BACKFITTING Meaning and
Definition
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Backfitting is a statistical method used in regression analysis and machine learning to iteratively estimate the parameters of a model by updating them based on the residuals from previous iterations. It involves fitting one component of the model while keeping the others fixed, and then updating the values of the fixed components based on the residuals obtained from that fit. This process is repeated until convergence is achieved.
The backfitting algorithm is commonly used in additive regression models, where the response variable is approximated as a sum of smoothly varying functions of the predictor variables. These functions are typically estimated using generalized additive models (GAMs), where each function is represented by basis functions and associated unknown coefficients.
The backfitting procedure iterates through each component of the model, fitting it to the data while holding all other components constant. The estimated values of the fixed components are updated based on the residuals obtained from the previous fit. This allows for a more flexible and non-parametric estimation of the functions in the model, as each component can be modeled independently.
Backfitting has proven to be computationally efficient and can be easily applied to a wide range of regression problems. It is particularly useful when dealing with large datasets or complex models, as it allows for a stepwise refinement of the estimates and provides a flexible framework for handling various types of data.
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