func MaxEntComputeInstanceDerivative(
weights *util.Matrix, instance *data.Instance, instanceDerivative *util.Matrix) {
// 定义偏导和特征向量
features := instance.Features
// 得到维度信息
numLabels := weights.NumLabels() + 1
// 计算 z = 1 + exp(sum(w_i * x_i))
label := instance.Output.Label
z := ComputeZ(weights, features, label, instanceDerivative)
inverseZ := float64(1) / z
for iLabel := 1; iLabel < numLabels; iLabel++ {
vec := instanceDerivative.GetValues(iLabel - 1)
if label == 0 || label != iLabel {
vec.Multiply(inverseZ, 0, features)
} else {
vec.Multiply(inverseZ, -1, features)
}
}
}
// 计算 z = 1 + sum(exp(sum(w_i * x_i)))
//
// 在temp中保存 exp(sum(w_i * x_i))
func ComputeZ(weights *util.Matrix, features *util.Vector, label int, temp *util.Matrix) float64 {
result := float64(1.0)
numLabels := weights.NumLabels() + 1
for iLabel := 1; iLabel < numLabels; iLabel++ {
exp := math.Exp(util.VecDotProduct(features, weights.GetValues(iLabel-1)))
result += exp
tempVec := temp.GetValues(iLabel - 1)
if tempVec.IsSparse() {
for _, k := range features.Keys() {
tempVec.Set(k, exp)
}
} else {
tempVec.SetAll(exp)
}
}
return result
}
func (opt *gdOptimizer) OptimizeWeights(
weights *util.Matrix, derivative_func ComputeInstanceDerivativeFunc, set data.Dataset) {
// 偏导数向量
derivative := weights.Populate()
// 学习率计算器
learningRate := NewLearningRate(opt.options)
// 优化循环
iterator := set.CreateIterator()
step := 0
var learning_rate float64
convergingSteps := 0
oldWeights := weights.Populate()
weightsDelta := weights.Populate()
instanceDerivative := weights.Populate()
log.Print("开始梯度递降优化")
for {
if opt.options.MaxIterations > 0 && step >= opt.options.MaxIterations {
break
}
step++
// 每次遍历样本前对偏导数向量清零
derivative.Clear()
// 遍历所有样本，计算偏导数向量并累加
iterator.Start()
instancesProcessed := 0
for !iterator.End() {
instance := iterator.GetInstance()
derivative_func(weights, instance, instanceDerivative)
derivative.Increment(instanceDerivative, 1.0/float64(set.NumInstances()))
iterator.Next()
instancesProcessed++
if opt.options.GDBatchSize > 0 && instancesProcessed >= opt.options.GDBatchSize {
// 添加正则化项
derivative.Increment(ComputeRegularization(weights, opt.options),
float64(instancesProcessed)/(float64(set.NumInstances())*float64(set.NumInstances())))
// 计算特征权重的增量
delta := opt.GetDeltaX(weights, derivative)
// 根据学习率更新权重
learning_rate = learningRate.ComputeLearningRate(delta)
weights.Increment(delta, learning_rate)
// 重置
derivative.Clear()
instancesProcessed = 0
}
}
if instancesProcessed > 0 {
// 处理剩余的样本
derivative.Increment(ComputeRegularization(weights, opt.options),
float64(instancesProcessed)/(float64(set.NumInstances())*float64(set.NumInstances())))
delta := opt.GetDeltaX(weights, derivative)
learning_rate = learningRate.ComputeLearningRate(delta)
weights.Increment(delta, learning_rate)
}
weightsDelta.WeightedSum(weights, oldWeights, 1, -1)
oldWeights.DeepCopy(weights)
weightsNorm := weights.Norm()
weightsDeltaNorm := weightsDelta.Norm()
log.Printf("#%d |w|=%1.3g |dw|/|w|=%1.3g lr=%1.3g", step, weightsNorm, weightsDeltaNorm/weightsNorm, learning_rate)
// 判断是否溢出
if math.IsNaN(weightsNorm) {
log.Fatal("优化失败：不收敛")
}
// 判断是否收敛
if weightsDelta.Norm()/weights.Norm() < opt.options.ConvergingDeltaWeight {
convergingSteps++
if convergingSteps > opt.options.ConvergingSteps {
log.Printf("收敛")
break
}
}
}
}
// 输入x_k和g_k，返回x需要更新的增量 d_k = - g_k
func (opt *gdOptimizer) GetDeltaX(x, g *util.Matrix) *util.Matrix {
return g.Opposite()
}
// 根据正则化方法计算偏导数向量需要添加正则化项
func ComputeRegularization(weights *util.Matrix, options OptimizerOptions) *util.Matrix {
reg := weights.Populate()
if options.RegularizationScheme == 1 {
// L-1正则化
for iLabel := 0; iLabel < weights.NumLabels(); iLabel++ {
for _, k := range weights.GetValues(iLabel).Keys() {
if weights.Get(iLabel, k) > 0 {
reg.Set(iLabel, k, options.RegularizationFactor)
} else {
reg.Set(iLabel, k, -options.RegularizationFactor)
}
}
}
} else if options.RegularizationScheme == 2 {
// L-2正则化
for iLabel := 0; iLabel < weights.NumLabels(); iLabel++ {
for _, k := range weights.GetValues(iLabel).Keys() {
reg.Set(iLabel, k, options.RegularizationFactor*float64(2)*weights.Get(iLabel, k))
}
}
}
return reg
}
func (opt *lbfgsOptimizer) OptimizeWeights(
