Unified Mathematical Model
General high-level computing formula for recommendations;
We have a function that computes a score for items that also relies on user, query and context. Based on this, we can then see the domain search and discovery as different cases of the same general problem of recommending the best items to a user, be it based on user profile, a search query, the context or a combination thereof.
From Scoring to Recommendation
Similar to the raw scoring function, we can define an ordering function for a set of items I as;
The most basic one would be, score each item in set using the scoring function. Order by score descending and truncate after n items for a list of recommendations.
Of course, this doesn’t factor in factors like diversity, novelty, serendipity, value of items or other objectives that you might have that might affect how you want to generate the list of recommendations.
Similarly, semantic understanding of how items relate might mean some are deemed irrelevant. If you’ve bought and read the hard-cover version of a book, being recommended the pocket version might not be of much use.
Lastly, you might consider the number of items n as an input for the ordering function, as you might want different logic depending on how big the output set will be.
Psychology of Preferences
Explicit ratings are oftentimes not as stable as people assume and much more contextual. We articulate how we like something based on our feelings in that moment. Asking the same person again later about the same item might yield another rating.
Oftentimes, evaluating individual items is hard to do fair due to multiple aspects being included in a single score (artistic movies will on average get higher ratings, but aren’t very predictive over what we will want to watch next time).
Comparing multiple items relatively to each-other can help clarify and reveal actual preferences too even when the absolute score might be the same for items.
In real-life decision situations, this is also a common difference. Either you make an individual rating, or you give a relative judgement.
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