsN).ValueV.Len());
if (SplitAttr.Val1.Val1 != -1 && (EstG > Eps || (EstG <= Eps && Eps < TieBreaking))) {
printf("[DEBUG] best = %d :: tie = %d\n", EstG > Eps, EstG <= Eps && Eps < TieBreaking);
printf("[DEBUG] t = %f :: n = %d\n", Eps, Leaf->ExamplesN);
printf("[DEBUG] Splitting at %d examples on attribute `%s' with confidence %f\n", Leaf->ExamplesN, AttrManV.GetVal(SplitAttr.Val1.Val1).Nm.CStr(), 1.0-SplitConfidence);
if (Leaf->UsedAttrs.Len() > 0) {
printf("[DEBUG] Previous attribute = %d; so far used %d attributes on this path.\n", Leaf->UsedAttrs.Last(), Leaf->UsedAttrs.LastValN()+1);
}
Leaf->Split(SplitAttr.Val1.Val1, AttrManV, IdGen);
}
}
}
void THoeffdingTree::ProcessCls(PExample Example) {
//////
//TStr FNm = ConceptDriftP ? "err-cvfdt.dat" : "err-vfdt.dat";
//Salpha = 0.995*Salpha+(Example->Label != Classify(Example));
//Nalpha = 0.995*Nalpha+1;
//if (Root->TestModeN == 9999) {
// PSOut FOut = TFOut::New(FNm, true);
// FOut->PutFlt(Salpha/Nalpha); FOut->PutLn();
//}
//////
PNode CrrNode = Root;
int MxId = 0;
if (ConceptDriftP) {
ExampleQ.Push(Example);
if (ExampleQ.Len() > WindowSize) { // INVARIANT: ExampleQ.Len() <= WindowSize+1
PExample LastExample = ExampleQ.Top();
ExampleQ.Pop(); // Delete it from the window
ForgetCls(LastExample); // Update sufficient statistics
}
TSStack<PNode> NodeS;
NodeS.Push(CrrNode);
while (!NodeS.Empty()) {
CrrNode = NodeS.Top(); NodeS.Pop();
if (IsLeaf(CrrNode)) { // Leaf node
MxId = TMath::Mx<int>(MxId, CrrNode->Id);
ProcessLeafCls(CrrNode, Example);
} else {
if (TestMode(CrrNode)) { // Don't update counts --- sacrifice the next 2000 or so examples for internal evaluation
SelfEval(CrrNode, Example);
} else { // Everything goes as usual
IncCounts(CrrNode, Example); // Update sufficient statistics
NodeS.Push(GetNextNodeCls(CrrNode, Example));
for (auto It = CrrNode->AltTreesV.BegI(); It != CrrNode->AltTreesV.EndI(); ++It) {
NodeS.Push(*It);
}
}
}
}
Example->SetLeafId(TMath::Mx<int>(MxId, Example->LeafId));
if (Root->HistH.Empty()) { Example->SetBinId(IdGen->GetNextBinId()); } /* Hack */
if (++DriftExamplesN >= DriftCheck) {
DriftExamplesN = 0;
CheckSplitValidityCls();
}
} else { // No concept drift detection
if (!TestMode(CrrNode)) {
while (!IsLeaf(CrrNode)) { CrrNode = GetNextNodeCls(CrrNode, Example); }
ProcessLeafCls(CrrNode, Example);
} else {
SelfEval(CrrNode, Example);
}
}
}
void THoeffdingTree::ProcessReg(PExample Example) {
PNode CrrNode = Root;
while (!IsLeaf(CrrNode)) { CrrNode = GetNextNodeCls(CrrNode, Example); }
ProcessLeafReg(CrrNode, Example);
}
void THoeffdingTree::SelfEval(PNode Node, PExample Example) const {
#ifdef GLIB_OK
Node->SeenH.AddDat(*Example, true);
#else
Node->seen_h[*Example] = true;
#endif
// Update classification error for alternate trees
for (auto It = Node->AltTreesV.BegI(); It != Node->AltTreesV.EndI(); ++It) {
PNode CrrNode = *It;
while (!IsLeaf(CrrNode)) { CrrNode = GetNextNodeCls(CrrNode, Example); }
(*It)->Correct += Example->Label == NaiveBayes(CrrNode, Example);
++(*It)->All;
}
// Update classfication error for the main subtree
PNode CrrNode = Node;
while (!IsLeaf(CrrNode)) { CrrNode = GetNextNodeCls(CrrNode, Example); }
