Nonlinear Transformation In these problems, we again apply Linear Regression for classification. Consider the target function: f(11, 12) = sign(ri+r3 -0.6) Generate a training set of N = 1000 points on x = (-1,1] x [-1,1] with a uniform probability of picking each x E X. Generate simulated noise by flipping the sign of the output in a randomly selected 10% subset of the generated training set. 8. Carry out Linear Regression without transformation, i.e., with feature vector: (1, 11, 12), to find the weight w. What is the closest value to the classification in sample error Ein? (Run the experiment 1000 times and take the average Ein to reduce variation in your results.) (a) o (b) 0.1 (c) 0.3 (d) 0.5 (e) 0.8 9. Now, transform the N = 1000 training data into the following nonlinear feature vector: (1,11,12,1112,11,13) (1) Find the vector w that corresponds to the solution of Linear Regression. Which of the following hypotheses is closest to the one you find? Closest here means agrees the most with your hypothesis (has the highest probability of agreeing on a randomly selected point). Average over a few runs to make sure your answer is stable. (a) g(11,12)=sign(-1 -0.0571 +0.08.12 +0.131112 +1.571 +1.5r3) (b) g(11, 12) =sign(-1 -0.05r +0.0812 +0.13r112 +1.57 + 15z) (c) g(11,12)=sign(-1 -0.05r1 +0.081, +0.131 12 + 1571 +1.5r3) (d) g(11, 12) =sign(-1 1.5r1 +0.0819 +0.131112 +0.05r; +0.0523) (e) g(11, 12) =sign(-1 -0.0571 +0.0812 +1.51112 +0.15r +0.15r) Nonlinear Transformation In these problems, we again apply Linear Regression for classification. Consider the target function: f(11, 12) = sign(ri+r3 -0.6) Generate a training set of N = 1000 points on x = (-1,1] x [-1,1] with a uniform probability of picking each x E X. Generate simulated noise by flipping the sign of the output in a randomly selected 10% subset of the generated training set. 8. Carry out Linear Regression without transformation, i.e., with feature vector: (1, 11, 12), to find the weight w. What is the closest value to the classification in sample error Ein? (Run the experiment 1000 times and take the average Ein to reduce variation in your results.) (a) o (b) 0.1 (c) 0.3 (d) 0.5 (e) 0.8 9. Now, transform the N = 1000 training data into the following nonlinear feature vector: (1,11,12,1112,11,13) (1) Find the vector w that corresponds to the solution of Linear Regression. Which of the following hypotheses is closest to the one you find? Closest here means agrees the most with your hypothesis (has the highest probability of agreeing on a randomly selected point). Average over a few runs to make sure your answer is stable. (a) g(11,12)=sign(-1 -0.0571 +0.08.12 +0.131112 +1.571 +1.5r3) (b) g(11, 12) =sign(-1 -0.05r +0.0812 +0.13r112 +1.57 + 15z) (c) g(11,12)=sign(-1 -0.05r1 +0.081, +0.131 12 + 1571 +1.5r3) (d) g(11, 12) =sign(-1 1.5r1 +0.0819 +0.131112 +0.05r; +0.0523) (e) g(11, 12) =sign(-1 -0.0571 +0.0812 +1.51112 +0.15r +0.15r)