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In this research paper, it is discussed how to combine deep learning with wide (shallow) learning to achieve both generalisation and the ability to learn correlation/association rules.

The input vector of such network is an n-dimensional vector of features $\mathbf{x} = (x_1, x_2, x_3,\dots, x_n)$. While training, the following objective function is maximised: $$ P(Y=1|\mathbf{x}) $$

Within the context of recommender systems (which is one of the main applications of this paper) how does one cope with the problem of missing data (unseen products)?

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  • $\begingroup$ Regularisation and dealing with missing data are two different things. Could you either explain how the title relates to your question, or perhaps edit it to summarise what you are asking? $\endgroup$ – Neil Slater Jul 4 '16 at 16:48
  • $\begingroup$ Dealing with missing data is, indeed, a regularisation of the model. I changed the title anyway to avoid confusion. $\endgroup$ – Bob Jul 4 '16 at 17:26
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This depends on what you mean by 'unseen products'. If your definition is like in the paper

[...] new  feature  combinations  that have  never  or  rarely 
occurred  in the  past.

then you're thinking along the lines of algorithms like collaborative filtering. Those see the tastes of people as missing values in a matrix and try to complete it using a low-dimensional representation. Now these can be overly generic, depending on how low you choose that dimension to be.

Another, older, approach is something like association rules, which can be deducted using algorithms like apriori, which however rely on the product combinations seen in the past, so they won't ever be able recommend product combinations not seen in the past.

While the former set of algorithms can deal with what under the definition above would be called 'missing data', the latter cannot. Those however tend to give better recommendations. The paper you quote uses neural networks in what looks like a successful attempt to get the best of those two worlds.

If hover you mean by 'missing data' completely new products, than you're out of luck using any of the algorithms described above. If you don't have meta-data about those products, it's near impossible to recommend anything. Just imagine you have a list of products A, B, and C and who bought them. Now you get product D. Who will buy it? Without any additional information on D, you're dead in the water.

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