Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Questions tagged [least-absolute-deviations]

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

3
votes
0answers
34 views

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 ...
0
votes
0answers
48 views

Optimization options to minimize mean absolute error when model is a Neural network

Lately I've seen some advantages mostly in model generalization of minimizing an the mean absolute error (or I guess Laplacian MLE would be an equivalent way of saying it). I'm debating first on what ...
1
vote
1answer
40 views

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 ...
6
votes
0answers
140 views

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 ...
3
votes
0answers
126 views

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 $$\beta_1 = \rho(x,y) \frac{\sigma(y)}{\sigma(x)},$$ ...
1
vote
1answer
355 views

Can I use gradient descent for Least Absolute Deviation Regression?

I've read in some posts that the absolute function is not differentiable. However, it is not differentiable only at 0. Can I not check the value at each training point to calculate the derivative. ...
3
votes
2answers
555 views

Model that optimizes mean absolute error always gives same prediction

My gradient boosting regression model (GBM) is trained to minimize mean absolute error (MAE) but gives the same prediction for every record on my highly skewed dataset. I believe there is a quick fix ...
1
vote
0answers
26 views

Fisher Information in LAD model for ML estimator

Considering an i.i.d. sample from a linear model $y_i=\alpha x_i+u_i$ (both $y$ and $x$ are centered with respect to their means) errors are homoscedastic and are distributed as: $$u\sim\frac{1}{\sqrt{...
1
vote
1answer
188 views

For syntax of least absolute deviation from package 'L1pack' [closed]

I am trying to use the least absolute deviation regression from my dataset which has one column of dependent variable and multiple columns of independent variables. I tried using the following syntax ...
1
vote
0answers
666 views

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*. ...
6
votes
1answer
612 views

What is the maximum likelihood/GLM version of least absolute deviations for robust linear regression?

Robust linear regression from minimising the absolute deviationresults in a regression line of medians conditional on covariates, instead of means using the standard least squares methodology: Is ...
12
votes
2answers
2k views

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 ...
1
vote
0answers
130 views

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 ...
2
votes
1answer
514 views

$R^2$ 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".
1
vote
0answers
35 views

What is the standard measure of fit quality for least absolute deviation regression (the analog of $R^2$) [duplicate]

When one runs an OLS regression, one often prefers to look at $R^2$ rather than the mean squared error, though both measure goodness of fit. $R^2$ is dimensionless and has some advantageous properties:...
7
votes
1answer
182 views

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 ...