In linguistics, regularization is the process of making irregular forms regular (e.g., "oxen" becomes "oxes;" "grew" becomes "growed"). In physics, especially quantum field theory, regularization is a method of dealing with infinite, divergent, and non-sensical expressions by introducing an auxiliary concept of a regulator (for example, the minimal distance in space which is useful if the divergences arise from short-distance physical effects). ... In mathematics, inverse problems are often ill-posed. ... The term regularization in machine learning refers to the various measures which may be used to prevent overfitting of data by models, most of which implicitly or explicitly penalize models based on the number of parameters they employ. ...
Regularization is also the act of giving legal residency and identity documents to an illegal alien. See also naturalization (acquiring a new nationality). Residency is a stage of postgraduate medical training in North America which leads to eligibility for board certification in a primary care or referral specialty. ... China ID card, front (top) back (bottom). ... It has been suggested that this article or section be merged into illegal immigration. ... Naturalization is the act whereby a person voluntarily and actively acquires a nationality which is not his or her nationality at birth. ...
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Although at first the choice of the solution to this regularized problem may look artificial, and indeed the parameter α seems rather arbitrary, the process can be justified in a Bayesian point of view.
This demonstrates the effect of the Tikhonov parameter on the condition number of the regularized problem.