# EM 알고리즘

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## 노트

### 말뭉치

1. The more complex EM algorithm can find model parameters even if you have missing data.
2. The EM Algorithm always improves a parameter’s estimation through this multi-step process.
3. The EM algorithm can be very slow, even on the fastest computer.
4. The results indicate that EM algorithm, as expected is heavily impacted by the initial values.
5. We'll use this below in the EM algorithm but this computation can also be used for GMM classifiers to find out which class \(x_i\) most likely belongs to.
6. The former problem is the general unsupervised learning problem that we'll solve with the EM algorithm (e.g. finding the neighborhoods).
7. The latter is a specific problem that we'll indirectly use as one of the steps in the EM algorithm.
8. In this section, we'll go over some of the derivations and proofs related to the EM algorithm.
9. The EM algorithm (Dempster, Laird, & Rubin 1977) finds maximum likelihood estimates of parameters in probabilistic models.
10. The EM algorithm is a method of finding maximum likelihood parameter estimates when data contain some missing variables.
11. The EM algorithm is proceeded by an iteration of two steps: an Expectation (E) step and a Maximization (M) step.
12. The procedure of the EM algorithm is implemented through the following steps: Step 1: Initialization.
13. The authors propose a feasible EM algorithm for the 3PLM, namely expectation-maximization-maximization (EMM).
14. Sem of another flavour: two new applications of the supplemented em algorithm.
15. Covariance structure model fit testing under missing data: an application of the supplemented em algorithm.
16. Covariance structure model fit testing under missing data: an application of the supplemented EM algorithm.
17. Improving the convergence rate of the EM algorithm for a mixture model fitted to grouped truncated data.
18. We look at several issues encountered when calculating the maximum likelihood estimates of the Gaussian mixed model using an Expectation Maximization algorithm.
19. The model is trained by using the EM algorithm on an incomplete data set and is further improved by using a gradient-based discriminative method.
20. We then describe the EM algorithm for a GMM, the kernel method, and eventually the proposed modified EM algorithm for GMM in Section 3.
21. The main objective of the EM algorithm is to find the value of that maximizes (2).
22. And you don’t need the EM algorithm.
23. In the EM algorithm, we assume we know how to model p(θ₂ |x, θ₁) easily.
24. If not, the EM algorithm will not be helpful.
25. The success of the EM algorithm subjects to how simple are they and how easy to optimize the later one.
26. Expectation Maximization (EM) is a classic algorithm developed in the 60s and 70s with diverse applications.
27. Stepping back a bit, I want to emphasize the power and usefulness of the EM algorithm.
28. Finally, I want to note that there is plenty more to say about the EM algorithm.
29. The EM algorithm is used to find (local) maximum likelihood parameters of a statistical model in cases where the equations cannot be solved directly.
30. The EM algorithm proceeds from the observation that there is a way to solve these two sets of equations numerically.
31. For multimodal distributions, this means that an EM algorithm may converge to a local maximum of the observed data likelihood function, depending on starting values.
32. The Q-function used in the EM algorithm is based on the log likelihood.
33. The expectation-maximization algorithm is an approach for performing maximum likelihood estimation in the presence of latent variables.
34. The EM algorithm is an iterative approach that cycles between two modes.
35. # example of fitting a gaussian mixture model with expectation maximization from numpy import hstack from numpy .
36. Running the example fits the Gaussian mixture model on the prepared dataset using the EM algorithm.
37. This technical report describes the statistical method of expectation maximization (EM) for parameter estimation.
38. Expectation Maximization (EM) model components are often treated as clusters.
39. Expectation Maximization algorithmThe basic approach and logic of this clustering method is as follows.
40. Put another way, the EM algorithm attempts to approximate the observed distributions of values based on mixtures of different distributions in different clusters.
41. The EM algorithm does not compute actual assignments of observations to clusters, but classification probabilities.