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I'm thinking how to tackle such a problem.

Let's say we have a set of products, each have some numeric characteristics (x1, x2, x3). A customer is given a choice of n such products and buys one. Only a few of products are shown and the choice is made only between them based solely on the characteristics. The number of products for selection varies. Now assuming that I have a good amount of data describing the sets given for choice and the choice made, how do I build a model to predict the outcome of similar experiment in the future? That is, we give n products and want to find which will be the choice based on their characteristics.

My first thought was neural network, but that would work only if I have a constant set of inputs and here it varies. Any suggestions are welcome.

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It's more of a ranking problem, since you need to pick one item out of a set. There's a number of algorithms available, I believe.

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I'd also take a look at P. Diaconis papers on "Random Walk with Reinforcement" and "Reinforcement Learning" approaches

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I'd recommend collaborative filtering for this! It's used all the time for similar problems.

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  • $\begingroup$ As I mentioned, the subject of research is not preference of users but 'goodness' of products. This method is more about recognizing preferences of specific users... $\endgroup$ – sashkello Oct 8 '12 at 23:15
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I think that is is similar to so called conjoint analysis. Statistical technique used in marketing. It especially determines how people value different features.

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  • $\begingroup$ Yes, but that's not an approach to the problem, just one of the ways of classifying it... $\endgroup$ – sashkello Oct 9 '12 at 6:59

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