MullOverThing

Useful tips for everyday

# How is KL loss calculated?

## How is KL loss 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 same as cross-entropy?

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.

### Is minimizing DKL the same thing as minimizing cross-entropy?

Both the cross-entropy and the KL divergence are tools to measure the distance between two probability distributions, but what is the difference between them? Moreover, it turns out that the minimization of KL divergence is equivalent to the minimization of cross-entropy.

Is KL divergence symmetric?

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. It is not symmetric: the KL from p(x) to q(x) is generally not the same as the KL from q(x) to p(x).

## Is KL divergence a loss function?

Cross Entropy as a loss function. So, KL divergence in simple term is a measure of how two probability distributions (say ‘p’ and ‘q’) are different from each other. So this is exactly what we care about while calculating the loss function.

What is a large KL divergence?

“…the K-L divergence represents the number of extra bits necessary to code a source whose symbols were drawn from the distribution P, given that the coder was designed for a source whose symbols were drawn from Q.” Quora. and. “…it is the amount of information lost when Q is used to approximate P.”

### Why is cross-entropy better than MSE?

Practical understanding: First, Cross-entropy (or softmax loss, but cross-entropy works better) is a better measure than MSE for classification, because the decision boundary in a classification task is large (in comparison with regression). For regression problems, you would almost always use the MSE.

When should I use KL divergence?

As we’ve seen, we can use KL divergence to minimize how much information loss we have when approximating a distribution. Combining KL divergence with neural networks allows us to learn very complex approximating distribution for our data.

## Why do we use KL divergence?

Very often in Probability and Statistics we’ll replace observed data or a complex distributions with a simpler, approximating distribution. KL Divergence helps us to measure just how much information we lose when we choose an approximation.

What is the cross entropy loss function?

Cross-entropy loss, or log loss, measures the performance of a classification model whose output is a probability value between 0 and 1. Cross-entropy loss increases as the predicted probability diverges from the actual label. As the predicted probability decreases, however, the log loss increases rapidly.

### Is KL divergence positive or negative?

So, the KL divergence is a non-negative value that indicates how close two probability distributions are.

Why do we need KL divergence?