Node->Correct += Example->Label == NaiveBayes(CrrNode, Example);
++Node->All;
}
bool THoeffdingTree::TestMode(PNode Node) {
if (Node->AltTreesV.Empty() && Node->Type != TNodeType::ROOT) { return false; }
if (Node->All == 2000) { // Swap with the best performing subtree
PNode BestAlt = Node;
const double Acc = 1.0*BestAlt->Correct/BestAlt->All; // Classification accuracy
for (auto It = Node->AltTreesV.BegI(); It != Node->AltTreesV.EndI(); ++It) {
if (1.0*(*It)->Correct/(*It)->All > 1.0*BestAlt->Correct/BestAlt->All) { BestAlt = *It; }
else { (*It)->All = (*It)->Correct = 0; } // Reset
}
if (BestAlt != Node) {
printf("[DEBUG] Swapping node with an alternate tree.\n");
// Export("exports/titanic-"+TInt(ExportN++).GetStr()+".gv", TExportType::DOT);
if(Node->Type == TNodeType::ROOT) { BestAlt->Type = TNodeType::ROOT; }
*Node = *BestAlt;
}
Node->All = Node->Correct = 0; // Reset
/*
if(Node->Type == TNodeType::ROOT) {
TStr FNm = ConceptDriftP ? "err-cvfdt.dat" : "err-vfdt.dat";
PSOut FOut = TFOut::New(FNm, true);
FOut->PutFlt(1.0-Acc); FOut->PutLn();
}
*/
return false;
} else if (Node->All == 0 && Node->TestModeN >= 10000) {
// printf("Entering test mode...\n");
Node->TestModeN = 0;
return true;
} else if (Node->All > 0) { return true; }
++Node->TestModeN;
return false;
}
PExample THoeffdingTree::Preprocess(const TStr& Line, const TCh& Delimiter) const {
TStrV LineV; TVec<TAttribute> AttributesV;
Line.SplitOnAllCh(Delimiter, LineV);
int ValN;
EAssertR(AttrsHashV.Len() == LineV.Len(), "Number of attributes in the dataset doesn't match the number of attributes in the configuration file.");
const int AttrsN = LineV.Len()-1;
for (int CountN = 0; CountN < AttrsN; ++CountN) {
// (1) Get appropriate hash table
// (2) Get appropriate raw value from input attribute vector
// (3) Map raw attribute value to TInt with hash table
switch (AttrManV.GetVal(CountN).Type) {
case TAttrType::DISCRETE:
if (LineV.GetVal(CountN) == "?") {
// EFailR("Missing values are not allowed.");
// printf("[WARNING] Missing value; assuming default.\n");
ValN = 0;
} else {
ValN = AttrsHashV.GetVal(CountN).GetDat(LineV.GetVal(CountN));
}
AttributesV.Add(TAttribute(CountN, ValN));
break;
case TAttrType::CONTINUOUS:
AttributesV.Add(TAttribute(CountN, LineV.GetVal(CountN).GetFlt()));
break;
default:
EFailR("Unsupported attribute type.");
}
}
if (TaskType == TTaskType::CLASSIFICATION) {
return TExample::New(AttributesV, AttrsHashV.GetVal(AttrsN).GetDat(LineV.GetVal(AttrsN)));
} else {
return TExample::New(AttributesV, LineV.Last().GetFlt());
}
}
PNode THoeffdingTree::GetNextNodeCls(PNode Node, PExample Example) const {
if (!IsLeaf(Node)) {
const TAttrType AttrType = AttrManV.GetVal(Node->CndAttrIdx).Type;
if (AttrType == TAttrType::DISCRETE) {
return Node->ChildrenV.GetVal(Example->AttributesV.GetVal(Node->CndAttrIdx).Value);
} else { // Numeric attribute
const double Num = Example->AttributesV.GetVal(Node->CndAttrIdx).Num;
const int Idx = Num <= Node->Val ? 0 : 1;
return Node->ChildrenV.GetVal(Idx);
}
}
return nullptr; // No children
}
void THoeffdingTree::Clr(PNode Node, PNode SubRoot) {
