Kullback–Leibler divergence

As explained in Causal AI

Kullback–Leibler divergence quantifies the difference between two probability distributions.

from pyro.infer import SVI, Trace_ELBO
from pyro.optim import Adam

pyro.clear_param_store()     #1
vae = VAE()    #2
train_loader, test_loader = setup_dataloaders(batch_size=256)    #3
svi_adam = Adam({"lr": 1.0e-3})     #4
model = vae.training_model    #5
guide = vae.training_guide    #5
svi = SVI(model, guide, svi_adam, loss=Trace_ELBO())     #5

How Causal AI covers it

How deep it goes

Defines the measure operationally and connects it to negative ELBO, but does not derive its mathematical formula.

Examples

Uses Q(Z|X, is-handwritten, digit) and P(Z|image, is-handwritten, digit) as approximating and target distributions.

What you can do after

Apply it via Pyro's Trace_ELBO within stochastic variational inference training.

How it connects

Connects variational inference, ELBO, stochastic variational inference, variational autoencoders, encoders, and guide functions.

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Also explained in

• 

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  Reinforcement Learning from Human FeedbackForward KL divergence is KL divergence from a target distribution to an approximating distribution, with expectation taken under the target distribution.
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  Graph Neural Networks in ActionA measure of the difference between two probability distributions, quantifying the information cost of approximating one with another.
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  Math and Architectures of Deep LearningA loss term based on Kullback-Leibler divergence that penalizes differences between probability distributions, such as an encoder's latent distribution and a chosen prior.
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  Learn Generative AI with PyTorchA divergence measure used as a regularization term to encourage a latent-variable distribution to resemble a normal distribution.
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  Build a Reasoning Model (From Scratch)A measure of how different two probability distributions are, used here for soft distillation.
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  Machine Learning Algorithms in DepthKullback-Leibler divergence is a nonnegative measure of the discrepancy between two probability distributions.
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  Evolutionary Deep Learning: Genetic algorithms and neural networksA divergence-based measure comparing probability distributions through differences in their information content.
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  Data Without LabelsKullback-Leibler divergence is a directed measure of the difference between two probability distributions based on their relative information content.
• 

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  Bayesian Optimization in ActionKullback–Leibler divergence is a nonnegative statistical divergence that quantifies how one probability distribution differs from another.
• 

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  Optimization Algorithms: AI techniques for design, planning, and control problemsKullback–Leibler divergence is a metric quantifying the dissimilarity between two probability distributions.
• 

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  Deep Learning with R, Third EditionKullback–Leibler divergence is a measure of how one probability distribution differs from a reference probability distribution.

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Related concepts

• Group Relative Policy Optimizationpart of · Group Relative Policy Optimization is a reinforcement-learning algorithm that updates a policy using relative rewards or advantages estimated from groups of sampled outputs or actions.
• t-SNEused by · t-SNE is a nonlinear dimensionality-reduction technique that maps high-dimensional data to a lower-dimensional space while emphasizing local similarities or neighborhood relationships.
• variational inferenceused by · Variational inference is an approximate inference technique that optimizes a tractable family of probability distributions to approximate a target distribution, often a posterior.
• variational Gaussian processused by · A variational Gaussian process is a scalable approximation to a Gaussian process whose posterior is represented through variational inference over a finite set of inducing points.

This explainer was generated by Manning's knowledge graph from the text of Causal AI. The section links point to the parts of the book it draws on.