Maximum Likelihood Methods in Unknown Latent Variables: Difference between revisions

Revision as of 15:47, 15 February 2023

In this problem, the goal is to compute maximum-likelihood estimates when the observations can be viewed as incomplete data.

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Name	Year	Time	Space	Approximation Factor	Model	Reference
Expectation-Maximization (EM) algorithm	1977	$O(n^{3})$	$O(n+r)$?	Exact	Deterministic	Time
EM with Quasi-Newton Methods (Jamshidian; Mortaza; Jennrich; Robert I.)	1997	$O(n^{2} log^{3} n)$	$O(n+r^{2})$?	Exact	Deterministic	Time
Parameter-expanded expectation maximization (PX-EM)	1998	$O(n^{3})$	$O(n+r)$?	Exact	Deterministic	Time
Expectation conditional maximization (ECM)	1993	$O(n^{3})$	$O(n+r)$?	Exact	Deterministic	Time
Expectation conditional maximization either (ECME) (Liu; Chuanhai; Rubin; Donald B)	1994	$O(n^{3})$	$O(n+r)$?	Exact	Deterministic	Time
α-EM Algorithm	2003	$O(n^{3})$	$O(n+r)$?	Exact	Deterministic	Time
Shaban; Amirreza; Mehrdad; Farajtabar	2015	$O(n^{2} log^{2} n)$	$O(kd+d^{3})$??	Exact	Deterministic	Time
alpha-HMM (Matsuyama, Yasuo)	2011	$O(n^{2} log^{2} n)$		Exact	Deterministic	Time

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 [[File:Maximum Likelihood Methods in Unknown Latent Variables - Space.png|1000px]]
-== Pareto Frontier Improvements Graph ==
+== Time-Space Tradeoff ==
 [[File:Maximum Likelihood Methods in Unknown Latent Variables - Pareto Frontier.png|1000px]]