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2439Why Asymmetric Loss Moves the Target Away From the MeanWhy does an asymmetric loss generally make the optimal constant prediction move away from the mean of the target distribution?机器学习困难essay未尝试面试订阅2475Why Duplicate Features Cause Non-Unique Coefficients 5Why do two perfectly duplicated features make the OLS coefficient vector non-unique even though fitted predictions can stay unique?机器学习困难essay未尝试面试订阅2479Why Multicollinearity Hurts Coefficient Stability More Than Fit 10Why can severe multicollinearity make coefficients unstable even when training predictions barely change?机器学习中等essay未尝试面试订阅2480Orthogonal Features Give Coordinatewise Coefficients 9Suppose two features x1 and x2 are centered and orthogonal. Derive the OLS coefficients in terms of x1 T y, x2 T y, ||x1|| 2, and ||x2|| 2.机器学习困难derivation未尝试面试订阅2490Why OLS Can Still Predict Well Under Misspecification 20Why can OLS remain a useful predictor even when the true data-generating process is not exactly linear?机器学习困难essay未尝试面试订阅2492Why Feature Scaling Helps Gradient Descent More Than Closed Form 22Why is feature scaling often crucial for gradient-descent training of OLS even though the closed-form solution itself is scale-equivariant?机器学习简单essay未尝试免费2499Soft-Thresholded Lasso Coefficient 4In an orthogonal one-feature problem with x T x = d and x T y = z > 0, derive the lasso coefficient when 0 < lambda < z.机器学习中等derivation未尝试面试订阅2506Why Standardization Matters for Lasso 8Why can lasso unfairly prefer one feature over another if raw feature scales are left unstandardized?机器学习简单essay未尝试免费2508Why Elastic Net Keeps the Lasso Threshold but Adds Ridge Shrinkage 14Why does elastic net still need |z| to clear an L1 threshold before a coordinate activates, but then shrink the active coefficient more than lasso does?机器学习中等derivation未尝试面试订阅2510Zero Lambda Recovers OLS 16Why do ridge and lasso both reduce to OLS when their regularization parameter is set to zero?机器学习困难derivation未尝试面试订阅2511Why L1 Produces Corners and Corners Produce Sparsity 11Why is the geometry of the L1 ball often used to explain why lasso creates sparse solutions?机器学习简单essay未尝试免费2513Why Correlated Features Frustrate Pure Lasso 17Why does pure lasso often behave erratically when several features are highly correlated and similarly predictive?机器学习中等essay未尝试面试订阅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