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GATE DA 2025 Set 1 — Question 22

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MCQ+1 / -0.33MediumClassificationMachine Learning

Machine Learning → Classification

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Consider designing a linear classifiery=sign(f(x;w,b)),f(x;w,b)=w⊤x+by = \text{sign}(f(x;w, b)), \quad f(x;w, b) = w^\top x + bon a dataset D={(x1,y1),(x2,y2),…,(xN,yN)}D = \{(x_1, y_1),(x_2, y_2), \dots ,(x_N, y_N)\}, xi∈Rdx_i \in \mathbb{R}^d, yi∈{+1,−1}y_i \in \{+1, -1\}, i=1,2,…,Ni = 1, 2, \dots, N. Recall that the sign function outputs +1+1 if the argument is positive, and −1-1 if the argument is non-positive. The parameters ww and bb are updated as per the following training algorithm:wnew=wold+ynxn,bnew=bold+ynw_{new} = w_{old} + y_n x_n, \quad b_{new} = b_{old} + y_nwhenever sign(f(xn;wold,bold))≠yn\text{sign}(f(x_n;w_{old}, b_{old})) \neq y_n. In other words, whenever the classifier wrongly predicts a sample (xn,yn)(x_n, y_n) from the dataset, woldw_{old} gets updated to wneww_{new}, and likewise boldb_{old} gets updated to bnewb_{new}. Consider the case (xn,+1)(x_n, +1), f(xn;wold,bold)<0f(x_n;w_{old}, b_{old}) < 0. Then
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