Method and Apparatus for Ordering Recommendations According to a Mean/Variance Tradeoff
Aspects of the present disclosure are directed to systems and methods that facilitate the recommendation of an item to a user. One particular aspect includes a method including the steps of: a) receiving a user request for a new recommendation including rating information for previously-selected items, b) retrieving a mean vector and a covariance matrix representing estimates of prior ratings for a plurality of items by other users, c) calculating a selection likelihood statistics as a function of the estimated mean vector, the estimated covariance matrix and the rating information provided by the, d) calculating ranking statistics as a function of the selection likelihood statistics, and e) transmitting a response to the user recommending at least one of the items not previously selected as a function of the ranking statistics. The recommended item may, for example, be a movie.
1 . A computer-implemented method for recommending an item, the method comprising:
executing code to determine statistical information in response to a recommendation request associated with a user, the statistical information including a mean vector and a covariance matrix, the mean vector and the covariance matrix being estimated based on rating information associated with previously selected items;
calculating a selection likelihood statistic, specific to the user, for a previously unselected item available for selection by the user, the selection likelihood statistic being calculated based on the estimated mean vector, the estimated covariance matrix, and rating information associated with the previously selected item; and
programmatically outputting a recommendation for the previously unselected item based on the selection likelihood statistic.
2 . The method of claim 1 , further comprising calculating a ranking statistic for the previously unselected item based on the selection likelihood statistic.
3 . The method of claim 1 , wherein outputting the recommendation comprises transmitting a response to the recommendation request, the response including a recommendation recommending the previously unselected item.
4 . The method of claim 3 , wherein outputting the recommendation comprises transmitting the recommendation to the user.
5 . The method of claim 3 , wherein outputting the recommendation comprises transmitting the recommendation to a provider of the previously unselected item.
6 . The method of claim 1 , wherein the selection likelihood statistic comprises a conditional mean vector associated with the user and a conditional covariance matrix associated with the user.
7 . The method of claim 6 , further comprising calculating a ranking statistic for the previously unselected item based on the selection likelihood statistic, and
wherein the ranking statistic comprises one or more weights calculated as the product of the inverse of the conditional covariance matrix and the conditional mean vector.
8 . The method of claim 7 , wherein the value of the ranking statistic for the previously unselected item is highest or lowest among a set of values of the ranking statistic for other previously unselected items.
9 . The method of claim 1 , wherein the items comprise one or more of movies or television programs.
10 . The method of claim 1 , wherein the items comprise one or more of printed publications, e-books, CDs, or DVDs.
11 . The method of claim 1 , wherein the items comprise grocery items.
12 . The method of claim 1 , wherein the items comprise electronic dating service candidates.
13 . The method of claim 1 , wherein the rating information corresponds to ratings received from the user for the previously selected items by the user.
14 . The method of claim 1 , wherein the rating information corresponds to ratings received from one or more other users for the previously selected items by the one or more other users.
15 . A non-transitory computer-readable storage medium storing instructions, wherein execution of the instructions by the processing device causes the processing device to perform a method for recommending an item comprising:
executing code to determine statistical information in response to a recommendation request associated with a user, the statistical information including a mean vector and a covariance matrix, the mean vector and the covariance matrix being estimated based on rating information associated with previously selected items;
calculating a selection likelihood statistic, specific to the user, for a previously unselected item available for selection by the user, the selection likelihood statistic being calculated based on the estimated mean vector, the estimated covariance matrix, and rating information associated with the previously selected item; and
programmatically outputting a recommendation for the previously unselected item based on the selection likelihood statistic.
16 . The medium of claim 15 , wherein the method performed upon execution of the instructions further comprises calculating a ranking statistic for the previously unselected item based on the selection likelihood statistic.
17 . The medium of claim 15 , wherein recommending the previously unselected item comprises transmitting a response to the recommendation request, the response including a recommendation recommending the previously unselected item.
18 . The medium of claim 15 , wherein the selection likelihood statistic comprises a conditional mean vector associated with the user and a conditional covariance matrix associated with the user.
19 . The medium of claim 18 , wherein the method performed upon execution of the instructions further comprises calculating a ranking statistic for the previously unselected item based on the selection likelihood statistic, and
wherein the ranking statistic comprises one or more weights calculated as the product of the inverse of the conditional covariance matrix and the conditional mean vector.
20 . A system for recommending an item comprising:
a non-transitory computer-readable medium storing instructions for execution of a recommendation process; and
a processing device in communication with the non-transitory computer-readable medium, the processing device being programmed to execute the instructions to:
determine statistical information in response to a recommendation request associated with a user, the statistical information including a mean vector and a covariance matrix, the mean vector and the covariance matrix being estimated based on rating information associated with previously selected items;
calculate a selection likelihood statistic, specific to the user, for a previously unselected item available for selection by the user, the selection likelihood statistic being calculated based on the estimated mean vector, the estimated covariance matrix, and rating information associated with the previously selected item; and
output a recommendation for the previously unselected item based on the selection likelihood statistic.
21 . The system of claim 20 , wherein the selection likelihood statistic comprises a conditional mean vector associated with the user and a conditional covariance matrix associated with the user.
22 . The system of claim 20 , wherein the processing device is programmed to calculate a ranking statistic for the previously unselected item based on the selection likelihood statistic, and
wherein the ranking statistic comprises one or more weights calculated as the product of the inverse of the conditional covariance matrix and the conditional mean vector.