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4465Before Declaring DiversificationWhat should you check first before saying that adding five more signals makes the ensemble diversified?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5041Recover the Missing Fold Gap 1A 5-fold cross-validation comparison records four paired score differences (model A minus model B): [0.02, 0.01, -0.01, 0.03]. The desk report says the overall mean fold difference across all 5 folds was 0.01. What was the missing fifth-fold difference?机器学习中等数值题未尝试面试订阅5042Recover the Missing Fold Gap 2A 5-fold cross-validation comparison records four paired score differences (model A minus model B): [0.05, 0.02, 0.04, -0.01]. The desk report says the overall mean fold difference across all 5 folds was 0.026. What was the missing fifth-fold difference?机器学习中等数值题未尝试面试订阅5043Recover the Missing Fold Gap 3A 5-fold cross-validation comparison records four paired score differences (model A minus model B): [-0.02, 0.01, 0.0, -0.01]. The desk report says the overall mean fold difference across all 5 folds was 0.002. What was the missing fifth-fold difference?机器学习中等数值题未尝试面试订阅5044Recover the Missing Fold Gap 4A 5-fold cross-validation comparison records four paired score differences (model A minus model B): [0.01, 0.01, 0.02, 0.0]. The desk report says the overall mean fold difference across all 5 folds was 0.014. What was the missing fifth-fold difference?机器学习中等数值题未尝试面试订阅5045Recover the Missing Fold Gap 5A 5-fold cross-validation comparison records four paired score differences (model A minus model B): [0.04, -0.02, 0.01, 0.02]. The desk report says the overall mean fold difference across all 5 folds was 0.01. What was the missing fifth-fold difference?机器学习中等数值题未尝试面试订阅5046Recover Discordant Counts From McNemar Summary 6Two classifiers are compared on the same test set. The total number of discordant cases is b+c=16, model A is better so b>c, and the continuity-corrected McNemar statistic is 3.0625. What discordant counts (b,c) are implied?机器学习中等数值题未尝试面试订阅5051Cost-Sensitive Deployment Choice 11Model A makes 8 false positives and 2 false negatives on a validation set. Model B makes 6 false positives and 5 false negatives. If a false negative costs 10 units and a false positive costs 1 unit(s), which model has lower expected validation cost and what are the two costs?机器学习中等数值题未尝试面试订阅5061Why Nested Evaluation MattersWhy is it unfair to compare two tuned models on the same validation folds that were also used to pick their hyperparameters?机器学习困难essay未尝试面试订阅5062Why Dependence MattersWhy can standard iid significance arguments be too optimistic when model scores come from overlapping rolling windows?机器学习困难essay未尝试面试订阅