Statistical Models of Dependencies
In the models and data-generating processes we have considered in previous chapters of Part IV, all of the variables or features were treated essentially in the same way. In this chapter, we consider models in which a subset of variables, often just one, is of special interest. This variable is the “response”, and we seek to understand its dependence on the other variables. “Dependence” here refers to a stochastic relationship, not a causal one. By knowing the relationship of the other variables to the response variable, we may better understand the data-generating process, or we may be able to predict the response, given the values of the associated variables. The models we consider in this chapter describe the stochastic behavior of one variable, Y , possibly a vector, as a function of other variables. Models of this type that express dependencies are called regression models if Y is a numeric variable or classification models if Y is a categorical variable. If Y is a numeric variable that takes on only a countable number of values, the model can be considered either a regression model (sometimes a “generalized model”) or a classification model.
KeywordsFeature Space Variable Selection Terminal Node Random Component Ridge Regression
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