Transcription of Logistic Regression - Carnegie Mellon University
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Chapter 12 Logistic Modeling Conditional ProbabilitiesSo far, we either looked at estimating the conditional expectations of continuousvariables (as in Regression ), or at estimating distributions. There are many situationswhere however we are interested in input-output relationships, as in Regression , butthe output variable is discrete rather than continuous. In particular there are manysituations where we have binary outcomes (it snows in Pittsburgh on a given day, orit doesn t; this squirrel carries plague, or it doesn t; this loan will be paid back, orit won t; this person will get heart disease in the next five years, or they won t).
12.2.1 Likelihood Function for Logistic Regression Because logistic regression predicts probabilities, rather than just classes, we can fit it using likelihood. For each training data-point, we have a vector of features, x i, and an observed class, y i. The probability of that class was either p, if y i =1, or 1− p, if y i =0. The likelihood ...
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