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Chapter 4. Linear Models for Classification Wei Pan Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455 Email: weip@biostat.umn.edu PubH 7475/8475 Wei Pan c Linear Model and Least Squares

Chapter 4. Linear Models for Classification Wei Pan Division of Biostatistics, School of Public Health, University of Minnesota, Minneapolis, MN 55455 Email: weip@biostat.umn.edu PubH 7475/8475 � Wei Pan c
Linear Model and Least Squares ◮ Data: ( Y i , X i ), X i = ( X i 1 , ..., X ip ) ′ , i = 1 , ..., n . Y i : categorical with K classes; often K = 2. ◮ LM: defined y k = I (class k ), f k ( x ) = E ( y k | x ) = Pr ( G = k | x ) = β 0 k + β ′ k x ◮ Dedcision boundary: f k ( x ) = f l ( x ), linear ◮ Use LSE ◮ Is it ok to use LM? Yes, but ...masking ◮ can be formulated as multivariat/multiple response LM.

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