Quiz on Expectation-Maximization (EM) Algorithm

Introduction to the EM Algorithm Answers 1. What is a primary disadvantage of the EM algorithm? A. It can be prone to overfitting with small datasets. B. It always guarantees quick convergence. C. It may converge to a local maximum instead of the global maximum. D. It requires a significantly low number of parameters. Answer: It may converge to a local maximum instead of the global maximum. (C) The EM algorithm can converge to local maxima depending on the initial parameter values, posing a challenge in optimization. 2. Which of the following is NOT an application of the EM algorithm? A. Gaussian Mixture Models B. Decision Tree Classification C. Missing Data Imputation D. Hidden Markov Models (HMMs) Answer: Decision Tree Classification (B) The EM algorithm is not used for Decision Tree Classification; it is more suited for models involving latent variables and missing data. 3. What practical consideration is crucial for the EM algorithm's performance? A. The number of data points should remain constant. B. Data should be normalized before applying the algorithm. C. The initial parameter values must be chosen well. D. The algorithm should not involve iterations. Answer: The initial parameter values must be chosen well. (C) Good initial parameter values are vital as they significantly influence the convergence and effectiveness of the EM algorithm. 4. What is the role of the E-step in the EM algorithm? A. To generate new data points for the model. B. To maximize the likelihood function directly. C. To update the model parameters based on current estimates. D. To compute expected values of the latent variables. Answer: To compute expected values of the latent variables. (D) The E-step computes expected values of the latent variables based on current estimates, which is central to the EM algorithm's iterative process. 5. Which of the following statements about the convergence criteria in the EM algorithm is true? A. Change in log-likelihood is not a suitable measure for convergence. B. No initial parameter values are needed for determining convergence. C. Convergence criteria should be defined to prevent unnecessary iterations. D. Convergence criteria are unnecessary as the algorithm always converges. Answer: Convergence criteria should be defined to prevent unnecessary iterations. (C) Defining appropriate convergence criteria, such as changes in log-likelihood, is crucial to ensure efficiency and effectiveness in the iterations of the EM algorithm. 6. What is the primary purpose of the EM algorithm? A. To perform hypothesis testing on observed data B. To create complete datasets from incomplete data C. To visualize statistical models effectively D. To estimate maximum likelihood parameters in models with hidden variables Answer: To estimate maximum likelihood parameters in models with hidden variables (D) The primary purpose of the EM algorithm is to estimate parameters in models that involve hidden variables, especially when dealing with incomplete data. 7. Which step in the EM algorithm involves predicting the missing data? A. M-step (Maximization Step) B. Convergence Check C. Initialization Step D. E-step (Expectation Step) Answer: E-step (Expectation Step) (D) The E-step (Expectation Step) is responsible for calculating the expected value of the complete-data log-likelihood to predict the missing data. 8. What does the M-step of the EM algorithm aim to accomplish? A. Set initial values for parameters B. Estimate the probability of hidden variables C. Check for convergence of parameter estimates D. Maximize the expected complete-data log-likelihood Answer: Maximize the expected complete-data log-likelihood (D) The M-step maximizes the expected complete-data log-likelihood based on the estimates provided in the E-step. 9. Which of the following is **not** a characteristic of the EM algorithm? A. May converge to a local maximum B. Designed to handle missing data C. Directly calculates the maximum likelihood estimation D. Iterative improvement of parameter estimates Answer: Directly calculates the maximum likelihood estimation (C) The EM algorithm does not directly calculate maximum likelihood estimates; instead, it iteratively approaches a local maximum. 10. What type of data does the EM algorithm specifically address? A. Incomplete data with missing or unobserved points B. Homogeneous datasets without hidden variables C. Structured data with clear dependencies D. Complete data without any missing values Answer: Incomplete data with missing or unobserved points (A) The EM algorithm is particularly useful for incomplete data problems, dealing with cases where some data points are missing or unobserved. 11. What is essential for the convergence of the EM algorithm to be considered successful? A. The change in log-likelihood must meet a predetermined threshold B. All parameters must be initialized to zero C. The likelihood function must be quadratic D. The variance of data must remain constant Answer: The change in log-likelihood must meet a predetermined threshold (A) Convergence in the EM algorithm is assessed by the change in log-likelihood between iterations, which must meet a predetermined threshold for the algorithm to stop. 12. Which statement about hidden variables in the context of the EM algorithm is true? A. Hidden variables are always unobserved and irrelevant B. All hidden variables must be observed for the EM algorithm to work C. Hidden variables impact the observed data and are accounted for in the model D. The EM algorithm cannot incorporate hidden variables in its estimation Answer: Hidden variables impact the observed data and are accounted for in the model (C) Hidden variables influence the observed data and the EM algorithm is designed to account for them in parameter estimation. 13. What limitation does the EM algorithm have regarding the optimization of the likelihood function? A. It always guarantees the finding of the global maximum B. It may converge to a local maximum based on initial parameter values C. It can only optimize when data is complete D. It requires linear relationships between variables Answer: It may converge to a local maximum based on initial parameter values (B) The EM algorithm is designed to find a local maximum rather than guaranteeing a global maximum, which can depend on the initial values of parameters.