EM Algorithm And Naive Bayes With K-means Clustering.pdf

Key Concepts:

Naive Bayes Classifier: A probabilistic classifier based on Bayes' theorem with strong independence assumptions between features. Maximum Likelihood Estimation (MLE) is used to find optimal parameters.
K-means Clustering: An iterative unsupervised learning algorithm that groups data points into K clusters by minimizing the average distance within clusters.
Expectation-Maximization (EM) Algorithm: An iterative procedure for finding maximum likelihood estimates of parameters in a mixture model when some data are missing or latent. It alternates between:
E-step: Computing expected values of latent variables given current parameter estimates.
M-step: Updating parameter estimates based on the expected values from the E-step.
Lower Bound (Q): EM constructs a lower bound (Q) on the log-likelihood function that can be maximized iteratively, leading to convergence to a local maximum.

Theoretical Analysis:

EM guarantees finding a local optimum of data log likelihood due to its construction of a concave lower bound.
The algorithm is applicable to a broader class of models than Naive Bayes by using a general joint distribution and introducing an arbitrary distribution over latent variables (q(Z)).
Variations of EM, like Generalized EM (GEM), can be used for finding local optima that improve but may not maximize the lower bound.

Applications:

The document highlights the use of EM in:

Mixture Models: For tasks like clustering and topic modeling where data points arise from a mixture of distributions.
* Probabilistic Graphical Models: Where latent variables represent hidden states or factors that influence observed data.