Questions tagged [tikhonov-regularization]

Tikhonov regularization, named for Andrey Tikhonov, is the most commonly used method of regularization of ill-posed problems, and is a generalization of ridge regression.

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2answers
9k views

Is Tikhonov regularization the same as Ridge Regression?

Tikhonov regularization and ridge regression are terms often used as if they were identical. Is it possible to specify exactly what the difference is?
28
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3answers
1k views

The origin of the term “regularization”

When I introduce concepts to my students, I often find it fun to tell them where the terminology originates ("regression", for example, is a term with an interesting origin). I haven't been able to ...
5
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1answer
1k views

Applying L1, L2 and Tikhonov Regularization to Neural Nets: Possible Misconceptions

I'm interested in applying several different types of regularization to neural nets and want to make sure I haven't learned the material incorrectly. I have successfully coded Weight Decay and Dropout,...
2
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1answer
1k views

Tikhonov regularization in the context of deconvolution

I came across "Tikhonov regularization" and I have bare knowledge on it. It seems that it is a type of regularization that is important for deconvolution. Are there any good resources and examples? ...
2
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0answers
80 views

$L^2$ Regularization and Hessian Matrix [duplicate]

In the second paragraph it is mentioned that eigenvector of $H$ is rescaled by a factor of $\frac{\lambda_i} {\lambda_i +\alpha}$ What exactly meant by that ?
2
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0answers
231 views

Difference Between Two Tikhonov Regularization Schemes

For the solution of $Ax = b$, where $A$ is a square matrix, what is the difference between these two regularized solutions: $x = (A + \alpha I)^{-1}b$ -- coressponding to eq.3 below $x = (A^TA + \...
1
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3answers
76 views

Why does $l_2$ norm regularization not have a square root?

Specifically talking about Ridge Regression's cost function since Ridge Regression is based off of the $l_2$ norm. We should expect the cost function to be: $$J(\theta)=MSE(\theta) + \alpha\sqrt{\...
1
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0answers
24 views

non-linear tikhonov/ridge regularization?

For traditional ridge regression, the loss function is $loss\_function = ||A\mathbf{x}-\mathbf{b}||_2^2 + ||\Gamma\mathbf{x}||_2^2$ https://en.wikipedia.org/wiki/Tikhonov_regularization Is there a ...
1
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0answers
62 views

Sequential Least Squares for Tikhonov Regularization [duplicate]

Given a Weighted Linear Least Squares problem where the cost function is given by: $$ J = { \left( x - H \Theta \right) }^{T} {C}^{-1} { \left( x - H \Theta \right) } $$ There is a Sequential ...
0
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1answer
73 views

Derivation of ridge regression for multi-value-target vectors

At university, I learned with these slides about ridge regression and its derivation with the assumption that the target- and predicted values have the dimensions $1\times1$. However, now I need to ...