人工智能教学资料 5ai Classification part3.pdfVIP

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人工智能教学资料 5ai Classification part3.pdf

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Artificial Intelligence Classification Yanghui Rao Assistant Prof., Ph.D School of Mobile Information Engineering, Sun Yat-sen University Artificial Intelligence: Classification Logistic Regression Model ? If using the ordinary least squares (OLS) regression ? The error terms u are heteroskedastic ? u is not normally distributed because y takes on only two values ? The predicted probabilities can be greater than 1 or less than 0 0 1 T d j j j y w w x u ? ? ? ? ? ? W X? ? Artificial Intelligence: Classification Logistic Regression Model AGE (years) S ig n s o f c o ro n a ry d is e a s e No Yes 0 20 40 60 80 100 Artificial Intelligence: Classification Logistic Regression Model ? The logistic distribution constrains the estimated probabilities to lie between 0 and 1. ? The estimated probability p(y=1|X) is: ? if you let , then p = 0.5 ? as gets really big, p approaches 1 ? as gets really small, p approaches 0 0 1 0 0 1 1 T T T + + 1 = 1 1+ 1 1 1 d j j j d d j j j j j j w w x w w x w w x e p e e e e e ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? W X W X W X ? ? ? ? ? ? 0 1 + =0 d j j j w w x ? ? 0 1 + d j j j w w x ? ? 0 1 + d j j j w w x ? ? Artificial Intelligence: Classification Logistic Regression Model 0 1 LR Model Logit Model Artificial Intelligence: Classification Logistic Regression Model ? The logit model solves these problems: ? p is the probability that the event y occurs, p(y=1|X) ? p/(1-p) is the odds ratio (e.g., odds of disease) ? log[p/(1-p)] is the log odds ratio, or logit 0 1 T log 1 d j j j p w w x u p ? ? ? ? ? ?? ? ?? ? ? ? W X? ? Artificial Intelligence: Classification Logistic Regression Model ? Recall that OLS Regression could utilized an “ordinary least squares” formula to create the “linear model” we used. ? The Logistic Regression model will be constructed by an iterative maximum likelihood procedure. ? This is a computer dependent program that: ? starts with arbitrary values of the regression coefficients and constructs an initial model for predicting t