So while going through the topic of Preference learning, I came to know about "instance ranking". Since the problem which I'm working on requires me to rank the instances (data point), is there any algorithm which can determine scoring function (Utility function in PL jargon)?

The only relevant paper I found was Ranking the Best Instances, which happens to be bit technical for me, I am interested in paper/source which underlines the algorithm to do so (score instances so as to rank them; learn and improve from previous data {supervised learning}).

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    $\begingroup$ Pretty much any general purpose classification approach gives a decision value that you can use directly to rank instances (including SVM, neural networks, random forests, logistic regression). You can choose any of these you like and get started! $\endgroup$ – Marc Claesen Dec 17 '15 at 10:54
  • $\begingroup$ @MarcClaesen Let's just say, we use Logistic regression, in that case, our aim is to find weights (to be multiplied by attribute values); then in training data, I have subsets ranked (not scored), so the problem again reverts to how to arrive at scoring function which scores instances in such a way that it aligns with ranking? $\endgroup$ – Manu Dec 17 '15 at 10:59
  • $\begingroup$ The output of a logistic regression model is a probability, which you can use directly to rank instances: higher probability $\rightarrow$ higher rank. $\endgroup$ – Marc Claesen Dec 17 '15 at 11:04
  • $\begingroup$ @MarcClaesen But then, how to choose optimum weights? Is there atleast an algorithm for learning/refining parameters? Sorry, I'm a newbie! $\endgroup$ – Manu Dec 17 '15 at 11:08
  • $\begingroup$ Optimizing the weights is part of training logistic regression, which involves maximizing the conditional log likelihood. Any software package out there can do this for you, no need to reinvent the wheel (e.g., R, scikit-learn, ...). $\endgroup$ – Marc Claesen Dec 17 '15 at 14:54

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