# What is a utility function in recommender systems?

Let us go back to recommender systems as I did not mention last week.   Last month I found that customers’ preference and items features are key to provide recommendations. Then I started developing the model used in recommender systems.  Now I think I should explain the initial problem setting in recommender systems.  This week I looked at “Mining Massive datasets” in Coursera and I found that problem setting of recommender systems in this course is simple and easy to understand.  So I decided to follow this. If you are interested in this more detail,  I recommend to look at this course, excellent MOOCs in Coursera.

Let us introduce a utility function, which tells us how customers are satisfied with the items. The term of “utility function ” is coming from micro economics. So some of you may learn it before.  I think it is good to use a utility function here because we can use the method of economics when we analyze the impacts of recommender systems to our society going forward.  I hope  more people, who are not data-scientists, are getting interested in recommender systems.

The utility function is expressed as follows

U*x→R

U:utility of customers,  θ:customers’preferences,  x:Item features,  R:ratings of the items for the customers

This is simple and easy to understand what utility function is.  I would like to use this definition going forward. I think ratings may be one, two, three…, or it may be a continuous number according to recommender systems.

When we look at the simple models, such as linear regression model and logistic regression model,  Key metrics are explanatory variables or features and its weight or parameters. It is represented as x and θ respectively.  And product of θx shows us how much it has an impact on variables, which we want to predict. Therefore I would like to introduce θx as a critical part of my recommender engine.   ”θx” means that each x is multiplied to it’s correspondent weight θ and summing up all products .This is critically important for recommender systems. Mathematically θx is calculations of products of vectors/matrices. It is simple but has a strong power to provide recommendations effectively. I would like to develop my recommender engine by using θx next week.

Yes, we should consider what color of shirts maximize our utility functions, for example.  In futures, utility functions of every person might be stored in computers and recommendations might be provided automatically in order to maximize our utility functions. So everyone may be satisfied with everyday life. What a wonderful world it is!