Maximum Likelihood Methods in Unknown Latent Variables (Maximum Likelihood Methods in Unknown Latent Variables)

Description

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

Parameters

$n$: number of observations in sample

$r$: number of parameters + latent variables

Table of Algorithms

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

Time Complexity Graph

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Space Complexity Graph

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Time-Space Tradeoff

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