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The phenomenon is of particular interest in deep neural networks, but is studied from a theoretical perspective in the context of much simpler models, such as linear regression. In particular, it has been shown that overparameterization is essential for benign overfitting in this setting. In other words, the number of directions in parameter ...
In machine learning, a key challenge is enabling models to accurately predict outcomes on unseen data, not just on familiar training data.Regularization is crucial for addressing overfitting—where a model memorizes training data details but can't generalize to new data.
Bayesian linear regression can also be used, which by its nature is more or less immune to the problem of overfitting. (In fact, ridge regression and lasso regression can both be viewed as special cases of Bayesian linear regression, with particular types of prior distributions placed on the regression coefficients.)
In statistics, the one in ten rule is a rule of thumb for how many predictor parameters can be estimated from data when doing regression analysis (in particular proportional hazards models in survival analysis and logistic regression) while keeping the risk of overfitting and finding spurious correlations low. The rule states that one ...
Overfitting occurs when the learned function becomes sensitive to the noise in the sample. As a result, the function will perform well on the training set but not perform well on other data from the joint probability distribution of x {\displaystyle x} and y {\displaystyle y} .
The bias–variance decomposition forms the conceptual basis for regression regularization methods such as LASSO and ridge regression. Regularization methods introduce bias into the regression solution that can reduce variance considerably relative to the ordinary least squares (OLS) solution. Although the OLS solution provides non-biased ...
When fitting models, it is possible to increase the maximum likelihood by adding parameters, but doing so may result in overfitting. Both BIC and AIC attempt to resolve this problem by introducing a penalty term for the number of parameters in the model; the penalty term is larger in BIC than in AIC for sample sizes greater than 7.
Double descent occurs in linear regression with isotropic Gaussian covariates and isotropic Gaussian noise. [11] A model of double descent at the thermodynamic limit has been analyzed using the replica trick, and the result has been confirmed numerically. [12]