# Questions tagged [least-absolute-deviations]

A regression that minimizes the sum of absolute errors (instead of the sum of squared errors).

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### Is there any geometric intuition on least absolute deviation regression?

There are a lot of geometric intuitions for regression with least square, e.g., projection, orthogonal, etc. (This and this answers are good examples.) Is there similar geometric intuition for least ...
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### Most efficient LAD solver

What is the most efficient way to solve linear Least absolute deviation regression problem? I know it can be solved using linear programming, is there a better/faster method? Edit: I'm interested ...
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### Interpretation of the least absolute deviations linear regression coefficient

In linear regression of $y$ onto $x$, one finds a $\beta_0$ and $\beta_1$ minimizing $\sum \|y - (\beta_1 x + \beta_0)\|^2$. One can show that $$\beta_1 = \rho(x,y) \frac{\sigma(y)}{\sigma(x)},$$ ...
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### Why is there no improvement when training Xgboost with pseudo-Huber loss?

In this StackOverflow post I asked if there was something wrong with my syntax when training an XGboost model (in R) with the native pseudo-Huber loss ...
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### Asymptotic for LAD - Problem 16, p.84 Van der Vaart

From Van der Vaart's Asymptotics Statistics, we have the derivation of the asymptotics for the least square regression (Example 5.27). Now, the problem 16 of the same section regards the asymptotics ...
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### Generalisation of Absolute Deviation and Least Squares Deviation: Statistical Use?

This linked answer defines Least Absolute Deviation (LAD) and Least Squares Deviation (LSD), as follows: $$LAD = \Sigma^n_{i=1} |y_i-f(x_i)|$$ And: $$LSD = \Sigma^n_{i=1} (y_i-f(x_i))^2$$ ...
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### Consistency of least absolute deviation estimator (LAD) vs OLS

If we know that OLS estimator of beta in linear regression model is unbiased and consistent and we don't have any further assumptions (on errors or anything), will LAD estimator of beta be also ...
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### Is it possible to force least absolute deviations (LAD) regression to return the 'median' value when infinite solutions are possible?

I have a problem where LAD regressions is not giving me a solution as the R package (L1pack) errors whenever there is an infinite number of possible solutions*. ...
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### Why is Coordinate Descent not used to solve Least Absolute Deviation?

I have recently been looking into why Least Absolute Deviation (LAD) is not used in place of OLS for machine learning, and it appears the primary reason is due to difficulty in computing a solution ...
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### Recover Primal Linear Programming Solution from Dual with LAD Regression?

This link discusses different ways of writing a classic LAD regression with a linear program. The classic way of writing LAD regression ($y = X \beta + r$) as a linear program is \...
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### Orthogonal regression that minimizes absolute error instead of squared error

Fitting a line through 3D points is usually done by orthogonal least squares (aka "total least squares"), i.e., by minimizing the mean squared orthogonal distance between the points and the ...
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### Regression coefficients while minimizing absolute error

I understand that we like working with square error instead of absolute error because it makes the calculus easy. But I was wondering about the parameters of Linear Regression minimized for absolute ...
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### well maintained lad-regression solution

https://www.real-statistics.com/multiple-regression/lad-regression/ I am trying to understand what is the best package (in R or python) for lad-regression. But the following one says "but least ...
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### Least Absolute Values Regression

I have the data: x <- c(0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0) y <- c(2.06, 2.12, 2.32, 2.02, 2.76, 3.04, 2.83, 3.15, 3.36, 3.68, 3.96) I ...
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### Bayesian least absolute deviations

Ordinary Least Squares have a bayesian equivalent. For instance, fitting the linear model $$y \sim a + bx + \epsilon$$ using OLS is equivalent to defining the following Bayesian linear model:  y \...
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