Transcription of Logistic Regression
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Logistic Regression
Logistic RegressionLogistic RegressionJia LiDepartment of StatisticsThe Pennsylvania State UniversityEmail: jialiJia Li jialiLogistic RegressionLogistic RegressionPreserve linear classification the Bayes rule: G(x) = arg maxkPr(G=k|X=x).IDecision boundary between classkandlis determined by theequation:Pr(G=k|X=x) =Pr(G=l|X=x).IDivide both sides byPr(G=l|X=x) and take log. Theabove equation is equivalent tologPr(G=k|X=x)Pr(G=l|X=x)= Li jialiLogistic RegressionISince we enforce linear boundary, we can assumelogPr(G=k|X=x)Pr(G=l|X=x)=a(k,l)0+ p j=1a(k,l) Logistic Regression , there are restrictive relations betweena(k,l)for different pairs of (k,l).
Logistic Regression I The Newton-Raphson step is βnew = βold +(XTWX)−1XT(y −p) = (XTWX)−1XTW(Xβold +W−1(y −p)) = (XTWX)−1XTWz , where z , Xβold +W−1(y −p). I If z is viewed as a response and X is the input matrix, βnew is the solution to a weighted least square problem: βnew ←argmin β (z−Xβ)TW(z−Xβ) . I Recall that linear regression by least square is …
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