# Questions tagged [kl-divergence]

For questions related to the Kullback–Leibler (KL) divergence, which is a measure (that is not a metric, but it is pre-metric, because it does not satisfy all properties of metrics, i.e. it is not symmetric) of divergence (or distance) between two probability measures (density functions, or mass functions), which is commonly used in many machine learning settings, e.g. in the context of variational auto-encoders (VAES).

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• 287
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### What is the impact of scaling the KL divergence and reconstruction loss in the VAE objective function?

Variational autoencoders have two components in their loss function. The first component is the reconstruction loss, which for image data, is the pixel-wise difference between the input image and ...
• 141
347 views

### When should one prefer using Total Variational Divergence over KL divergence in RL

In RL, both the KL divergence (DKL) and Total variational divergence (DTV) are used to measure the distance between two policies. I'm most familiar with using DKL as an early stopping metric during ...
• 509
274 views

### What is the reason for mode collapse in GAN as opposed to WGAN?

In this article I am reading: $D_{KL}$ gives us inifity when two distributions are disjoint. The value of $D_{JS}$ has sudden jump, not differentiable at $\theta=0$. Only Wasserstein metric provides ...
• 131
719 views

### Why does the KL divergence not satisfy the triangle inequality?

The KL divergence is defined as $$D_{KL}=\sum_i p(x_i)log\left(\frac{p(x_i)}{q(x_i)}\right)$$ Why does $D_{KL}$ not satisfy the triangle inequality? Also, can't you make it satisfy the triangle ...
• 597
462 views

### Why is the evidence equal to the KL divergence plus the loss?

Why is the equation $$\log p_{\theta}(x^1,...,x^N)=D_{KL}(q_{\theta}(z|x^i)||p_{\phi}(z|x^i))+\mathbb{L}(\phi,\theta;x^i)$$ true, where $x^i$ are data points and $z$ are latent variables? I was ...
• 597
591 views

### Why is the Jensen-Shannon divergence preferred over the KL divergence in measuring the performance of a generative network?

I have read articles on how Jensen-Shannon divergence is preferred over Kullback-Leibler in measuring how good a distribution mapping is learned in a generative network because of the fact that JS-...
• 1,359
137 views

### How does the Kullback-Leibler divergence give "knowledge gained"?

I'm reading about the KL divergence on Wikipedia. I don't understand how the equation gives "information gained" as it says in the "Interpretations" section Expressed in the ...
• 351
2k views

### What are the advantages of the Kullback-Leibler over the MSE/RMSE?

I've recently encountered different articles that are recommending to use the KL divergence instead of the MSE/RMSE (as the loss function), when trying to learn a probability distribution, but none of ...
• 1,098