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2427Decision Threshold Under Asymmetric Classification CostA false negative costs 5 and a false positive costs 1. If p is the predicted probability of the positive class, above what threshold should you classify as positive?机器学习中等derivation未尝试面试订阅2428Weighted-Absolute-Loss Constant ForecastDemand Y takes values 0, 2, and 5 with probabilities 0.5, 0.3, and 0.2. Under a loss of 3(Y-a) + + 1(a-Y) +, what constant forecast a minimizes expected loss?机器学习中等derivation未尝试面试订阅2429Total Huber Loss on a Residual SetUsing Huber loss with delta = 1, compute the total loss on residuals 0.5, -1.2, and 3.0.机器学习中等数值题未尝试面试订阅2431Pseudo-Huber Gradient 8For pseudo-Huber loss ell(r)=delta 2(sqrt(1+(r/delta) 2)-1), derive d ell / d r.机器学习简单derivation未尝试免费2432Squared-Loss Bayes Act for a Discrete TargetY takes values 1, 1, 4, and 7 with equal probability. What constant forecast minimizes expected squared loss?机器学习简单derivation未尝试免费2435Why Log-Loss Punishes Overconfidence More Than Brier LossWhy does log-loss react much more harshly than Brier loss when a model assigns near-certainty to the wrong class?机器学习困难essay未尝试面试订阅2437Why Huber Sits Between Squared and Absolute LossWhy is Huber loss often described as sitting 'between' squared loss and absolute loss?机器学习中等essay未尝试面试订阅2438Why Convexity Makes Averaging Predictions SafeWhy does convexity of a loss function support the intuition that averaging similar predictors often cannot hurt too much?机器学习困难essay未尝试面试订阅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