1 vote
265 views

### KL divergence between two multivariate gaussians where $p$ is $N(\mu, I)$ [duplicate]

We know if we try to get $D_{KL}(q||p)$, where $p$ is a standard normal distribution, so mean is 0, variance is the identity matrix, and $q$ is a multivariate normal distribution, it can be calculated ...
191k views

### KL divergence between two univariate Gaussians

I need to determine the KL-divergence between two Gaussians. I am comparing my results to these, but I can't reproduce their result. My result is obviously wrong, because the KL is not 0 for KL(p, p). ...
• 13.7k
19k views

### Deriving the KL divergence loss for VAEs

In a VAE, the encoder learns to output two vectors: $$\mathbf{\mu} \in\ \mathbb{R}^{z}$$ $$\mathbf{\sigma} \in\ \mathbb{R}^{z}$$ which are the mean and variances for the latent vector $\mathbf{z}$, ...
• 1,221
9k views

### How to use Kullback-leibler divergence if mean and standard deviation of of two Gaussian Distribution is provided?

With Apache Spark MLLib library I am trying to find Clusters within a dataset by using Gaussian Mixture Model (number cluster =3) . Now it returns 3 different values of mean and standard deviation. I ...
2k views

### KL divergence for joint probability distributions?

I have a pair of joint probability distributions. I want to measure their similarity/dissimilarity. If they were single-dimensional probability distributions, then I could measure the Kullback–Leibler ...
• 2,932
2k views

### Combine overlapping Gaussian distributions

Given the mean and covariance matrix of the pair-wise (multivariate normal) distributions \begin{align} P(X_1,X_2) &\sim \mathcal{N}(\mu_{12},\Sigma_{12}),\\ P(X_2,X_3) &\sim \mathcal{N}(\mu_{...
2k views

### textbook example of KL Divergence [duplicate]

I have read what KL Divergence is about: assess differences in probability distributions between two sets. I have also read, and digested, that it is emphatically not a true metric because of ...
• 8,747
3k views

### KL divergence between two bivariate Gaussian distribution

KL divergence between two multivariate Gaussians and univariate Gaussians have been discussed. I was wondering if there exists a simpler computation for the KL divergence between two bivariate ...
3k views

• 611
1 vote
308 views

### skew G-Jensen-Shannon divergence between multivariate gaussian calculation discrepancy

I'm trying to calculate the Jensen-Shannon divergence between two multivariate Gaussians. I found a closed-form expression both for the KL divergence and JS divergence between two Gaussians in this ...
1 vote