Ranking systems and methods using a dynamic bayesian network exposure model

A computer-implemented method, comprising:

• receiving a query from a computing device via a network;
• determining a set of items to be ranked based on the query;
• determining relevance scores for the items, respectively, using a fairness function and a utility function;
• determining a polytope using an exposure model based on the relevance scores;
• determining a point that lies within the polytope;
• performing a Carathéodory decomposition;
• generating a distribution for the items based on a result of the Carathéodory decomposition;
• sampling from the distribution;
• determining rankings for the items based on the sampling;
• and
• in response to the query, transmitting the rankings of the items to the computing device via the network for displaying at least a subset of the set of objects on a display according to the rankings.

A system comprising:

• a computing device;
• one or more processors;
• and
• memory including code that, when executed by the one or more processors, perform to:
• receive a query from the computing device via a network;
• determine a set of items to be ranked based on the query;
• determine relevance scores for the items, respectively, using a fairness function and a utility function;
• determine a polytope using an exposure model based on the relevance scores;
• determine a point that lies within the polytope;
• perform a Carathéodory decomposition;
• generate a distribution for the items based on a result of the Carathéodory decomposition;
• sample from the distribution;
• determine rankings for the items based on the sampling;
• and
• transmit the rankings of the items to the computing device via the network,
• wherein the computing device is configured to display at least a subset of the set of objects on a display according to the rankings.