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1777Lasso Threshold Calibration 2A standardized lasso fit has absolute score magnitudes (3.8, 2.5, 0.9). What is the smallest lambda that zeroes the weakest feature while leaving the other two still active?统计简单essay未尝试免费1787Ridge Effective Degrees of Freedom 2A standardized ridge model has singular-value squares d j 2 = [16, 4] and penalty lambda = 4. What is the effective degrees of freedom tr(S lambda) = sum d j 2/(d j 2+lambda)?统计中等derivation未尝试免费1794Duplicate Feature Under Pure LassoIf two predictors are exactly identical and the model uses pure Lasso, what modeling pathology should you expect?统计中等essay未尝试免费1845ARMA Identification or Simplification 5You observe the diagnostic statement: (1-0.5L) X t = (1-0.5L) e t. What is the correct modeling conclusion?统计困难essay未尝试面试订阅2396Variance of an Equal-Weight Correlated EnsembleFive base models each have prediction variance 4, and every pair of model predictions has correlation 0.25. If you average the five predictions equally, what is the ensemble variance?机器学习简单derivation未尝试免费2397Sample Size Crossover Between Two Model FamiliesModel A has excess test MSE 0.04 + 18/n, while model B has excess test MSE 0.16 + 4/n, where n is sample size. At what sample size do they tie?机器学习简单derivation未尝试免费2398Bias Budget Implied by a Variance ReductionA regularization change reduces a model's variance term from 0.30 to 0.11 while leaving irreducible noise unchanged. How much extra bias squared could you add before the total MSE stops improving?机器学习中等derivation未尝试免费2399Optimal Weight on a Noisy Unbiased ModelModel A is unbiased with variance 9. Model B has variance 1.44 and fixed bias 0.6. If you blend them as P w = wA + (1-w)B and treat their errors as independent, what weight w minimizes MSE?机器学习困难derivation未尝试面试订阅2400How Many Independent Fits to Hit a Variance TargetEach independently trained model has variance 2.4 and negligible bias. How many equally weighted independent fits must you average to bring the variance term below 0.3?机器学习中等derivation未尝试免费2401Total Error After the Dataset QuadruplesA model currently has bias 2 = 0.09, variance = 0.24, and irreducible noise = 0.50. If quadrupling the dataset quarters the variance term while leaving the other two terms unchanged, what is the new test MSE?机器学习简单derivation未尝试免费2402Second Crossover With a Lower-Bias Flexible ModelA flexible model has excess error 0.02 + 24/n, while a simpler model has excess error 0.14 + 6/n. At what sample size do they tie?机器学习中等derivation未尝试面试订阅2403Variance of a Correlated Five-Model CommitteeFive models each have variance 1.6 and pairwise correlation 0.4. What is the variance of their equal-weight average?机器学习中等derivation未尝试免费2404Data Multiplier Needed to Push Variance Below a Noise Floor FractionA model's variance term is currently 0.30, and irreducible noise is 0.05. If variance scales exactly like 1/n, by what factor must the dataset grow so the variance term falls to 0.05?机器学习中等derivation未尝试面试订阅2405Recover the Irreducible NoiseA model has test MSE 0.92, bias 2 0.15, and variance 0.27. What irreducible noise term is implied?机器学习简单数值题未尝试面试订阅2406Choose the Better Model at a Given Sample SizeAt sample size n=60, compare model A with excess error 0.04 + 12/n to model B with excess error 0.16 + 2/n. Which one has smaller excess test error?机器学习简单数值题未尝试免费2407Improvement in Excess Error From a Regularization MoveA regularization change raises bias 2 from 0.03 to 0.07 but cuts variance from 0.22 to 0.08. By how much does excess test error improve?机器学习简单数值题未尝试免费2408Variance of a Three-Model Independent AverageThree independently trained models each have variance 1.8 and negligible bias. What is the variance of their equal-weight average?机器学习简单数值题未尝试面试订阅2409Why More Data Usually Helps a Variance-Dominated Model FirstWhy does collecting more data usually help a high-variance model more than a high-bias model?机器学习困难essay未尝试面试订阅2410Why Regularization Can Raise Train Error but Lower Test ErrorWhy is it perfectly consistent for regularization to worsen train fit but improve out-of-sample MSE?机器学习中等essay未尝试面试订阅2411Why Feature Expansion Can Worsen Test Error Without Adding SignalWhy can adding many flexible features worsen test error even if the true predictive signal has not changed at all?机器学习简单essay未尝试免费