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lecture11-vector-classify-handout-6-per

# In general lots of possible solutions for abc 31

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Unformatted text preview: s low variance and high bias.   Decision surface has to be linear (hyperplane – see later)   Consider asking a botanist: Is an object a tree?   Too much capacity/variance, low bias   Botanist who memorizes   Will always say “no” to new object (e.g., diﬀerent # of leaves)   Not enough capacity/variance, high bias   Lazy botanist   Says “yes” if the object is green   You want the middle ground Introduc)on to Informa)on Retrieval (Example due to C. Burges) 27 Sec.14.4 Linear classiﬁers and binary and mul)class classiﬁca)on 28 Introduc)on to Informa)on Retrieval Sec.14.4 Separa)on by Hyperplanes   A strong high ­bias assump)on is linear separability:   in 2 dimensions, can separate classes by a line   in higher dimensions, need hyperplanes   Can ﬁnd separa)ng hyperplane by linear programming   Consider 2 class problems   Deciding between two classes, perhaps, government and non ­government   One ­versus ­rest classiﬁca)on   How do we deﬁne (and ﬁnd) the separa)ng surface?   How do we decide which region a test doc is in? 29 (or can itera)vely ﬁt solu)on via perceptron):   separator can be expressed as ax + by = c 30 5 Sec.14.4 Introduc)on to Informa)on Retrieval Linear programming / Perceptron Sec.14.4 Introduc)on to Informa)on Retrieval Which Hyperplane? Find a,b,c, such that ax + by > c for red points ax + by < c for blue points. In general, lots of possible solutions f...
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