The impact of this is that we can no longer understand the predictions as a linear combination of the inputs as we can with linear regression, for example, continuing on from above, the model can be stated as: Logistic regression is a linear method, but the predictions are transformed using the logistic function. More on this later when we talk about making predictions. Note that the probability prediction must be transformed into a binary values (0 or 1) in order to actually make a probability prediction. We’re predicting probabilities? I thought logistic regression was a classification algorithm? Written another way, we are modeling the probability that an input (X) belongs to the default class (Y=1), we can write this formally as: the first class).įor example, if we are modeling people’s sex as male or female from their height, then the first class could be male and the logistic regression model could be written as the probability of male given a person’s height, or more formally:
Logistic regression models the probability of the default class (e.g. Logistic Regression Predicts Probabilities (Technical Interlude)
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Sample of the handy machine learning algorithms mind map. The actual representation of the model that you would store in memory or in a file are the coefficients in the equation (the beta value or b’s). Each column in your input data has an associated b coefficient (a constant real value) that must be learned from your training data. Where y is the predicted output, b0 is the bias or intercept term and b1 is the coefficient for the single input value (x). A key difference from linear regression is that the output value being modeled is a binary values (0 or 1) rather than a numeric value.īelow is an example logistic regression equation: Input values (x) are combined linearly using weights or coefficient values (referred to as the Greek capital letter Beta) to predict an output value (y). Logistic regression uses an equation as the representation, very much like linear regression. Representation Used for Logistic Regression Now that we know what the logistic function is, let’s see how it is used in logistic regression. Kick-start your project with my new book Master Machine Learning Algorithms, including step-by-step tutorials and the Excel Spreadsheet files for all examples. You do not need to have a background in linear algebra or statistics.
This post was written for developers interested in applied machine learning, specifically predictive modeling.
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