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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2576Why Feature Subsampling Helps When One Predictor Dominates 12Why can random feature subsampling improve a forest when one very strong predictor would otherwise appear at the top of almost every tree?机器学习简单essay未尝试免费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2578Why Tiny max_features Can Raise Bias 14Why can making max features too small hurt a random forest even though it lowers correlation?机器学习中等essay未尝试免费2579Infer Tree Correlation From the Variance Floor 23A single tree has variance 6, while an extremely large forest appears to level off at variance 1.8. What pairwise tree correlation rho is implied?机器学习中等数值题未尝试面试订阅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2581Why Random-Forest Regression Extrapolates Poorly 16Why does random-forest regression usually fail to extrapolate a trend far beyond the training range?机器学习简单essay未尝试免费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2591Why OOB Can Be Noisy on Small Samples 19Why can out-of-bag error fluctuate a lot on a small dataset even when the forest itself is reasonably stable?机器学习简单essay未尝试免费2592Effective Independent Tree Count 8Define B eff by matching the correlated-forest variance sigma 2 [rho + (1-rho)/B] to the variance sigma 2 / B eff of averaging independent trees. Derive B eff.机器学习简单derivation未尝试免费2593Why Averaging Cannot Cure Systematic Label Noise 20Why can a larger forest fail to repair performance when the training labels themselves are systematically corrupted?机器学习中等essay未尝试面试订阅2596Optimal Leaf Update Under Squared Loss 1In gradient boosting for squared error, a terminal region R is assigned one constant update gamma. Derive the gamma that minimizes sum i in R (r i-gamma) 2, where r i are the current residuals.机器学习简单derivation未尝试免费2597Weighted Region Update 2If observations in a boosting region R carry positive weights w i, derive the constant update gamma that minimizes sum i in R w i (r i-gamma) 2.机器学习简单derivation未尝试免费2598Final Prediction After Three Boosting Rounds 23A boosting model starts from F 0(x)=10. For one observation, the leaf updates along its path are +1.2, -0.5, and +0.8 across three rounds, with learning rate eta=0.1 each round. What is the final prediction?机器学习中等数值题未尝试免费