Content deleted Content added
Citation bot (talk | contribs) m Add: isbn, doi, jstor. Removed URL that duplicated unique identifier. | You can use this bot yourself. Report bugs here.| Activated by User:Headbomb |
added f* to the exp,savage and tangent losses |
||
Line 136:
The exponential loss is convex and grows exponentially for negative values which makes it more sensitive to outliers. The exponential loss is used in the [[AdaBoost|AdaBoost algorithm]].
The minimizer of <math>I[f]</math> for the exponential loss function can be directly found from equation (1) as
:<math>f^*_\text{Logistic}= \frac{1}{2}\log\left(\frac{\eta}{1-\eta}\right)=\frac{1}{2}\log\left(\frac{p(1\mid x)}{1-p(1\mid x)}\right).</math>
== Savage loss ==
Line 143 ⟶ 147:
The Savage loss is quasi-convex and is bounded for large negative values which makes it less sensitive to outliers. The Savage loss has been used in [[Gradient boosting|Gradient Boosting]] and the SavageBoost algorithm.
The minimizer of <math>I[f]</math> for the Savage loss function can be directly found from equation (1) as
:<math>f^*_\text{Logistic}= \log\left(\frac{\eta}{1-\eta}\right)=\log\left(\frac{p(1\mid x)}{1-p(1\mid x)}\right).</math>
== Tangent loss ==
Line 150 ⟶ 158:
The Tangent loss is quasi-convex and is bounded for large negative values which makes it less sensitive to outliers. Interestingly, the Tangent loss also assigns a bounded penalty to data points that have been classified "too correctly". This can help prevent over training on the data set. The Tangent loss has been used in [[Gradient boosting|Gradient Boosting]], the TangentBoost algorithm and Alternating Decision Forests<ref>{{Cite journal|last=Schulter|first=S.|last2=Wohlhart|first2=P.|last3=Leistner|first3=C.|last4=Saffari|first4=A.|last5=Roth|first5=P. M.|last6=Bischof|first6=H.|date=2013-6|title=Alternating Decision Forests|url=https://ieeexplore.ieee.org/document/6618916|journal=2013 IEEE Conference on Computer Vision and Pattern Recognition|pages=508–515|doi=10.1109/CVPR.2013.72|isbn=978-0-7695-4989-7}}</ref>.
The minimizer of <math>I[f]</math> for the Tangent loss function can be directly found from equation (1) as
:<math>f^*_\text{Logistic}= \tan(\eta-\frac{1}{2})=\tan(p(1\mid x)-\frac{1}{2}).</math>
== Hinge loss ==
| |||