What is the relationship between entropy cross entropy and KL divergence?

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.

How is KL divergence calculated?

KL divergence can be calculated as the negative sum of probability of each event in P multiplied by the log of the probability of the event in Q over the probability of the event in P. The value within the sum is the divergence for a given event.

Is KL divergence differentiable?

Smaller KL Divergence values indicate more similar distributions and, since this loss function is differentiable, we can use gradient descent to minimize the KL divergence between network outputs and some target distribution. …

Why do we use cross-entropy loss?

Cross-entropy loss is used when adjusting model weights during training. The aim is to minimize the loss, i.e, the smaller the loss the better the model. A perfect model has a cross-entropy loss of 0.

Where is KL divergence used?

To measure the difference between two probability distributions over the same variable x, a measure, called the Kullback-Leibler divergence, or simply, the KL divergence, has been popularly used in the data mining literature. The concept was originated in probability theory and information theory.

What is KL divergence in deep learning?

The Kullback-Leibler divergence (hereafter written as KL divergence) is a measure of how a probability distribution differs from another probability distribution. In this context, the KL divergence measures the distance from the approximate distribution Q to the true distribution P .

Is KL divergence a metric?

Although the KL divergence measures the “distance” between two distri- butions, it is not a distance measure. This is because that the KL divergence is not a metric measure.

How do you reduce KL divergence?

Optimization problem is convex when qθ is an exponential family—i.e., for any p the optimization problem is “easy.” You can think of maximum likelihood estimation (MLE) as a method which minimizes KL divergence based on samples of p. In this case, p is the true data distribution!

What is forward and reverse KL divergence?

The forward/reverse formulations of KL divergence are distinguished by having mean/mode-seeking behavior. The typical example for using KL to optimize a distribution Qθ to fit a distribution P (e.g. see this blog) is a bimodal true distribution P and a unimodal Gaussian Qθ.

Why MSE is not good for classification?

There are two reasons why Mean Squared Error(MSE) is a bad choice for binary classification problems: If we use maximum likelihood estimation(MLE), assuming that the data is from a normal distribution(a wrong assumption, by the way), we get the MSE as a Cost function for optimizing our model.

What is the relationship between entropy and KL divergence?

Cross entropy and KL divergence. Cross entropy is, at its core, a way of measuring the “distance” between two probability distributions P and Q. As you observed, entropy on its own is just a measure of a single probability distribution.

When is the KL divergence of a distribution low?

If they are close together, then the KL divergence will be low. Another interpretation of KL divergence, from a Bayesian perspective, is intuitive – this interpretation says KL divergence is the information gained when we move from a prior distribution Q to a posterior distribution P.

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).

How to calculate the entropy of a log?

Entropy = – (0.35 * log (0.35) + 0.35 * log (0.35) + 0.1 * log (0.1) + 0.1 * log (0.1) + 0.04 * log (0.04) + 0.04 * log (0.04) + 0.01 * log (0.01) + 0.01 * log (0.01)) Entropy = 2.23 bits Note that the log used here is a binary log. So, on average, the weather station sends 3 bits but the recipient gets only 2.23 useful bits.