Flow-based generative model: Difference between revisions

Revision as of 23:34, 11 March 2021

Revision as of 21:33, 12 March 2021

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{{Machine learning bar}}

A '''flow-based generative model''' is a [[generative model]] used in [[machine learning]] that explicitly models a [[probability distribution]] by leveraging '''normalizing flow'''<ref>{{cite arXiv | eprint=1505.05770| author1=Danilo Jimenez Rezende| last2=Mohamed| first2=Shakir| title=Variational Inference with Normalizing Flows| year=2015| class=stat.ML}}</ref>, which is a statistical method using the [[Probability density function#Function of random variables and change of variables in the probability density function|change-of-variable]] law of probabilities to transform a simple distribution into a complex one.

The direct modeling of likelihood provides many advantages. For example, the negative log-likelihood can be directly computed and minimized as the [[loss function]]. Additionally, novel samples can be generated by sampling from the initial distribution, and applying the flow transformation.

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: <math>\log p_K(z_K) = \log p_0(z_0) - \sum_{i=1}^{K} \log \left|\det \frac{df_i(z_{i-1})}{dz_{i-1}}\right|</math>

To efficiently compute the log likelihood, the functions <math>f_1, ..., f_K</math> should be 1. easy to invert, and 2. easy to compute the determinant of its Jacobian. In practice, the functions <math>f_1, ..., f_K</math> are modeled using [[Deep learning|deep neural networks]], and are trained to minimize the negative log-likelihood of data samples from the target distribution. These architectures are usually designed such that only the forward pass of the neural network is required in both the inverse and the Jacobian determinant calculations. Examples of such architectures include NICE<ref>{{cite arXiv | eprint=1410.8516| last1=Dinh| first1=Laurent| last2=Krueger| first2=David| last3=Bengio| first3=Yoshua| title=NICE: Non-linear Independent Components Estimation| year=2014| class=cs.LG}}</ref>, RealNVP<ref>{{cite arXiv | eprint=1605.08803| last1=Dinh| first1=Laurent| last2=Sohl-Dickstein| first2=Jascha| last3=Bengio| first3=Samy| title=Density estimation using Real NVP| year=2016| class=cs.LG}}</ref>, and Glow<ref name="glow">{{cite arXiv | eprint=1807.03039| last1=Kingma| first1=Diederik P.| last2=Dhariwal| first2=Prafulla| title=Glow: Generative Flow with Invertible 1x1 Convolutions| year=2018| class=stat.ML}}</ref>.

=== Derivation of log likelihood ===

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Flow-based generative models have been applied on a variety of modeling tasks, including:

* Audio generation<ref>{{cite arXiv | eprint=1912.01219| last1=Ping| first1=Wei| last2=Peng| first2=Kainan| last3=Zhao| first3=Kexin| last4=Song| first4=Zhao| title=WaveFlow: A Compact Flow-based Model for Raw Audio| year=2019| class=cs.SD}}</ref>

* Image generation<ref name="glow" />

* Molecular graph generation<ref>{{cite arXiv | eprint=2001.09382| last1=Shi| first1=Chence| last2=Xu| first2=Minkai| last3=Zhu| first3=Zhaocheng| last4=Zhang| first4=Weinan| last5=Zhang| first5=Ming| last6=Tang| first6=Jian| title=GraphAF: A Flow-based Autoregressive Model for Molecular Graph Generation| year=2020| class=cs.LG}}</ref>

* Point-cloud modeling<ref>{{cite arXiv | eprint=1906.12320| last1=Yang| first1=Guandao| last2=Huang| first2=Xun| last3=Hao| first3=Zekun| last4=Liu| first4=Ming-Yu| last5=Belongie| first5=Serge| last6=Hariharan| first6=Bharath| title=PointFlow: 3D Point Cloud Generation with Continuous Normalizing Flows| year=2019| class=cs.CV}}</ref>

* Point-cloud modeling<ref>{{cite arXiv | eprint=1906.12320}}</ref>

* Video generation<ref>{{cite arXiv | eprint=1903.01434| last1=Kumar| first1=Manoj| last2=Babaeizadeh| first2=Mohammad| last3=Erhan| first3=Dumitru| last4=Finn| first4=Chelsea| last5=Levine| first5=Sergey| last6=Dinh| first6=Laurent| last7=Kingma| first7=Durk| title=VideoFlow: A Conditional Flow-Based Model for Stochastic Video Generation| year=2019| class=cs.CV}}</ref>

* Video generation<ref>{{cite arXiv | eprint=1903.01434}}</ref>

== References ==