Question

can you please solve the question ?

We try to solve the binary classification task ilustrated in the below figure with a simple linear log istic regression model Notice that the training data can be separated with zero training error with a linear separator. Consider training regularized linear logistic regression models where we try to maximize for very large . The regularization penalties used in penalized conditional lag likelihood estimation are -Cu, where(0,1.2). In other words, only one of the parameters is regularized in each case. Given the training data in the figure above, how does the training error change with regularization of each parameter ω,? State whether the training error increases or stays the same (zero) for each wj for very large C. Provide a brief justification for each of your (a) By regularizing w2 (b) By regularizing (c) By regularizing w

Answer 1

Ans. (a) By regularizing w2, for a large value of C value of w2 regularizes or decreases causing the approximated line to tend vertical and some part of both the classes remains on the same side of the line causing the training error to increase.

(b) Similarly by regularizing w1, for a large value of C value of w1 decreases causing the approximated line to tend horizontal and some part of both the classes remains on the same side of the line and the training error increases.

(c) By regularizing w0, for a large value of C approximated line remains inclined and the training error remains the same since both the classes can be easily distinguished.

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