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2540Intercept Shift for a Deployment Prior ChangeA logistic model was trained under class prior 0.5 and has intercept -0.4. At deployment the base rate falls to 0.2 while feature likelihood ratios are assumed unchanged. What adjusted intercept should be used?机器学习困难数值题未尝试面试订阅2546Legal Threshold Count With a Leaf-Size Floor 15A sorted feature has 31 observations, and each child leaf must contain at least 6 observations. How many legal split positions are there?机器学习简单数值题未尝试免费2547Numeric Weakest-Link Alpha 16A node has leaf error 18 if pruned into a single leaf. Its current subtree has training error 10 and 3 leaves. What is the weakest-link alpha for pruning this subtree?机器学习简单数值题未尝试免费2549Penalized Split Decision on a Regression Node 18A regression leaf has SSE 260. Splitting it would reduce child SSE to 230. If the complexity penalty is 12 per extra leaf, should you keep the split?机器学习中等数值题未尝试免费2550Optimal Leaf Label Under Asymmetric Trading CostsA classification leaf contains 6 positive cases and 14 negative cases. Predicting positive costs 1 per false positive, while predicting negative costs 4 per false negative. Which class should the leaf predict to minimize expected leaf loss?机器学习困难derivation未尝试面试订阅2551Why Pre-Pruning Can Miss a Good Two-Step Split 9Why can an aggressive pre-pruning rule reject a first split that looks weak locally even though it would unlock a much better second-level structure?机器学习简单essay未尝试免费2552Which Split Becomes Best After a Perturbation 19Split A originally has gain 1.20 and split B has gain 1.05. After one row is corrected, A loses 0.10 gain while B gains 0.08. Which split is now best?机器学习中等数值题未尝试免费2553Maximum Balanced Depth Numerically 20A tree starts with 96 observations at the root and every split is perfectly balanced. If each leaf must contain at least 12 observations, what is the maximum possible depth?机器学习中等数值题未尝试面试订阅2554Cost-Sensitive Leaf Label 21A leaf contains 7 positives and 13 negatives. Predicting negative incurs false-negative cost 4 on each hidden positive, while predicting positive incurs false-positive cost 1 on each hidden negative. Which class should the leaf predict?机器学习中等数值题未尝试面试订阅2555Best Valid Split Under a Minimum-Leaf ConstraintThree candidate splits on the same node have Gini gains 0.18, 0.16, and 0.11, with smaller-child sizes 3, 4, and 7 respectively. If the minimum allowed leaf size is 4, which split is actually chosen?机器学习困难derivation未尝试面试订阅2556Grouped Values and Feasible Thresholds 22A sorted feature has five distinct-value blocks of sizes [3, 5, 2, 4, 6], and splits are allowed only between distinct-value blocks. If each child leaf must contain at least 6 observations, how many legal thresholds exist?机器学习简单数值题未尝试免费2559Expected Misroutes From a Surrogate SplitA surrogate split agrees with the primary split on 34 of 40 training cases where both features are present. If 12 production cases are missing the primary split feature and are routed by the surrogate, what is the expected number of misroutes?机器学习困难derivation未尝试面试订阅2560Global Weight Rescaling Leaves Split Ranking Unchanged 5If every sample weight in a node is multiplied by the same constant c>0, how does each candidate split's weighted impurity decrease change?机器学习困难derivation未尝试面试订阅2564Validation Penalty Threshold for Keeping a SplitA stump has validation loss 30. Splitting it into two leaves lowers validation loss to 22 but adds an instability penalty lambda per extra leaf. For what largest lambda is the split still preferred?机器学习困难derivation未尝试面试订阅2565Validation Pruning With an Alpha Charge 23Replacing a single leaf by a 3-leaf subtree reduces validation loss by 4.5. If the complexity charge is alpha = 1.2 per extra leaf, should you keep the subtree?机器学习困难数值题未尝试面试订阅2571Variance of an Average of Correlated Trees 1Suppose B trees each have variance sigma 2 and every pair has correlation rho. Derive the variance of their simple average.机器学习简单derivation未尝试免费2572Numeric Ensemble Variance 22Each tree has variance 9, pairwise correlation 0.2, and the forest has 25 trees. What is the variance of the forest average?机器学习简单数值题未尝试免费2573Infinite-Forest Variance Floor 2Using the equicorrelated-tree variance formula, derive the prediction variance as the number of trees B tends to infinity.机器学习中等derivation未尝试免费2574Why Bagging Helps Unstable Learners Most 10Why does bagging usually help deep trees much more than it helps already-stable learners?机器学习中等essay未尝试免费2575Why Bagging Rarely Fixes High Bias 11Why should you not expect bagging alone to rescue a learner whose individual trees are systematically misspecified?机器学习困难essay未尝试面试订阅