weights *util.Matrix, derivative_func ComputeInstanceDerivativeFunc, set data.Dataset) {
// 学习率计算器
learningRate := NewLearningRate(opt.options)
// 偏导数向量
derivative := weights.Populate()
// 优化循环
step := 0
convergingSteps := 0
oldWeights := weights.Populate()
weightsDelta := weights.Populate()
// 为各个工作协程开辟临时资源
numLbfgsThreads := *lbfgs_threads
if numLbfgsThreads == 0 {
numLbfgsThreads = runtime.NumCPU()
}
workerSet := make([]data.Dataset, numLbfgsThreads)
workerDerivative := make([]*util.Matrix, numLbfgsThreads)
workerInstanceDerivative := make([]*util.Matrix, numLbfgsThreads)
for iWorker := 0; iWorker < numLbfgsThreads; iWorker++ {
workerBuckets := []data.SkipBucket{
{true, iWorker},
{false, 1},
{true, numLbfgsThreads - 1 - iWorker},
}
workerSet[iWorker] = data.NewSkipDataset(set, workerBuckets)
workerDerivative[iWorker] = weights.Populate()
workerInstanceDerivative[iWorker] = weights.Populate()
}
log.Print("开始L-BFGS优化")
for {
if opt.options.MaxIterations > 0 && step >= opt.options.MaxIterations {
break
}
step++
// 开始工作协程
workerChannel := make(chan int, numLbfgsThreads)
for iWorker := 0; iWorker < numLbfgsThreads; iWorker++ {
go func(iw int) {
workerDerivative[iw].Clear()
iterator := workerSet[iw].CreateIterator()
iterator.Start()
for !iterator.End() {
instance := iterator.GetInstance()
derivative_func(
weights, instance, workerInstanceDerivative[iw])
// log.Print(workerInstanceDerivative[iw].GetValues(0))
workerDerivative[iw].Increment(
workerInstanceDerivative[iw], float64(1)/float64(set.NumInstances()))
iterator.Next()
}
workerChannel <- iw
}(iWorker)
}
derivative.Clear()
// 等待工作协程结束
for iWorker := 0; iWorker < numLbfgsThreads; iWorker++ {
<-workerChannel
}
for iWorker := 0; iWorker < numLbfgsThreads; iWorker++ {
derivative.Increment(workerDerivative[iWorker], 1)
}
// 添加正则化项
derivative.Increment(ComputeRegularization(weights, opt.options), 1.0/float64(set.NumInstances()))
// 计算特征权重的增量
delta := opt.GetDeltaX(weights, derivative)
// 根据学习率更新权重
learning_rate := learningRate.ComputeLearningRate(delta)
weights.Increment(delta, learning_rate)
weightsDelta.WeightedSum(weights, oldWeights, 1, -1)
oldWeights.DeepCopy(weights)
weightsNorm := weights.Norm()
weightsDeltaNorm := weightsDelta.Norm()
log.Printf("#%d |dw|/|w|=%f |w|=%f lr=%1.3g", step, weightsDeltaNorm/weightsNorm, weightsNorm, learning_rate)
// 判断是否溢出
if math.IsNaN(weightsNorm) {
log.Fatal("优化失败：不收敛")
}
// 判断是否收敛
if weightsDeltaNorm/weightsNorm < opt.options.ConvergingDeltaWeight {
convergingSteps++
if convergingSteps > opt.options.ConvergingSteps {
log.Printf("收敛")
break
}
} else {
convergingSteps = 0
}
}
}
// 输入x_k和g_k，返回x需要更新的增量 d_k = - H_k * g_k
func (opt *lbfgsOptimizer) GetDeltaX(x, g *util.Matrix) *util.Matrix {
if x.NumLabels() != g.NumLabels() {
log.Fatal("x和g的维度不一致")
}
// 第一次调用时开辟内存
if opt.k == 0 {
if x.IsSparse() {
opt.initStruct(x.NumLabels(), 0, x.IsSparse())
} else {
opt.initStruct(x.NumLabels(), x.NumValues(), x.IsSparse())
}
}
currIndex := util.Mod(opt.k, *lbfgs_history_size)
// 更新x_k
opt.x[currIndex].DeepCopy(x)
// 更新g_k
opt.g[currIndex].DeepCopy(g)
// 当为第0步时，使用简单的gradient descent
if opt.k == 0 {
opt.k++
return g.Opposite()
}
prevIndex := util.Mod(opt.k-1, *lbfgs_history_size)
// 更新s_(k-1)
opt.s[prevIndex].WeightedSum(opt.x[currIndex], opt.x[prevIndex], 1, -1)
// 更新y_(k-1)
opt.y[prevIndex].WeightedSum(opt.g[currIndex], opt.g[prevIndex], 1, -1)
// 更新ro_(k-1)
opt.ro.Set(prevIndex, 1.0/util.MatrixDotProduct(opt.y[prevIndex], opt.s[prevIndex]))
// 计算两个循环的下限
lowerBound := opt.k - *lbfgs_history_size
if lowerBound < 0 {
lowerBound = 0
}
// 第一个循环
opt.q.DeepCopy(g)
for i := opt.k - 1; i >= lowerBound; i-- {
currIndex := util.Mod(i, *lbfgs_history_size)
opt.alpha.Set(currIndex,
opt.ro.Get(currIndex)*util.MatrixDotProduct(opt.s[currIndex], opt.q))
opt.q.Increment(opt.y[currIndex], -opt.alpha.Get(currIndex))
}
// 第二个循环
opt.z.DeepCopy(opt.q)
for i := lowerBound; i <= opt.k-1; i++ {
currIndex := util.Mod(i, *lbfgs_history_size)
opt.beta.Set(currIndex,
opt.ro.Get(currIndex)*util.MatrixDotProduct(opt.y[currIndex], opt.z))
opt.z.Increment(opt.s[currIndex],
opt.alpha.Get(currIndex)-opt.beta.Get(currIndex))
}
// 更新k
opt.k++
return opt.z.Opposite()
}