Search results
Results from the WOW.Com Content Network
In mathematical statistics, the Kullback–Leibler (KL) divergence (also called relative entropy and I-divergence [1]), denoted (), is a type of statistical distance: a measure of how much a model probability distribution Q is different from a true probability distribution P.
where is the Kullback–Leibler divergence, and is the outer product distribution which assigns probability () to each (,).. Notice, as per property of the Kullback–Leibler divergence, that (;) is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when and are independent (and hence observing tells you nothing about ).
The total variation distance is related to the Kullback–Leibler divergence by Pinsker’s inequality: (,) ().One also has the following inequality, due to Bretagnolle and Huber [2] (see also [3]), which has the advantage of providing a non-vacuous bound even when () >:
Thus (; |) is the expected (with respect to ) Kullback–Leibler divergence from the conditional joint distribution (,) | to the product of the conditional marginals | and |. Compare with the definition of mutual information.
When NMF is obtained by minimizing the Kullback–Leibler divergence, it is in fact equivalent to another instance of multinomial PCA, probabilistic latent semantic analysis, [45] trained by maximum likelihood estimation. That method is commonly used for analyzing and clustering textual data and is also related to the latent class model.
The G-test statistic is proportional to the Kullback–Leibler divergence of the ... In Python, use scipy.stats.power_divergence ... G 2 /Log-likelihood calculator
The Kullback–Leibler divergence between two Cauchy distributions has the following symmetric closed-form formula: [11] (,,:,,) = (+) + (,,). Any f-divergence between two Cauchy distributions is symmetric and can be expressed as a function of the chi-squared divergence. [ 12 ]
Kullback–Leibler divergence See § Kullback–Leibler divergence In probability theory and statistics , the multivariate normal distribution , multivariate Gaussian distribution , or joint normal distribution is a generalization of the one-dimensional ( univariate ) normal distribution to higher dimensions .