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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2541One Gradient Step on a Single Logistic Observation 22For one observation with x = 2, y = 1, current weight w = 0, and learning rate eta = 0.4, what is one gradient-descent update on the negative log-likelihood?机器学习简单数值题未尝试免费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2557Why Small Data Perturbations Can Rewrite the Whole Tree 10Why are deep decision trees often called unstable learners?机器学习简单essay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2566Choose the Weakest-Link Node to Prune 24Node A would have leaf error 12 if pruned, while its current subtree has error 7 and 3 leaves. Node B would have leaf error 9 if pruned, while its current subtree has error 6 and 2 leaves. Which node is the weaker link and should be pruned first under cost-complexity pruning?机器学习简单数值题未尝试免费2567Why Two Nearly-Tied First Splits Can Diverge Later 13Why can two root splits with almost identical immediate gain still lead to very different final trees?机器学习简单essay未尝试免费2568Compare Penalized Tree Options 25A parent node left uncut has SSE 70. A 2-leaf split gives total SSE 44. A 3-leaf subtree gives total SSE 36. If the complexity penalty is 10 per extra leaf relative to the uncut node, which option has the lowest penalized objective?机器学习中等数值题未尝试免费