# What is Renyi divergence?

## What is Renyi divergence?

The Rényi divergence of order α or alpha-divergence of a distribution P from a distribution Q is defined to be. when 0 < α < ∞ and α ≠ 1. We can define the Rényi divergence for the special values α = 0, 1, ∞ by taking a limit, and in particular the limit α → 1 gives the Kullback–Leibler divergence.

## What is the meaning of KL divergence?

the KL divergence is the average number of extra bits needed to encode the data, due to the fact that we used distribution q to encode the data instead of the true distribution p.

**What is divergence in information theory?**

In information geometry, a divergence is a kind of statistical distance: a binary function which establishes the “distance” from one probability distribution to another on a statistical manifold.

### How do you find Rényi entropy?

To obtain probability values, each histogram was normalized by dividing the number of RR intervals in each bin by the total RR intervals in the sequence. This resulted in estimates of the probability of each bin, and these 30 probability values were used to calculate the Renyi entropy for the participant.

### Can Rényi entropy be negative?

Then, Renyi (1961) generalized it for one parameter families of entropies. This entropy for discrete random variables is non-negative but it can be negative in continuous case.

**What is data divergence?**

The sum of all differences between two datasets (data-data divergence) or between a single dataset and reality (data-world divergence). Sources of data divergence include: data ageing, response errors, coding or data entry errors, differences in coding and the effect of disclosure control.

#### What is divergent data?

Measurements that move apart from the norm. They move ahead of the common point or fail to approach the limit of a distribution.

#### What is collision entropy?

Definition The collision entropy of a probability distribution on a finite set is the Rényi entropy at order 2: S2(p)=−log(n∑i=1p2i), hence is the negative logarithm of the “collision probability”, i.e., of the probability that two independent random variables, both described by p, will take the same value.

**Is Rényi entropy additive?**

No, the Renyi entropy is not subadditive. It also lacks several other “natural” properties of entropies. See this paper on “Additive entropies of degree-q and the Tsallis Entropy by B. H. Lavenda and J.