Parameter Estimation and EM Algorithm

The lecture covers parameter estimation for complete and incomplete data, focusing on maximum likelihood estimation. It introduces the Expectation Maximization (EM) algorithm, explaining its application, challenges, and convergence issues. The discussion includes handling missing data and practical considerations for implementing EM.

What is a key property of maximum likelihood estimates when the data set is complete?

• They are always the same as Bayesian estimates.

• They cannot be computed in closed form.

• They are unique and maximize the likelihood of the data.

• They are always biased.

In the context of incomplete data, what does it mean when a variable is described as 'latent'?

• The variable is irrelevant.

• The variable is sometimes observed.

• The variable is always missing.

• The variable is always observed.

What is the implication of data being 'missing at random'?

• The missing data can be ignored without any consequence.

• The missing data provides no information about the missing values themselves.

• The missing data is always due to a systematic error.

• The missing data can be easily predicted.

Which of the following is a characteristic of local search methods for parameter estimation?

• They guarantee finding the global optimum.

• They start with initial estimates and iteratively improve them.

• They are faster than methods for complete data.

• They do not require any initial estimates.

What is the main purpose of the Expectation-Maximization (EM) algorithm?

• To eliminate the need for initial estimates.

• To estimate parameters in the presence of incomplete data.

• To simplify the data set by removing missing values.

• To find the global maximum of a function.

Why might the EM algorithm converge slowly?

• Due to the complexity of the data set.

• Because it does not use any iterative process.

• Because it is sensitive to the starting point.

• Because it always finds the global maximum.

How does gradient ascent differ from the EM algorithm in terms of parameter estimation?

• Gradient ascent focuses on optimizing a function of many variables.

• Gradient ascent guarantees finding the global maximum.

• Gradient ascent is not iterative.

• Gradient ascent does not require computing gradients.