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Regularization: Regularization is a technique used to prevent overfitting by adding a penalty term to the loss function that discourages large parameter values. It can also be used to prevent underfitting by controlling the complexity of the model. [15] Ensemble Methods: Ensemble methods combine multiple models to create a more accurate ...
A regularization term (or regularizer) () is added to a loss function: = ((),) + where is an underlying loss function that describes the cost of predicting () when the label is , such as the square loss or hinge loss; and is a parameter which controls the importance of the regularization term.
It's easy to check that the logistic loss and binary cross-entropy loss (Log loss) are in fact the same (up to a multiplicative constant ()). The cross-entropy loss is closely related to the Kullback–Leibler divergence between the empirical distribution and the predicted distribution.
The form the population iteration, which converges to , but cannot be used in computation, while the form the sample iteration which usually converges to an overfitting solution. We want to control the difference between the expected risk of the sample iteration and the minimum expected risk, that is, the expected risk of the regression function:
Two very commonly used loss functions are the squared loss, () =, and the absolute loss, () = | |.The squared loss function results in an arithmetic mean-unbiased estimator, and the absolute-value loss function results in a median-unbiased estimator (in the one-dimensional case, and a geometric median-unbiased estimator for the multi-dimensional case).
[8] [9] The goal of cross-validation is to test the model's ability to predict new data that was not used in estimating it, in order to flag problems like overfitting or selection bias [10] and to give an insight on how the model will generalize to an independent dataset (i.e., an unknown dataset, for instance from a real problem).
In statistics, Mallows's, [1] [2] named for Colin Lingwood Mallows, is used to assess the fit of a regression model that has been estimated using ordinary least squares.It is applied in the context of model selection, where a number of predictor variables are available for predicting some outcome, and the goal is to find the best model involving a subset of these predictors.
Pruning reduces the complexity of the final classifier, and hence improves predictive accuracy by the reduction of overfitting. One of the questions that arises in a decision tree algorithm is the optimal size of the final tree. A tree that is too large risks overfitting the training data and poorly generalizing to new samples. A small tree ...