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2526Why Separable Data Pushes Coefficients Outward 7Why do logistic-regression coefficients tend to diverge on perfectly linearly separable data if no regularization is used?机器学习简单essay未尝试免费2527Probability From a Logit Score 8If a logistic model outputs score z = ln 3, what probability does it assign to class 1?机器学习中等数值题未尝试免费2528Why Log-Loss Rewards Calibration 9Why does a well-calibrated probability forecaster typically fare better under log-loss than a forecaster that only gets rankings right?机器学习中等essay未尝试免费2531Why One-vs-Rest Scores Need Not Sum to One 15Why can independently trained one-vs-rest logistic classifiers produce class probabilities that do not sum to one?机器学习简单essay未尝试免费2532Hessian of Logistic Negative Log-Likelihood 4For one observation with score z = w T x, what is the Hessian of the negative log-likelihood with respect to w?机器学习简单derivation未尝试免费2536Why Softmax Fixes Joint Normalization 16What does the softmax construction add that one-vs-rest logistic models do not provide automatically?机器学习简单essay未尝试免费2538Why Logistic Beats Hard Threshold Rules for Training 23Why is a smooth probabilistic loss easier to optimize than training directly against a hard classification rule?机器学习中等essay未尝试免费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2569Why Axis-Aligned Trees Struggle on Rotated Boundaries 14Why can a decision tree need many small rectangles to approximate a simple diagonal boundary?机器学习中等essay未尝试面试订阅2570Surrogate Split Agreement Rate 8A primary split is missing for some rows, so a surrogate split is trained on the M rows where the primary feature is observed. If it sends A of those rows to the same side as the primary split, what is its agreement rate?机器学习困难derivation未尝试面试订阅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