/// <summary>
/// pVal is the probability that we would observe as big an AUC diff as we
/// did if the ROC curves were drawn from the null hypothesis (which is that
/// one model does not perform better than the other)
///
/// think of it this way: we want a null distribution which says that there
/// is no difference between the ROCs. Since an AUC difference
/// cannot arise from any entries in the ordered lists that match up, we can
/// ignore these (though we could include them as well, but it would fall out
/// in the wash). So instead, we assume (know) that all the information in the
/// differences in AUCs is contained in the mismatched pairs, and we want to
/// destroy this info for the null, so we swap the values between the two
/// models. However, we want to keep the number of positive/negative samples
/// the same, so when we swap one pair, we must also swap another in the
/// other direction.
///
/// Note that in this method, we use a fast AUC computation which ignores ties.
/// This is fine for random experiemnts since the ties will fall out in the wash.
/// </summary>
/// <param name="roc1"></param>
/// <param name="roc2"></param>
/// <returns>pValue</returns>
public static double ROCswapPermTest(ROC roc1, ROC roc2, int numTrial, double maxFPR, ParallelOptions parallelOptions)
{
string randomStringSeed = "78923";//"123456";
Helper.CheckCondition(roc1._lowerScoreIsMoreLikelyClass1 == roc2._lowerScoreIsMoreLikelyClass1);
double realAUCdiff = Math.Abs(roc1._AUC - roc2._AUC);
DoubleArray permDiffs = new DoubleArray(1, numTrial);
//to make it the same as my matlab code, rename these:
DoubleArray orderedTargets1 = DoubleArray.From(roc1._classLabels);
DoubleArray orderedTargets2 = DoubleArray.From(roc2._classLabels);
//orderedTargets1.WriteToCSVNoDate("orderedTargets1");
//orderedTargets2.WriteToCSVNoDate("orderedTargets2");
if (orderedTargets1.Length == 0)
{
throw new Exception("empty ROCs given as input");
}
DoubleArray targetDiff = orderedTargets1 - orderedTargets2;
IntArray posDiffInd = targetDiff.Find(v => v > 0);
IntArray negDiffInd = targetDiff.Find(v => v < 0);
int numPos = posDiffInd.Length;
int numNeg = negDiffInd.Length;
//Helper.CheckCondition(Math.Abs(numPos - numNeg) <= 1, "don't think this should happen when non-truncated ROCs are used");
double pVal;
if (numPos == 0 || numNeg == 0)
{//ROCs are identical
pVal = 1;
return(pVal);
}
//bug checking:
int numPos1 = roc1._classLabels.ElementEQ(POS_LABEL).Sum();
int numNeg1 = roc1._classLabels.ElementEQ(NEG_LABEL).Sum();
int numPos2 = roc2._classLabels.ElementEQ(POS_LABEL).Sum();
int numNeg2 = roc2._classLabels.ElementEQ(NEG_LABEL).Sum();
//these won't be true if we're using a truncated ROC test
//Helper.CheckCondition(numPos1 == numPos2, "rocs must correspond to the same labelled data (i.e, # of 1/0 must be the same)");
//Helper.CheckCondition(numNeg1 == numNeg2, "rocs must correspond to the same labelled data (i.e, # of 1/0 must be the same)");
//for bug checking, keep track of avg number of swaps:
//DoubleArray numPairedSwaps = new DoubleArray(1, numTrial);
//DoubleArray auc1tmp= new DoubleArray(1, numTrial);
//DoubleArray auc2tmp = new DoubleArray(1, numTrial);
int numPairs = Math.Min(numPos, numNeg);
//for (int t = 0; t < numTrial; t++)
Parallel.For(0, numTrial, t =>
{
//Helper.CheckCondition((orderedTargets1 - orderedTargets2).Abs().Sum() != 0);
Random myRand = SpecialFunctions.GetRandFromSeedAndNullIndex(randomStringSeed, t + 1);
//randomly pair up each positive mismatch with each negative mismatch
