手法を比較

	No-U-Turn Sampler (NUTS)	変分推論
分野	ベイズ	ベイズ
系統	Bayesian methods	Bayesian methods
提唱年	2014	1999
提唱者	Matthew D. Hoffman & Andrew Gelman	Jordan, Ghahramani, Jaakkola & Saul
種類	Sampling algorithm (MCMC)	Approximate Bayesian inference
原典	Hoffman, M. D., & Gelman, A. (2014). The No-U-Turn Sampler: Adaptively setting path lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research, 15(47), 1593–1623.	Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., & Saul, L. K. (1999). An introduction to variational methods for graphical models. Machine Learning, 37(2), 183–233.
別名	NUTS, No-U-Turn HMC, adaptive Hamiltonian Monte Carlo, self-tuning HMC	VI, variational Bayes, VB, mean-field variational inference
関連	4	4
概要	The No-U-Turn Sampler (NUTS) is a self-tuning Markov chain Monte Carlo algorithm introduced by Hoffman and Gelman (2014) that extends Hamiltonian Monte Carlo (HMC) by automatically determining the optimal number of leapfrog steps, eliminating the most sensitive manual tuning parameter. NUTS is the default sampler in Stan and PyMC and has made large-scale, high-dimensional Bayesian inference practically accessible without requiring users to set trajectory lengths by hand.	Variational inference (VI) is a family of techniques that turn Bayesian posterior computation into an optimisation problem. Instead of drawing samples from the exact posterior — as Markov chain Monte Carlo does — VI posits a simpler, tractable family of distributions and finds the member of that family closest to the true posterior by maximising the evidence lower bound (ELBO). Introduced in its modern graphical-model form by Jordan, Ghahramani, Jaakkola and Saul (1999) and given a comprehensive statistical treatment by Blei, Kucukelbir and McAuliffe (2017), VI is now the standard scalable inference engine in probabilistic machine learning.