TSStack<PNode> NodeS;
for (auto It = Node->ChildrenV.BegI(); It != Node->ChildrenV.EndI(); ++It) {
NodeS.Push(*It);
}
for (auto It = Node->AltTreesV.BegI(); It != Node->AltTreesV.EndI(); ++It) {
if (*It != SubRoot) { NodeS.Push(*It); }
}
PNode CrrNode = nullptr;
while(!NodeS.Empty()) {
CrrNode = NodeS.Top(); NodeS.Pop();
for(auto It = CrrNode->ChildrenV.BegI(); It != CrrNode->ChildrenV.EndI(); ++It) {
NodeS.Push(*It);
}
for(auto It = CrrNode->AltTreesV.BegI(); It != CrrNode->AltTreesV.EndI(); ++It) {
NodeS.Push(*It);
}
CrrNode->Clr();
}
Node->Clr();
}
void THoeffdingTree::Export(const TStr& FileNm, const TExportType& ExportType) const {
printf("Writing the decision tree to `%s'.\n", FileNm.CStr());
TFOut FOut(FileNm);
switch (ExportType) {
case TExportType::XML:
FOut.PutStrLn("<?xml version=\"1.0\" encoding=\"ISO-8859-1\"?>");
FOut.PutStrFmtLn("<dt classes=%d>", LabelH.Len());
PrintXML(Root, 1, FOut);
FOut.PutStrFmtLn("</dt>");
break;
case TExportType::JSON:
EFailR("Not yet supported.");
case TExportType::DOT:
FOut.PutStrFmtLn("digraph dt_fig {"); // %s {", FileNm.GetFBase().CStr());
PrintDOT(Root, FOut);
FOut.PutStrLn("}");
break;
default:
EFailR("Uknown export format.");
}
FOut.Flush();
}
void THoeffdingTree::Init() {
AttrsHashV = Params.AttrsHV;
InvAttrsHashV = Params.InvAttrsHV;
LabelH = Params.DataFormatH;
InvLabelH = Params.InvDataFormatH;
// Create attribute manager object for each attribute
// NOTE: Label is also ``attribute-managed''
const int AttrsN = AttrsHashV.Len();
for (int CountN = 0; CountN < AttrsN; ++CountN) {
if (AttrsHashV.GetVal(CountN).Len() == 1) { // Continuous attributes have, in a sense, `single' value
AttrManV.Add(TAttrMan(AttrsHashV.GetVal(CountN), InvAttrsHashV.GetVal(CountN), CountN, InvLabelH.GetDat(CountN), TAttrType::CONTINUOUS));
} else {
AttrManV.Add(TAttrMan(AttrsHashV.GetVal(CountN), InvAttrsHashV.GetVal(CountN), CountN, InvLabelH.GetDat(CountN), TAttrType::DISCRETE));
}
}
const TAttrType PredType = AttrManV.Last().Type;
// EAssert(PredType == TAttrType::DISCRETE);
if (PredType == TAttrType::DISCRETE) {
TaskType = TTaskType::CLASSIFICATION;
} else {
TaskType = TTaskType::REGRESSION;
}
Root = TNode::New(LabelH.Len(), TVec<TInt>(), AttrManV, IdGen->GetNextLeafId(), TNodeType::ROOT); // Initialize the root node
}
// Pre-order depth-first tree traversal
void THoeffdingTree::PrintXML(PNode Node, const int& Depth, TFOut& FOut) const {
TStr Indent("");
for (int i = 0; i < Depth; ++i) { Indent += "\t"; }
if (!Node->ChildrenV.Len()) { // Leaf node
FOut.PutStr(Indent);
FOut.PutStrFmtLn("<leaf class=\"%s\"></leaf>", GetMajorityNm(Node).CStr());
return;
}
TStr ValNm;
const int ChildrenN = Node->ChildrenV.Len();
for (int ChildN = 0; ChildN < ChildrenN; ++ChildN) {
FOut.PutStr(Indent);
if (AttrManV.GetVal(Node->CndAttrIdx).Type == TAttrType::DISCRETE) {
ValNm = GetNodeValueNm(Node, ChildN);
} else {
ValNm = (ChildN ? ">" : "<=");
ValNm += TFlt::GetStr(Node->Val);
}
FOut.PutStrFmtLn("<node attribute=\"%s\" value=\"%s\">", GetNodeNm(Node).CStr(), ValNm.CStr());
PrintXML(Node->ChildrenV.GetVal(ChildN), Depth+1, FOut);
FOut.PutStr(Indent);