/// <inheritdoc/>
protected override void TrainWithoutLock(IProgressChannelProvider progress, FloatLabelCursor.Factory cursorFactory, IRandom rand,
IdToIdxLookup idToIdx, int numThreads, DualsTableBase duals, Float[] biasReg, Float[] invariants, Float lambdaNInv,
VBuffer <Float>[] weights, Float[] biasUnreg, VBuffer <Float>[] l1IntermediateWeights, Float[] l1IntermediateBias, Float[] featureNormSquared)
{
Contracts.AssertValueOrNull(progress);
Contracts.Assert(_args.L1Threshold.HasValue);
Contracts.AssertValueOrNull(idToIdx);
Contracts.AssertValueOrNull(invariants);
Contracts.AssertValueOrNull(featureNormSquared);
int weightArraySize = WeightArraySize;
Contracts.Assert(weightArraySize == _numClasses);
Contracts.Assert(Utils.Size(weights) == weightArraySize);
Contracts.Assert(Utils.Size(biasReg) == weightArraySize);
Contracts.Assert(Utils.Size(biasUnreg) == weightArraySize);
int maxUpdateTrials = 2 * numThreads;
var l1Threshold = _args.L1Threshold.Value;
bool l1ThresholdZero = l1Threshold == 0;
var lr = _args.BiasLearningRate * _args.L2Const.Value;
var pch = progress != null?progress.StartProgressChannel("Dual update") : null;
using (pch)
using (var cursor = _args.Shuffle ? cursorFactory.Create(rand) : cursorFactory.Create())
{
long rowCount = 0;
if (pch != null)
{
pch.SetHeader(new ProgressHeader("examples"), e => e.SetProgress(0, rowCount));
}
Func <UInt128, long> getIndexFromId = GetIndexFromIdGetter(idToIdx);
while (cursor.MoveNext())
{
long idx = getIndexFromId(cursor.Id);
long dualIndexInitPos = idx * weightArraySize;
var features = cursor.Features;
var label = (int)cursor.Label;
Float invariant;
Float normSquared;
if (invariants != null)
{
invariant = invariants[idx];
Contracts.AssertValue(featureNormSquared);
normSquared = featureNormSquared[idx];
}
else
{
normSquared = VectorUtils.NormSquared(features);
if (_args.BiasLearningRate == 0)
{
normSquared += 1;
}
invariant = _loss.ComputeDualUpdateInvariant(2 * normSquared * lambdaNInv * GetInstanceWeight(cursor));
}
// The output for the label class using current weights and bias.
var labelOutput = WDot(ref features, ref weights[label], biasReg[label] + biasUnreg[label]);
var instanceWeight = GetInstanceWeight(cursor);
// This will be the new dual variable corresponding to the label class.
Float labelDual = 0;
// This will be used to update the weights and regularized bias corresponding to the label class.
Float labelPrimalUpdate = 0;
// This will be used to update the unregularized bias corresponding to the label class.
Float labelAdjustment = 0;
// Iterates through all classes.
for (int iClass = 0; iClass < _numClasses; iClass++)
{
// Skip the dual/weights/bias update for label class. Will be taken care of at the end.
if (iClass == label)
{
continue;
}
// Loop trials for compare-and-swap updates of duals.
// In general, concurrent update conflict to the same dual variable is rare
// if data is shuffled.
for (int numTrials = 0; numTrials < maxUpdateTrials; numTrials++)
{
long dualIndex = iClass + dualIndexInitPos;
var dual = duals[dualIndex];
var output = labelOutput + labelPrimalUpdate * normSquared - WDot(ref features, ref weights[iClass], biasReg[iClass] + biasUnreg[iClass]);
var dualUpdate = _loss.DualUpdate(output, 1, dual, invariant, numThreads);
// The successive over-relaxation apporach to adjust the sum of dual variables (biasReg) to zero.
// Reference to details: http://stat.rutgers.edu/home/tzhang/papers/ml02_dual.pdf, pp. 16-17.
var adjustment = l1ThresholdZero ? lr * biasReg[iClass] : lr * l1IntermediateBias[iClass];
dualUpdate -= adjustment;
bool success = false;
duals.ApplyAt(dualIndex, (long index, ref Float value) =>
{
success = Interlocked.CompareExchange(ref value, dual + dualUpdate, dual) == dual;
});
if (success)
{
// Note: dualConstraint[iClass] = lambdaNInv * (sum of duals[iClass])
var primalUpdate = dualUpdate * lambdaNInv * instanceWeight;
labelDual -= dual + dualUpdate;
labelPrimalUpdate += primalUpdate;
biasUnreg[iClass] += adjustment * lambdaNInv * instanceWeight;
labelAdjustment -= adjustment;
if (l1ThresholdZero)
{
VectorUtils.AddMult(ref features, weights[iClass].Values, -primalUpdate);
biasReg[iClass] -= primalUpdate;
}
else
{
//Iterative shrinkage-thresholding (aka. soft-thresholding)
//Update v=denseWeights as if there's no L1
//Thresholding: if |v[j]| < threshold, turn off weights[j]
//If not, shrink: w[j] = v[i] - sign(v[j]) * threshold
l1IntermediateBias[iClass] -= primalUpdate;
if (_args.BiasLearningRate == 0)
{
biasReg[iClass] = Math.Abs(l1IntermediateBias[iClass]) - l1Threshold > 0.0
? l1IntermediateBias[iClass] - Math.Sign(l1IntermediateBias[iClass]) * l1Threshold
: 0;
}
if (features.IsDense)
{
SseUtils.SdcaL1UpdateDense(-primalUpdate, features.Length, features.Values, l1Threshold, l1IntermediateWeights[iClass].Values, weights[iClass].Values);
}
else if (features.Count > 0)
{
SseUtils.SdcaL1UpdateSparse(-primalUpdate, features.Length, features.Values, features.Indices, features.Count, l1Threshold, l1IntermediateWeights[iClass].Values, weights[iClass].Values);
}
}
break;
}
}
}
// Updating with label class weights and dual variable.
