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In artificial neural networks, the variance increases and the bias decreases as the number of hidden units increase, [12] although this classical assumption has been the subject of recent debate. [4] Like in GLMs, regularization is typically applied. In k-nearest neighbor models, a high value of k leads to high bias and low variance (see below).
This is known as the bias–variance tradeoff. Keeping a function simple to avoid overfitting may introduce a bias in the resulting predictions, while allowing it to be more complex leads to overfitting and a higher variance in the predictions. It is impossible to minimize both simultaneously.
But if the learning algorithm is too flexible, it will fit each training data set differently, and hence have high variance. A key aspect of many supervised learning methods is that they are able to adjust this tradeoff between bias and variance (either automatically or by providing a bias/variance parameter that the user can adjust).
In statistics, the bias of an estimator (or bias function) is the difference between this estimator's expected value and the true value of the parameter being estimated. An estimator or decision rule with zero bias is called unbiased. In statistics, "bias" is an objective property of an estimator.
The bias–variance tradeoff is often used to overcome overfit models. With a large set of explanatory variables that actually have no relation to the dependent variable being predicted, some variables will in general be falsely found to be statistically significant and the researcher may thus retain them in the model, thereby overfitting the ...
This is known as the bias–variance tradeoff. Ensemble averaging creates a group of networks, each with low bias and high variance, and combines them to form a new network which should theoretically exhibit low bias and low variance. Hence, this can be thought of as a resolution of the bias–variance tradeoff. [4]
In general, the method provides improved efficiency in parameter estimation problems in exchange for a tolerable amount of bias (see bias–variance tradeoff). [ 4 ] The theory was first introduced by Hoerl and Kennard in 1970 in their Technometrics papers "Ridge regressions: biased estimation of nonorthogonal problems" and "Ridge regressions ...
The majority of the arguments of how to bound the empirical process rely on symmetrization, maximal and concentration inequalities, and chaining.