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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.

Tikhonov regularization adds a regularization term to solve problems whose integrals are ill-posed, specifically for Fredholm integral equations of the first kind. The relationship to ridge regression is given here.

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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?
Carl
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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 turn up the history/background of the term…
Matthew Drury
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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, among others; in the case of Dropout it was a…
SQLServerSteve
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Tikhonov regularization equivalence to adding random noise

In Pattern Recognition and Machine Learning Ch 5.5.5 Bishop derives a regulariser for neural networks that is equivalent to the tangent propagation regulariser (a regulariser that is invariant to certain types of transformations). The regularisation…
tail_recursion
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Ridge regularization - intuition behind $\lambda$

I have seen many similar questions and I understand that $\lambda$ is some kind of a tuning parameter that decides how much we want to penalize the flexibility of our model. In other words $\lambda$ helps us decide how badly we want a perfect fit…
bajun65537
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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) +…
Nick L
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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? Also, can you explain briefly what it is?
RockTheStar
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Entropy regularization versus L2 norm regularization?

In multiple regression problems, the decision variable, coefficients $\beta$, can be regularized by its L2 (Euclidean) norm, shown below (in the second term) for least squares regression. This type of regularization reduces overfitting by reducing…
develarist
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Trace of the Hat Matrix in Ridge Regression

Generally, I know that the trace of the hat matrix ($H$) is equal to the rank of H since it is an orthogonal projection. If I wanted to show the trace of $H$ in ridge regression, would I be able to somehow prove that it equals the degrees of…
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Why we only use L1 and L2 in penalized regression

I understand we do not want to go lower than 1 because the problem is no longer convex. But why not use L3 for example? Is there any reason why L2 is so popular but not higher norm?
user3661376
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$L^2$ Regularization and Hessian Matrix

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 ?
Daksitha Withanage
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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 $x = (A^TA + \alpha I)^{-1}A^Tb$ -- corresponding to eq.2 below…
Cagdas Ozgenc
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Finite difference based regularization matrix

I've just started reading about Tikhonov Regularization. Would someone please help with a simple numerical example of a case where regularization matrix of the form of a second order finite difference (tridiagonal matrix with 1,-2 and 1 at…
user2696565
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effect of multiplying by Tikhonov regularization factor after an inverse?

I came across a repository which uses Tikhonov regularization to compute an inverse, but then in the inference step they multiply by the Tikhonov factor again... Compute $\Phi\Phi^T$ Compute the inverse $(\Phi\Phi^T + \lambda I)^{-1}$ Use the…
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Explain L1 vs. L2 regularization difference using the scientific mindset

I need to have job interview soon, one of the questions may be L1. vs L2 regularization. Yann LeCun explained best to my knowledge the difference between L1 and L2 regularization. L1 or Lasso: Weights are shrunk every iteration towards zero by a…
Nabuko
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