Is the Jensen Shannon divergence a metric?

The square root of the Jensen–Shannon divergence is a metric often referred to as Jensen-Shannon distance.

How is Jensen Shannon divergence calculated?

The JS divergence can be calculated as follows: JS(P || Q) = 1/2 * KL(P || M) + 1/2 * KL(Q || M)

Is Jensen Shannon divergence convex?

1A Jensen divergence is convex if and only if ∇2F(x) ≥ 1 2 ∇2((x + y)/2) for all x, y ∈ X. See [5] for further details. divergence notations. ).

What is the difference between KL divergence and cross-entropy?

Cross-entropy is commonly used in machine learning as a loss function. It is closely related to but is different from KL divergence that calculates the relative entropy between two probability distributions, whereas cross-entropy can be thought to calculate the total entropy between the distributions.

Can cross-entropy be more than 1?

Mathematically speaking, if your label is 1 and your predicted probability is low (like 0.1), the cross entropy can be greater than 1, like losses.

What are Kullback-Leibler and Jensen-Shannon divergence?

Two commonly used divergence scores from information theory are Kullback-Leibler Divergence and Jensen-Shannon Divergence. Jensen-Shannon divergence extends KL divergence to calculate a symmetrical score and distance measure of one probability distribution from another.

What is the quantum Jensen-Shannon divergence?

Quantum Jensen–Shannon divergence for and two density matrices is a symmetric function, everywhere defined, bounded and equal to zero only if two density matrices are the same. It is a square of a metric for pure states, and it was recently shown that this metric property holds for mixed states as well.

Why is JS-divergence not more often used?

KL divergence has clear information theoretical interpretation and is well-known; but I am first time to hear that the symmetrization of KL divergence is called JS divergence. The reason that JS-divergence is not so often used is probably that it is less well-known and does not offer must-have properties.

What is the Jensen-Shannon divergence for two probability distributions?

The Jensen–Shannon divergence is bounded by 1 for two probability distributions, given that one uses the base 2 logarithm. With this normalization, it is a lower bound on the total variation distance between P and Q: