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Normalizing flows for density estimation — the idea.

hard

Answer

  • Learn invertible neural network f_θ that maps simple base distribution (Gaussian) to complex data distribution.
  • Change of variables: log p(x) = log p(z)  +  log⁡∣det⁡p(z)\; + \;\operatorname{log} \mid \operatorname{det} JfJ_{f}^(-1)|.
  • Requires efficient Jacobian determinants → architectures: RealNVP, Glow, NICE (coupling layers), MAF, NSF.
  • Uses: exact density estimation, sampling, anomaly detection.
  • Modern: replaced by diffusion models for sampling but still competitive for exact-density needs.
Check yourself — multiple choice
  • Random
  • Invertible NN maps Gaussian → data; log p(x) = log p(z)  +  log⁡∣det⁡p(z)\; + \;\operatorname{log} \mid \operatorname{det} J|; RealNVP/Glow/MAF; exact density + sampling; superseded by diffusion for generation
  • Same as VAE
  • Not real

Normalizing flows: invertible NN + change of variables → exact density.

#density#deep-learning

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