We propose a practical algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors. Our algorithm, which we call TBMC (Tiling for Binary Matrix Completion), gives interpretable output in the form of binary factors which represent a decomposition of the matrix into tiles. Our approach is inspired by a popular algorithm from the data mining community called PROXIMUS: it adopts the same recursive partitioning approach while extending to missing data. The algorithm relies upon rankone approximations of incomplete binary matrices, and we propose a linear programming (LP) approach for solving this subproblem. We also prove a 2approximation result for the LP approach which holds for any level of subsampling and for any subsampling pattern. Our numerical experiments show that TBMC outperforms existing methods on recommender systems arising in the context of real datasets.
There are many channels which can be used for advertising – Google Ads, Facebook, Google Hotel Ads, Trivago, some of which allow direct communication with a single person, while other only allow to advertise to groups of people. A typical booking process through Google Ads looks as follows: the hotel creates an ad (potentially a personalized ad), a potential client searches for a hotel in Google, the ad is shown to the user, the user clicks on the ad and is redirected to the hotel’s website, and there makes a reservation. As the advertiser pays per click, the proper measure of the ad/offer performance is the average value per click. The main problem solved can be stated as follows: design hotel clients segmentation techniques coupled with automated offer generation methods allowing to maximize the value per click from an ad campaign.
The report is concerned with design of gamification model that would collect user feedback for use in heating and cooling system. The main incentive to the participants is energy efficiency resulting in smaller bills, however the model should consider a few other elements. There are different preferences of thermal comfort in apartments, financial goals and environmental awareness among apartment owners. Gamification model is not focused on one goal, e.g. energy efficiency, rather should reward being interactive and willingness to support preferences set by majority in the community.
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