IntArray posIndRand = posDiffInd.RandomPermutation(myRand);
IntArray negIndRand = negDiffInd.RandomPermutation(myRand);
//throw new NotImplementedException("Change to GetSlice()");
IntArray possiblePosPairs = posIndRand.GetColSlice(0, 1, numPairs - 1); //ColSlice(0, 1, numPairs - 1);
IntArray possibleNegPairs = negIndRand.GetColSlice(0, 1, numPairs - 1); //ColSlice(0, 1, numPairs - 1);
IntArray possiblePairs = ShoUtils.CatArrayCol(possiblePosPairs, possibleNegPairs).T;
//Helper.CheckCondition(possiblePairs.size1 == numPairs, "something went wrong");
//randomly pick each pair with prob=0.5 to include in the swap:
DoubleArray randVec = (new DoubleArray(1, numPairs)).FillRandUseSeed(myRand);
IntArray pairsOfPairsToBothSwapInd = randVec.Find(v => v >= 0.5);
List <int> listInd = pairsOfPairsToBothSwapInd.T.ToListOrEmpty();
//numPairedSwaps[t] = listInd.Count;
DoubleArray newTarg1 = DoubleArray.From(orderedTargets1);
DoubleArray newTarg2 = DoubleArray.From(orderedTargets2);
if (listInd.Count > 0)
{
//throw new NotImplementedException("Change to GetSlice()");
List <int> swapThesePairs = possiblePairs.GetRows(pairsOfPairsToBothSwapInd.T.ToList()).ToVector().ToList();
//swap the chosen pairs with a 1-x
//Helper.CheckCondition((newTarg1.GetColsE(swapThesePairs) - newTarg2.GetColsE(swapThesePairs)).Abs().Sum() == swapThesePairs.Count);
//throw new NotImplementedException("Change to SetSlice()");
newTarg1.SetCols(swapThesePairs, 1 - newTarg1.GetCols(swapThesePairs)); //.GetColsE(swapThesePairs));
newTarg2.SetCols(swapThesePairs, 1 - newTarg2.GetCols(swapThesePairs)); //GetColsE(swapThesePairs));
//newTarg1.WriteToCSVNoDate("newTarg1Swapped");
//newTarg2.WriteToCSVNoDate("newTarg2Swapped");
//Helper.CheckCondition(newTarg1.Sum() == orderedTargets1.Sum());
//Helper.CheckCondition((newTarg1 - newTarg2).Abs().Sum() == numPos + numNeg);
//Helper.CheckCondition((newTarg1 - newTarg2).Find(v => v != 0).Length == numPos + numNeg);
//Helper.CheckCondition((newTarg1 - orderedTargets1).Abs().Sum() == swapThesePairs.Count);
//Helper.CheckCondition((newTarg2 - orderedTargets2).Abs().Sum() == swapThesePairs.Count);
//Helper.CheckCondition((orderedTargets1 - orderedTargets2).Abs().Sum() != 0);
}
double AUC1, AUC2;
if (maxFPR == 1)
{
//do it the cheap way
AUC1 = ComputeAUCfromOrderedList(newTarg1);
AUC2 = ComputeAUCfromOrderedList(newTarg2);
}
else
{
//do it with manual integration, the more expensive way
AUC1 = new ROC(newTarg1, roc1._classProbs, roc1._lowerScoreIsMoreLikelyClass1, maxFPR, true)._AucAtMaxFpr;
AUC2 = new ROC(newTarg2, roc2._classProbs, roc2._lowerScoreIsMoreLikelyClass1, maxFPR, true)._AucAtMaxFpr;
}
//auc1tmp[t] = AUC1;
//auc2tmp[t] = AUC2;
//permDiffs[t] = Math.Abs(AUC1 - AUC2);
permDiffs[t] = (AUC1 - AUC2);
}
);
//double markerSize = 0.1;
//ShoUtils.MakePlotAndView(permDiffs, "permDiffs", false, markerSize, ".");
//ShoUtils.MakePlotAndView(numPairedSwaps, "numPairedSwaps", false, markerSize, "*");
permDiffs = permDiffs.Map(v => Math.Abs(v));
//debugging:
//permDiffs.WriteToCSVNoDate("permDiffs");
//numPairedSwaps.WriteToCSVNoDate("numPairedSwapsC#");
double pseudoCount = 1;
pVal = (pseudoCount + (double)(permDiffs >= realAUCdiff).Sum()) / (double)numTrial;
pVal = Math.Min(pVal, 1);
//ShoUtils.MakePlotAndView((auc1tmp-auc2tmp).Map(v=>Math.Abs(v)), "auc1-auc2", false, 0.2, ".");
//System.Console.WriteLine("Avg # swaps: " + numPairedSwaps.Mean() + " ( of " + numPairs + " total), numGreaterSwaps=" + (double)(permDiffs >= realAUCdiff).Sum() + ", p=" + pVal + ", realAUCdiff=" + String.Format("{0:0.00000}", realAUCdiff));
return(pVal);
}