PS#7

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California Lutheran University *

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IDS575

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Apr 3, 2024

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Q1 Generative vs Discriminative 24 Points Q1.1 5 Points For discriminative models, Which of the following probabilities would you use to best estimate whether or not to predict y given input X? Q1.2 5 Points Discriminative approaches do not work for multi-class classification problems. Q1.3 7 Points Select all correct about Generative models:  P ( X ∣ y ) P ( y )  P ( X ∣ y )  P ( y ∣ X )  P ( X , y )  P ( X ) P ( y ) True  False 

Q1.4 7 Points Select all examples of Discriminative Models: Q2 Parameter Estimation 29 Points Generative models predict the joint probability distribution – p(x,y)  Generative models work very well even on less training data Generative models are computationally expensive compared to discriminative models.  Generative models are useful for unsupervised machine learning tasks.  Generative models are impacted by the presence of outliers less than discriminative models. Generative models provide more ﬂexibility in introducing features. logistic regresson  decision tree  Support Vector Machines  k nearest neighbor 

Q2.1 7 Points The number of equality constraints in the design optimization problem can be (select all correct) Q2.2 5 Points Assume you have a program that prints one of the 3 labels A, B, C every time you run it. The distribution of the printed result of each run is P(A)=m, P(B)=m, P(C)=1-2m. Assume in a single trial, you run this program 15 times and observe 3 times of A, 1 time of B and 11 times of C in the printed outputs, according to MLE, what is the estimation of P(A)? Q2.3 10 Points subject to the constraint . Find the the optimum value of z subject to the given constraint. -3416.2666 larger than the number of variables less than the number of variables  equal the number of variables  1/15  2/15  1/6  1/5  z = x + 2 y − 2 5 xy + 4 + 2 y y = −2 x + 100

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Q2.4 7 Points For subject to , and is the solution of Lagrangian=0. Select all correct about constrained optimization: Q3 Soft Optimal Margin Classifer 12 Points Q3.1 5 Points If the data points are linearly separable, SVMs using a linear kernel will learn the same parameter regardless of the value of . Q3.2 7 Points Assume the purple line is the boundary of a soft-margin standard SVM where the points A, B, C are the support vectors. Choose ALL correct descriptions for individual points. maxf ( x , y ) g ( x , y ) = 0 ( x , y , λ ) ∗ ∗ ∗ ∇ The feasible region for an equality constraint is a subset of that for the same constraint expressed as an inequality  Standard design optimization model treats with “≤ type" and ≥ "type” inequality constraints. The optima solution found by making Lagrangian=0 is a global optima ∇ If at , then is a solution  ∇ f = x , y 0 ( x , y ) ∗ ∗ λ = ∗ 0 w ∗ C True  False 

slack of the point is equal to 0.  C slack of the point is equal to 1. C slack of the point is less than 1.  D 1 slack of the point is greater than 1. D 1 slack of the point is greater than 1. P slack of the point is greater than 0. L slack of the point is equal to 0. W slack of the point is greater than 1.  W slack of the point is greater than 2.  W

GRADED Problem Set (PS) #07 STUDENT Urvashiben Patel TOTAL POINTS 65 / 65 pts QUESTION 1 Generative vs Discriminative 24 / 24 pts 1.1 (no title) 5 / 5 pts 1.2 (no title) 5 / 5 pts 1.3 (no title) 7 / 7 pts 1.4 (no title) 7 / 7 pts QUESTION 2 Parameter Estimation 29 / 29 pts 2.1 (no title) 7 / 7 pts 2.2 (no title) 5 / 5 pts 2.3 (no title) R 10 / 10 pts 2.4 (no title) 7 / 7 pts QUESTION 3 Soft Optimal Margin Classifer 12 / 12 pts 3.1 (no title) 5 / 5 pts 3.2 (no title) 7 / 7 pts 

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