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2520Why L1 and L2 Pull Differently Near Zero 25Why does L1 regularization create a stronger qualitative push toward exact zero than L2 regularization near the origin?机器学习困难derivation未尝试面试订阅2522Intercept From the Positive Rate 2In an intercept-only logistic model, if the fitted probability is p hat, what intercept b solves sigma(b)=p hat?机器学习简单derivation未尝试免费2523Gradient of Logistic Negative Log-Likelihood 3For one observation (x,y) with y in 0,1 and score z = w T x, what is the gradient of the negative log-likelihood with respect to w?机器学习中等derivation未尝试免费2524Why No Closed Form in Logistic Regression 5Why does logistic regression usually require iterative optimization rather than a normal-equation-style closed form?机器学习中等essay未尝试免费2525One Newton Step for an Intercept-Only Logistic ModelAn intercept-only logistic model is fit to 7 positives and 3 negatives. Starting from b 0 = 0, what is one Newton step b 1 for minimizing the negative log-likelihood?机器学习困难数值题未尝试面试订阅2535Decision Threshold Under Asymmetric Classification CostsA desk incurs cost 1 for a false positive and cost 5 for a false negative. Under a calibrated logistic probability p = P(Y=1|x), above what threshold should it predict class 1 to minimize expected cost?机器学习困难derivation未尝试面试订阅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2577Why OOB Is Unsafe for Grouped or Temporal Data 13Why can out-of-bag error be misleading when rows are linked by entity or time rather than being exchangeable?机器学习中等essay未尝试面试订阅2580Why More Trees Usually Do Not Create Classical Overfit 15Why does adding more trees to a random forest typically plateau rather than create the kind of explosive overfit seen in some single-model families?机器学习困难essay未尝试面试订阅2584Marginal Variance Reduction From One More Tree 3Under the equicorrelated-tree model, derive how much the ensemble variance falls when you move from B trees to B+1 trees.机器学习困难derivation未尝试面试订阅2585Trees Needed for a Target Variance Cap 4Suppose each tree has variance sigma 2 and pairwise correlation rho. Derive the minimum B needed to make the ensemble variance at most V, assuming V > rho sigma 2.机器学习困难derivation未尝试面试订阅2589Bagged MSE When Bias Stays Fixed 7Assume each tree has the same squared bias b 2 and prediction noise floor nu, while bagging only changes the variance term according to the equicorrelated-tree formula. Derive the bagged test MSE with B trees.机器学习困难derivation未尝试面试订阅