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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1answer
44 views

How is this statement from a TensorFlow implementation of a certain KL-divergence formula related to the corresponding formula?

I am trying to understand a certain KL-divergence formula (which can be found on page 6 of the paper Evidential Deep Learning to Quantify Classification Uncertainty) and found a TensorFlow ...
0
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0answers
33 views

KL divergence coefficient update doesn't make sense in RLlib's PPO implementation

I am using RLlib (Ray 1.4.0)'s implementation of PPO for a multi-agent scenario with continuous actions, and I find that the loss includes the KL divergence penalty term, apart from the surrogate loss,...
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0answers
17 views

How do we get from entropy to KL divergence in this paper?

I'm reading through Regularizing Neural Networks By Penalizing Confident Output Distributions and I'm stuck on the equation in section 3.2. It's not clear to me at all that the self-entropy of the ...
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0answers
20 views

How can I avoid a negative covariance value in my variational auto-encoder?

I am implementing the variational auto-encoder from this paper (Section 3.1): https://arxiv.org/pdf/2004.06271.pdf My KL loss function is giving NaN values because some of my covariances are negative. ...
1
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0answers
103 views

Why does the VAE using a KL-divergence with a non-standard mean does not produce good images?

I know I can make a VAE do generation with a mean of 0 and std-dev of 1. I tested it with the following loss function: ...
5
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2answers
301 views

Why is "-0.5 * torch.sum(1 + sigma - mu.pow(2) - sigma.exp())" in Pytorch equivalent to the KL?

I found this code for the loss function of a VAE: -0.5 * torch.sum(1 + sigma - mu.pow(2) - sigma.exp()) From this link: https://debuggercafe.com/getting-started-...
3
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1answer
79 views

How do you calculate KL divergence on a three-dimensional space for a Variational Autoencoder?

I'm trying to implement a variational auto-encoder (as seen in Section 3.1 here: https://arxiv.org/pdf/2004.06271.pdf). It differs from a traditional VAE because it encodes its input images to three-...
6
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2answers
265 views

Why is KL divergence used so often in Machine Learning?

The KL Divergence is quite easy to compute in closed form for simple distributions -such as Gaussians- but has some not-very-nice properties. For example, it is not symmetrical (thus it is not a ...
3
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1answer
131 views

Are there some notions of distance between two policies?

I want to determine some distance between two policies $\pi_1 (a \mid s)$ and $\pi_2 (a \mid s)$, i.e. something like $\vert \vert \pi_1 (a \mid s) - \pi_2(a \mid s) \vert \vert$, where $\pi_i (a\mid ...
3
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1answer
376 views

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 ...
1
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2answers
111 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 ...
3
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1answer
202 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 ...
4
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1answer
281 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 ...
2
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1answer
102 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 ...