Optional stopping theorem: Difference between revisions

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'''LogitBoost''' is a [[Boosting (meta-algorithm)|boosting]] algorithm formulated by [[Jerome H. Friedman|Jerome Friedman]], [[Trevor Hastie]], and [[Robert Tibshirani]]. The original paper<ref>Jerome Friedman, Trevor Hastie and Robert Tibshirani. Additive logistic regression: a statistical view of boosting. Annals of Statistics 28(2), 2000.  337–407. http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.9525</ref> casts the [[AdaBoost]] algorithm into a statistical framework. Specifically, if one considers [[AdaBoost]] as a [[generalized additive model]] and then applies the cost functional of [[logistic regression]], one can derive the LogitBoost algorithm.
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==Minimizing the LogitBoost cost functional==
 
LogitBoost can be seen as a [[convex optimization]]. Specifically, given that we seek an additive model of the form
 
:<math>f = \sum_t \alpha_t h_t</math>
 
the LogitBoost algorithm minimizes the logistic loss:
 
:<math>\sum_i \log\left( 1 + e^{-y_i f(x_i)}\right)</math>
 
==References==
<div class="references-small">
<references />
</div>
 
==See also==
* [[Logistic model tree]]
 
[[Category:Classification algorithms]]
[[Category:Ensemble learning]]
[[Category:Machine learning algorithms]]

Latest revision as of 06:05, 2 January 2015

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