File:Fitting a straight line to a data with outliers.png
Original file (1,011 × 610 pixels, file size: 48 KB, MIME type: image/png)
Captions
Summary
[edit]DescriptionFitting a straight line to a data with outliers.png |
English: For Regression problems the Mean Square Error (MSE) is most frequently used.
However the MSE is very sensitive to outliers, and a differentiable approximation to the Mean Absolute Error (MAE) is desired. In particular if the training data for regression comes from a disctribution with a ”heavy tail”, the presence of many outliers will lead to large prediction errors if MSE is used during training. The MAE weights data equally and is robust to the presence of outliers, however its use is limited since it is not differentiable at the origin. Another problem with the MAE loss is that it has a large derivative (±1) close to the origin leading to oscillations about the minimum during gradient descent. ANN training loss functions have to be differentiable, since the Backpopagation algorithm requires the loss function to be differentiable. Thus differentiable and computationally cheap alternatives to the MSE loss like the Huber loss and loss have been explored in the past. From the figure it is clear that the SMAE loss proposed in https://arxiv.org/abs/2303.09935 is less affected by outliers than other loss functions. The robustness of the SMAE loss can be attributed to its close approximation to the ideal MAE loss compared to other loss functions. |
Date | |
Source | Own work |
Author | M.Zkuba |
Author: Mathew Mithra Noel (https://orcid.org/0000-0002-3442-1642)
Licensing
[edit]- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 16:53, 9 November 2023 | 1,011 × 610 (48 KB) | M.Zkuba (talk | contribs) | Uploaded own work with UploadWizard |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
File usage on other wikis
The following other wikis use this file:
- Usage on en.wikipedia.org
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
Horizontal resolution | 37.8 dpc |
---|---|
Vertical resolution | 37.8 dpc |
File change date and time | 11:42, 25 October 2023 |
Software used | |
Date and time of digitizing |
|