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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2599Why Boosting Mostly Attacks Bias 9Why is boosting usually described as a bias-reduction method more than a variance-reduction method?机器学习中等essay未尝试免费2613L2-Regularized Region Update 7In one boosting region, choose a constant update gamma to minimize sum i in R (r i-gamma) 2 + lambda gamma 2. Let S = sum i in R r i and n = |R|. Derive gamma.机器学习困难derivation未尝试面试订阅2648Why Random k-Fold Is Invalid for Overlapping Rolling FeaturesWhy can random k-fold cross-validation be invalid when each feature vector uses a rolling 20-day history from a time series?机器学习简单essay未尝试免费2651Why Repeated CV Replicates Are Not Independent ExperimentsWhy should a practitioner be cautious about treating 20 repeated CV scores as if they were 20 independent experiments?机器学习简单essay未尝试免费2654Expected Number of Times a Point Is Validated in Repeated k-Fold CVIn R repeats of ordinary k-fold CV, each point appears in exactly one validation fold per repeat. Derive the number of validation appearances of one point across all repeats.机器学习中等derivation未尝试面试订阅2658Repeated Fold Inspection as a Tuning ChannelA researcher keeps examining which dates underperform in each fold and then adjusts features accordingly. Why is this still overfitting even if no formal hyperparameter optimizer is used?机器学习中等essay未尝试面试订阅2664How Many Distinct Hyperparameter Winners Can Outer CV ProduceA nested CV uses 7 outer folds and selects exactly one hyperparameter setting inside each outer fold. What is the maximum possible number of distinct winning hyperparameter settings across outer folds?机器学习困难derivation未尝试面试订阅2671Effective Breadth Under Common Factor CorrelationA researcher tracks 100 cross-sectional alpha sleeves whose pairwise correlation is approximately 0.20. Using the rough equal-correlation breadth proxy n eff =n/(1+(n-1) ), what is the effective number of independent bets?机器学习简单数值题未尝试免费2672Autocorrelation-Corrected Sample SizeA monthly feature is observed for 60 months and behaves roughly like an AR(1) series with lag-1 autocorrelation =0.6. Using the heuristic n eff \approx n(1- )/(1+ ), what is the effective sample size?机器学习简单数值题未尝试面试订阅2673Average Edge Across Opposing RegimesA signal earns +6 bps on 70% of days in calm markets and -10 bps on 30% of days in stressed markets. What is its unconditional average daily edge in bps?机器学习中等数值题未尝试面试订阅2676A Tiny Tail Probability Can Dominate Average PnLA strategy makes +0.04% on 98% of days and loses -2.5% on the remaining 2% of days. What is the unconditional average daily return?机器学习简单数值题未尝试免费2677Half-Life Discounting of Old Regime DataSuppose predictive relevance decays with a half-life of 6 months. Relative to current-regime data, what weight should you attach to observations that are 18 months old under this exponential-decay heuristic?机器学习中等derivation未尝试面试订阅2679Why Hundreds of Stocks Do Not Mean Hundreds of Independent LabelsWhy does a daily cross-sectional equity sample with hundreds of names still provide much less information than its row count suggests?机器学习中等essay未尝试面试订阅