duals[label + dualIndexInitPos] = labelDual;
biasUnreg[label] += labelAdjustment * lambdaNInv * instanceWeight;
if (l1ThresholdZero)
{
VectorUtils.AddMult(ref features, weights[label].Values, labelPrimalUpdate);
biasReg[label] += labelPrimalUpdate;
}
else
{
l1IntermediateBias[label] += labelPrimalUpdate;
var intermediateBias = l1IntermediateBias[label];
biasReg[label] = Math.Abs(intermediateBias) - l1Threshold > 0.0
? intermediateBias - Math.Sign(intermediateBias) * l1Threshold
: 0;
if (features.IsDense)
{
SseUtils.SdcaL1UpdateDense(labelPrimalUpdate, features.Length, features.Values, l1Threshold, l1IntermediateWeights[label].Values, weights[label].Values);
}
else if (features.Count > 0)
{
SseUtils.SdcaL1UpdateSparse(labelPrimalUpdate, features.Length, features.Values, features.Indices, features.Count, l1Threshold, l1IntermediateWeights[label].Values, weights[label].Values);
}
}
rowCount++;
}
}
}
private PcaPredictor TrainCore(IChannel ch, RoleMappedData data, int dimension)
{
Host.AssertValue(ch);
ch.AssertValue(data);
if (_rank > dimension)
{
throw ch.Except("Rank ({0}) cannot be larger than the original dimension ({1})", _rank, dimension);
}
int oversampledRank = Math.Min(_rank + _oversampling, dimension);
//exact: (size of the 2 big matrices + other minor allocations) / (2^30)
Double memoryUsageEstimate = 2.0 * dimension * oversampledRank * sizeof(float) / 1e9;
if (memoryUsageEstimate > 2)
{
ch.Info("Estimate memory usage: {0:G2} GB. If running out of memory, reduce rank and oversampling factor.", memoryUsageEstimate);
}
var y = Zeros(oversampledRank, dimension);
var mean = _center ? VBufferUtils.CreateDense <float>(dimension) : VBufferUtils.CreateEmpty <float>(dimension);
var omega = GaussianMatrix(oversampledRank, dimension, _seed);
var cursorFactory = new FeatureFloatVectorCursor.Factory(data, CursOpt.Features | CursOpt.Weight);
long numBad;
Project(Host, cursorFactory, ref mean, omega, y, out numBad);
if (numBad > 0)
{
ch.Warning("Skipped {0} instances with missing features/weights during training", numBad);
}
//Orthonormalize Y in-place using stabilized Gram Schmidt algorithm.
//Ref: https://en.wikipedia.org/wiki/Gram-Schmidt#Algorithm
for (var i = 0; i < oversampledRank; ++i)
{
var v = y[i];
VectorUtils.ScaleBy(ref v, 1 / VectorUtils.Norm(y[i]));
// Make the next vectors in the queue orthogonal to the orthonormalized vectors.
for (var j = i + 1; j < oversampledRank; ++j) //subtract the projection of y[j] on v.
{
VectorUtils.AddMult(ref v, -VectorUtils.DotProduct(ref v, ref y[j]), ref y[j]);
}
}
var q = y; // q in QR decomposition.
var b = omega; // reuse the memory allocated by Omega.
Project(Host, cursorFactory, ref mean, q, b, out numBad);
//Compute B2 = B' * B
var b2 = new float[oversampledRank * oversampledRank];
for (var i = 0; i < oversampledRank; ++i)
{
for (var j = i; j < oversampledRank; ++j)
{
b2[i * oversampledRank + j] = b2[j * oversampledRank + i] = VectorUtils.DotProduct(ref b[i], ref b[j]);
}
}
float[] smallEigenvalues;// eigenvectors and eigenvalues of the small matrix B2.
float[] smallEigenvectors;
EigenUtils.EigenDecomposition(b2, out smallEigenvalues, out smallEigenvectors);
PostProcess(b, smallEigenvalues, smallEigenvectors, dimension, oversampledRank);
return(new PcaPredictor(Host, _rank, b, ref mean));
}