পদ্ধতির তুলনা করুন

	মাল্টিলেভেল ভ্যারিয়েশনাল ইনফারেন্স	ভ্যারিয়েশনাল ইনফারেন্স (Variational Inference)
ক্ষেত্র	বেইসীয়	বেইসীয়
পরিবার	Bayesian methods	Bayesian methods
উদ্ভবের বছর	2016	1999
প্রবর্তক	Ranganath, Altosaar, Tran, Blei (hierarchical VI formalization, 2016); Blei et al. (VI framework, 2017)	Jordan, Ghahramani, Jaakkola & Saul
ধরন	approximate Bayesian inference	Approximate Bayesian inference
মৌলিক উৎস	Blei, D. M., Kucukelbir, A., & McAuliffe, J. D. (2017). Variational inference: A review for statisticians. Journal of the American Statistical Association, 112(518), 859-877.	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.
অপর নাম	hierarchical variational inference, multilevel VI, variational Bayes for multilevel models, MLVI	VI, variational Bayes, VB, mean-field variational inference
সম্পর্কিত	4	4
সারসংক্ষেপ	Multilevel variational inference (MLVI) is a scalable approximate Bayesian method that fits hierarchical (multilevel) models by optimizing a variational approximation to the posterior, rather than drawing MCMC samples. It exploits the grouped structure of multilevel data — individuals nested within groups, groups nested within higher-level units — to derive efficient coordinate-wise updates, making Bayesian inference tractable for large clustered datasets.	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.