{ "key_pair_value_system": true, "answer_rating_count": "", "question_feedback_html": { "html_star": "", "html_star_feedback": "" }, "answer_average_rating_value": "", "answer_date_js": "2024-09-12T00:04:06-04:00", "answer_date": "2024-09-12 00:04:06", "is_docs_available": "", "is_excel_available": "", "is_pdf_available": "", "count_file_available": 0, "main_page": "student_question_view", "question_id": "10325416", "url": "\/study-help\/questions\/consider-a-binary-classification-problem-of-finding-the-binary-labels-10325416", "question_creation_date_js": "2024-09-12T00:04:06-04:00", "question_creation_date": "Sep 12, 2024 12:04 AM", "meta_title": "[Solved] Consider a binary classification problem | SolutionInn", "meta_description": "Answer of - Consider a binary classification problem of finding the binary labels y in { 1 , 1 } , for input examples of the form | SolutionInn", "meta_keywords": "binary,classification,problem,finding,labels,y,1,input,examples,form,x,times", "question_title_h1": "Consider a binary classification problem of finding the binary labels y in { 1 , 1 } , for input examples of the form x", "question_title": "Consider a binary classification problem of finding the binary labels y in", "question_title_for_js_snippet": "Consider a binary classification problem of finding the binary labels y in 1 , 1 , for input examples of the form x in R d times 1 We will use the following loss function which is based on margin m sy wT x y L ( m , w ) ( 0 5 m 2 for m 0 m Otherwise a For the case of d 2 i e x x 1 x 2 T , find the gradient of loss function wL ( m , w ) w r t unknown weight vector w w 1 w 2 T You may compute w 1 L ( m , w ) , and w 2 L ( m w ) and then stack them into the required gradient vector Please also note the following derivative rule that you may need 6 w f ( w ) f ( w ) f ( w ) w f ( w ) b Now, assume following training data having N 4 examples, is available 4 i Input xi Output yi 1 x 1 0 2 T y 1 1 2 x 2 0 1 T y 2 1 3 x 3 1 0 T y 3 1 4 x 4 1 0 T y 4 1 For the given loss function L ( m , w ) , and given training dataset, write down the average loss in terms of unknown weight vector w w 1 w 2 T as Lavg ( w ) 1 N XN i 1 L ( mi , w ) Compute the gradient vector of average loss Lavg ( w ) i e wLavg ( w ) w r t unknown weight vector w w 1 w 2 T c Starting from an initial weight vector w ( 0 ) 0 0 5 T , run single iteration of gradient descent algorithm to find w ( 1 ) with step size alpha 0 2 2 d Report the classification accuracy on the provided training data if you decide to use w ( 1 ) as your final weights for the model You can assume sign ( ) function as your activation function", "question_description": "