Maximum Likelihood Parameters (Maximum Likelihood Parameters)

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In these algorithms, the goal is to estimate hyperparameters using maximum likelihood.


$n$: 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
Newton–Raphson algorithm 1685 $O(n^{3})$ $O(n+r^{2})$? Exact Deterministic
Parameter-expanded expectation maximization (PX-EM) algorithm 1998 $O(n^{3})$ $O(n+r)$? Exact Deterministic Time
Expectation conditional maximization (ECM) 2017 $O(n^{2} \log n)$ $O(n+r)$? Exact Deterministic Time
Generalized expectation maximization (GEM) algorithm 1994 $O(n^{4} \log^{0.1}(.{5}n)$) $O(n+r)$? Exact Deterministic Time
α-EM algorithm 2003 $O(n^{3})$ $O(n+r)$? Exact Deterministic Time

Time Complexity Graph

Maximum Likelihood Parameters - Time.png