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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

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    $\begingroup$ Since you know the origin of this structure, it might be wise to include the reference in the question. $\endgroup$ – babou Apr 13 '15 at 15:32
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    $\begingroup$ What research have you done? This kind of classifier is widely used for facial detection, and as such is well-documented in many computer vision textbooks and courses (and presumably in the Viola-Jones paper as well). Have you tried research that to see what training method they use? We expect you to do significant research before asking and to show us in the question what research you've done. It's unlikely that there's an efficient way to find the "optimal" cascade, but there are likely reasonable heuristics. $\endgroup$ – D.W. Apr 13 '15 at 17:24
  • $\begingroup$ I've already looked through Google results on this issue and either didn't found what I was looking for or missed it. I'm aware of heuristics that they used, but I want for the cascade structure to be derived as a solution to some appropriately set optimization problem, $\endgroup$ – Marat Bakiev Apr 14 '15 at 16:45

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