In order for the KL divergence to be finite, the support of PP needs to be contained in the support of QQ. If a point xx exists with Q(x)=0Q(x)=0 but P(x)>0P(x)>0, then DKL(P∥Q)=∞DKL(P‖Q)=∞ Rewriting the Objective With some algebra, we can manipulate the definitio...
[1] KL Divergence for Machine Learning [2] Variational Refinement for Importance Sampling Using the Forward Kullback-Leibler Divergence [3] towardsdatascience.com/ [4] $KL(q | p)$ is mode-seeking [5] Divergence measures and message passing [6] BEYOND REVERSE KL: GENERALIZING DIRECT PREFERENCE...
前面说到, 三者的关系为:Cross-Entropy=Entropy+ KL Divergence 所以, KL-Divergence的计算式子如下所示: 我们计算一下上面那个天气的KL-Divergence, 下面是天气的真实概率分布, 和我们预测的概率分布: 于是KL-Divergence的计算结果如下: 下面是一些更加数学化的表示, 分别看一下离散概率分布和连续概率分布下的公式....
In information theory and machine learning, information gain is a synonym for Kullback–Leibler divergence. However, in the context of decision trees, the term is sometimes used synonymously with mutual information, which is the expectation value of the Kullback–Leibler divergence of a conditional pr...
KL散度(Kullback-Leibler_divergence) KL-divergence,俗称KL距离,常用来衡量两个概率分布的距离。 1. 根据shannon的信息论,给定一个字符集的概率分布,我们可以设计一种编码,使得表示该字符集组成的字符串平均需要的比特数最少。假设这个字符集是X,对x∈X,其出现概率为P(x),那么其最优编码平均需要的比特数等于这个...
至于general的统计距离,当然,它们其实没有本质差别。更广泛的来看,KL divergence可以看成是phi-divergence的一种特殊情况(phi取log)。注意下面的定义是针对discrete probability distribution,但是把sum换成integral很自然可以定义连续版本的。用其它的divergence理论来做上是没有本质区别的,只要phi是convex, closed的。...
最早KL divergence就是从信息论里引入的,不过既然题主问的是ML中的应用,就不多做具体介绍。只是简单概述给定真实概率分布P和近似分布Q,KL divergence所表达的就是如果我们用一套最优的压缩机制(compression scheme)来储存Q的分布,对每个从P来的sample我需要多用的bits(相比我直接用一套最优的压缩机制来储存P的分布...
In machine learning,gtypically represents the true distribution of data, whilefrepresents the model’s approximation of the distribution. Thus for our neural network we can write the KL divergence like this: Notice that the second term (colored in blue) depends only on the data, which are fixe...
IJCAI 2021, "Comparing Kullback-Leibler Divergence and Mean Squared Error Loss in Knowledge Distillation" machine-learning pytorch knowledge-distillation kl-divergence mean-squared-error ijcai2021 Updated Feb 1, 2023 Jupyter Notebook zheng-yanan / techniques-for-kl-vanishing Star 28 ...
code for JS divergence importscipy.statsdefJS_divergence(p,q):M=(p+q)/2return0.5*scipy.stats.entropy(p,M)+0.5*scipy.stats.entropy(q,M) Reference: Pattern Recognition and Machine Learning https://en.wikipedia.org/wiki/Entropy_(information_theory) ...