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4198Kernel Decision Function Evaluation 3Using the degree-3 polynomial kernel K(x,z)=(x·z+1) 3, what is K((1,1),(2,-1))?机器学习中等数值题未尝试面试订阅4201Polynomial KernelA soft-margin SVM sees y f(x) values [1.4, 0.8, -0.3, 1.0] on four points. Which points actively enter the hinge-loss term because they are strictly inside the margin or misclassified?机器学习中等derivation未尝试面试订阅4202Antisymmetric PseudokernelThree separating hyperplanes all classify the training set correctly, but their ||w|| values are 2.0, 4.0, and 1.6. Which one has the widest geometric margin?机器学习中等derivation未尝试面试订阅4203RBF KernelModel A has ||w|| 2=1.0 and total hinge loss 3.0. Model B has ||w|| 2=4.0 and total hinge loss 0.5. If C=0.2, which SVM objective is smaller?机器学习中等derivation未尝试面试订阅4204Negative Linear FormIn an SVM dual solution, one training point has α i=0.4 with C=1.0. What does that suggest about the point's role relative to the margin?机器学习中等derivation未尝试面试订阅4206Higher C in a Noisy DatasetAn RBF kernel uses distance squared 2. If γ doubles from 0.5 to 1.0, by what factor does the kernel similarity change?机器学习中等derivation未尝试面试订阅4207Smaller C and Margin ToleranceA degree-2 polynomial kernel is K=(x·z+1) 2. If x·z increases from 1.0 to 1.5, by what percentage does K increase?机器学习中等derivation未尝试面试订阅4208Larger Gamma in an RBF KernelA soft-margin SVM keeps ||w|| 2 and total hinge loss fixed, but C increases from 0.5 to 1.5 while total hinge loss is 2.0. How much does the objective increase?机器学习中等derivation未尝试面试订阅4209Smaller Gamma in an RBF KernelAt a test point, one support vector contributes +0.9. If its dual coefficient is halved and everything else stays fixed, what contribution remains from that support vector?机器学习中等derivation未尝试面试订阅4210When Kernels Beat Manual Feature LiftsA linear SVM score at a point is 1.2 before feature rescaling. If the relevant feature values are all doubled while w is held fixed, what new score contribution comes from that linear term?机器学习中等derivation未尝试面试订阅4211Why Only Support Vectors Matter at Prediction TimeIf your features are extremely sparse one-hot indicators with huge dimension, would you usually try a linear SVM or an RBF SVM first, and why?机器学习中等essay未尝试面试订阅4212Why the Dual Is Attractive in Kernel SVMsWhy is feature scaling especially important before using an RBF SVM?机器学习中等essay未尝试面试订阅4213Why Hard Margin Is FragileWhy do only support vectors matter at prediction time in an SVM?机器学习中等essay未尝试面试订阅4214Why Kernels Are Not FreeWhy can choosing C extremely large increase overfitting risk in a soft-margin SVM?机器学习中等essay未尝试面试订阅4215A Fast Sanity Check for Kernel-SVM AnswersWhy can a high-degree polynomial kernel become numerically and statistically awkward on unscaled features?机器学习中等essay未尝试面试订阅4216Normalized MDI Share 1A random forest reports total mean-decrease-in-impurity contributions spread=0.42, imbalance=0.21, id bucket=0.07. What are the normalized importance shares, and which feature ranks first?机器学习简单数值题未尝试面试订阅4217Normalized MDI Share 2A model has baseline validation AUC 0.62. After permuting three features separately, AUC becomes 0.57 for value signal, 0.60 for momentum, and 0.61 for zip code. What permutation-importance drops do these imply, and which feature ranks first?机器学习简单数值题未尝试面试订阅4218Normalized MDI Share 3A sector feature is represented by three one-hot columns with impurity-gain importances 0.04, 0.03, and 0.01. Two other features have importances 0.05 and 0.07. If you aggregate the one-hot block into a single group, what are the normalized group shares and which group ranks first?机器学习简单数值题未尝试面试订阅4219Normalized MDI Share 4Two trees contribute split gains to features A and B. Tree 1 contributes A=12, B=5. Tree 2 contributes A=8, B=10. What are the total normalized gain importances for A and B?机器学习简单数值题未尝试面试订阅4220Normalized MDI Share 5A model has baseline log loss 0.400. After permuting feature X, log loss rises to 0.455; after permuting feature Y, it rises to 0.420. What are the permutation importances under a log-loss metric, and which feature is more important?机器学习简单数值题未尝试面试订阅