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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36 votes
7 answers

Why is using squared error the standard when absolute error is more relevant to most problems? [duplicate]

I recognize that parts of this topic have been discussed on this forum. Some examples: Is minimizing squared error equivalent to minimizing absolute error? Why squared error is more popular than the ...
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13 votes
2 answers

How to solve least absolute deviation by simplex method?

Here is the least absolute deviation problem under concerned: $ \underset{\textbf{w}}{\arg\min} L(w)=\sum_{i=1}^{n}|y_{i}-\textbf{w}^T\textbf{x}|$. I know it can be rearranged as LP problem in ...
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3 votes
1 answer

$R^2$ for least absolute deviation regression

I know that $R^2$ is for the least square regression. Is there an analogous measure of fit to $R^2$ in LAD (Least Absolute Deviations) regression? Here I am concerned with the "fitting quality".
12 votes
2 answers

Residual using absolute loss linear regression

For ordinary least square linear regression, we have sum of residuals as zero, what about the sum of residuals for linear regression calculated using absolute loss?
  • 1,037
8 votes
1 answer

When does Least Square Regression (LSQ) line equal to Least Absolute Deviation (LAD) line?

I have the following question at hand. Suppose $(x_1,y_1),(x_2,y_2),\cdots,(x_{10},y_{10})$ represents a set of bi-variate observations on $(X,Y)$ such that $x_2=x_3=\cdots =x_{10}\ne x_1.$ Under ...
  • 1,237
4 votes
3 answers

Is there any library for least absolute deviation (LAD) regression with regularization terms?

We know that LASSO and ridge and ElasticNet all apply regularization terms on the coefficients of least squares regression. However, I have not yet found any R / python libraries that compute ...
  • 41
3 votes
1 answer

Reference for doing linear regression with mean absolute deviation?

I am looking for a resource that goes over how to derive the coefficients for a linear regression model while minimizing the mean absolute deviation. I am hoping for both a mathematical and ...
  • 2,613
3 votes
0 answers

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 ...
  • 1,021
2 votes
4 answers

How regression trees split, when all the Features and target have only continuous values

Can anyone please explain how splitting is performed in regression trees when we only have continuous features. I have referred to different papers, but all I could find is formulas or theorems. Can ...
  • 21
1 vote
0 answers

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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