KL散度

KL散度，又叫相對熵，用于衡量兩個分布（離散分布和連續(xù)分布）之間的距離。

設(shè) 、 是離散隨機(jī)變量的兩個概率分布，則 對 的KL散度是:

KLDivLoss

對于包含個樣本的batch數(shù)據(jù) ，是神經(jīng)網(wǎng)絡(luò)的輸出，并且進(jìn)行了歸一化和對數(shù)化；是真實的標(biāo)簽（默認(rèn)為概率），與同維度。

第個樣本的損失值計算如下:

class KLDivLoss(_Loss):
    __constants__ = ['reduction']
    def __init__(self, size_average=None, reduce=None, reduction='mean'):
        super(KLDivLoss, self).__init__(size_average, reduce, reduction)
    def forward(self, input, target):
        return F.kl_div(input, target, reduction=self.reduction)

pytorch中通過torch.nn.KLDivLoss類實現(xiàn)，也可以直接調(diào)用F.kl_div 函數(shù)，代碼中的size_average與reduce已經(jīng)棄用。reduction有四種取值mean,batchmean, sum, none，對應(yīng)不同的返回。 默認(rèn)為mean

例子：

import torch
import torch.nn as nn
import math

def validate_loss(output, target):
    val = 0
    for li_x, li_y in zip(output, target):
        for i, xy in enumerate(zip(li_x, li_y)):
            x, y = xy
            loss_val = y * (math.log(y, math.e) - x)
            val += loss_val
    return val / output.nelement()

torch.manual_seed(20)
loss = nn.KLDivLoss()
input = torch.Tensor([[-2, -6, -8], [-7, -1, -2], [-1, -9, -2.3], [-1.9, -2.8, -5.4]])
target = torch.Tensor([[0.8, 0.1, 0.1], [0.1, 0.7, 0.2], [0.5, 0.2, 0.3], [0.4, 0.3, 0.3]])
output = loss(input, target)
print("default loss:", output)

output = validate_loss(input, target)
print("validate loss:", output)

loss = nn.KLDivLoss(reduction="batchmean")
output = loss(input, target)
print("batchmean loss:", output)

loss = nn.KLDivLoss(reduction="mean")
output = loss(input, target)
print("mean loss:", output)

loss = nn.KLDivLoss(reduction="none")
output = loss(input, target)
print("none loss:", output)

輸出：

default loss: tensor(0.6209)
validate loss: tensor(0.6209)
batchmean loss: tensor(1.8626)
mean loss: tensor(0.6209)
none loss: tensor([[1.4215, 0.3697, 0.5697],
        [0.4697, 0.4503, 0.0781],
        [0.1534, 1.4781, 0.3288],
        [0.3935, 0.4788, 1.2588]])