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4191Hyperplane Score and Margin 1Using the polynomial kernel K(x,z)=(x·z+1) 2, what is K((1,2),(2,0))?机器学习中等数值题未尝试面试订阅4192Hyperplane Score and Margin 2An RBF SVM uses K(x,z)=exp(-γ||x-z|| 2) with γ=0.5. If ||x-z|| 2=4, what kernel similarity is produced?机器学习中等数值题未尝试面试订阅4193Hyperplane Score and Margin 3For a soft-margin SVM, a training point has label y=1 and score f(x)=0.3. What hinge loss max(0,1-yf(x)) does it incur?机器学习中等数值题未尝试面试订阅4194Hyperplane Score and Margin 4A soft-margin SVM uses objective 0.5||w|| 2 + C Σ hinge i. If one point has hinge loss 1.2 and C=2, what penalty contribution does that point add to the objective?机器学习中等数值题未尝试面试订阅4195Hyperplane Score and Margin 5If a linear SVM has ||w||=5, what is the geometric margin width 2/||w||?机器学习中等数值题未尝试面试订阅4196Kernel Decision Function Evaluation 1A kernel SVM prediction uses two support vectors. Their signed contributions at a test point are +1.2 and -0.4, and the bias is -0.1. What score and predicted class result?机器学习中等数值题未尝试面试订阅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