Consider a cascade of classifiers and a binary classification task. Cascade consists of some number of strong classifiers (n) each of which consists of some number of weak classifiers (m_i, where i = 1..n).
You have 3 numbers of interest: true positive rate, false positive rate and time of detection (you can choose by your own whether it will be mean time of worst case time).
You can arbitrarily choose n, m_i for each i and vector of weights of positive and negative examples for each i. Each weak classifier is just a decision tree of length 1. Also, some meaningful type of boosting (ada or real) occurs inside each strong classifier.
Time of detection is just a linear monotonic function of the total number of weak classifiers.
Can anyone suggest how to optimally train this cascade (this structure was developed by Viola and Jones for face detection) or maybe heard of some articles where this problem was solved?
First paper of Viola & Jones: https://www.cs.cmu.edu/~efros/courses/LBMV07/Papers/viola-cvpr-01.pdf
Second paper of Viola & Jones: http://www.vision.rwth-aachen.de/teaching/cvws08/additional/viola-facedetection-ijcv04.pdf