Contents
Can we minimize KL divergence directly?
No. It turns out that there a connection between the K-L divergence and the negative log-likelihood. Minimizing the K-L divergence is equivalent to minimizing the negative log-likelihood, which is equivalent to maximizing the likelihood between the Poisson model and the data.
What is the relationship between entropy cross-entropy and KL divergence?
Cross-entropy is not KL Divergence. Cross-entropy is related to divergence measures, such as the Kullback-Leibler, or KL, Divergence that quantifies how much one distribution differs from another. Specifically, the KL divergence measures a very similar quantity to cross-entropy.
What is the KL divergence of entropy and cross entropy?
This amount by which the cross-entropy exceeds the entropy is called the Relative Entropy or more commonly known as the Kullback-Leibler Divergence (KL Divergence). In short, K-L Divergence = CrossEntropy-Entropy = 4.58–2.23 = 2.35 bits. Now, let’s use Cross-Entropy in an application.
When is the entropy greater than the cross entropy?
But, if the distributions differ, then the cross-entropy will be greater than the entropy by some number of bits. This amount by which the cross-entropy exceeds the entropy is called the Relative Entropy or more commonly known as the Kullback-Leibler Divergence (KL Divergence).
Which is the correct equation for KL divergence?
For KL divergence, it can be written as $$H(q, p) = D_{KL}(p, q)+H(p) = -\\sum_i{p_ilog(q_i)}$$ From the equation, we could see that KL divergence can depart into a Cross-Entropy of p and q (the first part), and a global entropy of ground truth p (the second part).
Is the log likelihood the same as the cross entropy?
And here’s another summary from Jonathan Gordon on Quora: Maximizing the (log) likelihood is equivalent to minimizing the binary cross entropy. There is literally no difference between the two objective functions, so there can be no difference between the resulting model or its characteristics.