Structural risk minimization (SRM) is an inductive principle of use in machine learning.
Commonly in machine learning, a generalized model must be selected from a finite data set, with the consequent problem of overfitting – the model becoming too strongly tailored to the particularities of the training set and generalizing poorly to new data.
The SRM principle addresses this problem by balancing the model's complexity against its success at fitting the training data.
This principle was first set out in a 1974 book[1] by Vladimir Vapnik and Alexey Chervonenkis and uses the VC dimension.
In practical terms, Structural Risk Minimization is implemented by minimizing
is the train error, the function
is called a regularization function, and
is chosen such that it takes large values on parameters
that belong to high-capacity subsets of the parameter space.
in effect limits the capacity of the accessible subsets of the parameter space, thereby controlling the trade-off between minimizing the training error and minimizing the expected gap between the training error and test error.
[2] The SRM problem can be formulated in terms of data.
The first term is the mean squared error (MSE) term between the value of the learned model,
This term is the training error,
The second term, places a prior over the weights, to favor sparsity and penalize larger weights.
, is a hyperparameter that places more or less importance on the regularization term.
encourages sparser weights at the expense of a more optimal MSE, and smaller
relaxes regularization allowing the model to fit to data.
, the model typically suffers from overfitting.
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