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4290A Fast Sanity Check for Clustering AnswersWhy can clustering results vary a lot across random seeds even on the same dataset?机器学习中等essay未尝试面试订阅5016Infer Competing Density From Posterior Responsibility 1In a two-component Gaussian mixture, component 1 has weight 0.6, component 2 has weight 0.4, and the density of component 1 at an observation x is g1(x)=0.3. The E-step assigns posterior responsibility 0.75 to component 1. What density value g2(x) for component 2 is implied?机器学习简单数值题未尝试面试订阅5021Recover Missing Observation From EM Mean Update 6A Gaussian-mixture M-step updates one component mean to 0.875. Three observations contribute to that component with responsibilities 0.8, 0.6, and 0.1. Two observed values are 0 and 1, while the third observation x is missing from the log. What missing x is implied by the updated mean?机器学习中等数值题未尝试面试订阅5023Recover Missing Observation From EM Mean Update 8A Gaussian-mixture M-step updates one component mean to 0.4. Three observations contribute to that component with responsibilities 0.4, 0.4, and 0.2. Two observed values are -1 and 1, while the third observation x is missing from the log. What missing x is implied by the updated mean?机器学习中等数值题未尝试面试订阅5026Recover Effective Membership From Updated Mixture Weight 11An EM fit is run on 80 observations, and after the M-step the updated weight of one component is 0.35. What total responsibility mass was assigned to that component?机器学习简单数值题未尝试面试订阅5031BIC Improvement Threshold for an Extra Component 16A mixture model with one extra component would add Delta k = 3 free parameters on a sample of size n = 100. Under BIC = -2 log L + k log n, what minimum log-likelihood improvement Delta log L is needed before the larger model is preferred?机器学习中等数值题未尝试面试订阅5036EM Mixture Diagnostic 21Why does one EM component sometimes collapse onto a single point with near-zero variance during mixture training?机器学习困难essay未尝试面试订阅5037EM Mixture Diagnostic 22Why can two EM runs on the same data land on noticeably different mixture parameters even when they reach similar likelihoods?机器学习困难essay未尝试面试订阅5038EM Mixture Diagnostic 23Why is label switching not a bug in a mixture model but still a headache when you compare runs?机器学习困难essay未尝试面试订阅5039EM Mixture Diagnostic 24Why can k-means and a Gaussian mixture with shared spherical covariances give similar clusters, yet still disagree on borderline points?机器学习困难essay未尝试面试订阅5040EM Mixture Diagnostic 25Why should a desk be careful before interpreting mixture components as economic regimes rather than as a flexible density fit?机器学习困难essay未尝试面试订阅