Mobile App Recommendation: Maximize the Total App Downloads

Transcription

1 Mobie App Recommendation: Maximize the Tota App Downoads Zhuohua Chen Schoo of Economics and Management Tsinghua University Yinghui (Catherine) Yang Graduate Schoo of Management University of Caifornia, Davis Hongyan Liu Schoo of Economics and Management Tsinghua University Research questions Smart phones are now widey used to carry out a arge variety of activities. With the increasing use of smart phones, miions of smart phone appications (mobie apps) are avaiabe for downoad through apps markets (e.g. Appe's App Store and Googe Pay). Due to the arge number of mobie apps avaiabe on an apps market, it is getting increasingy more difficut for smart phone users to discover apps. A we-designed app recommendation system can guide users to find reevant apps, which acceerates more app downoads that coud subsequenty generate profit for the apps market provider as we as app deveopers. An app recommendation system normay generates a ist of apps (on the same screen) which are reated to a specific app a user is browsing or downoading. One of the most common ways to generate recommended apps is to recommend simiar apps to the foca app, which impies that the recommended apps are aso simiar to each other. For exampe, when a user is browsing a fashight app, many other fashight apps are recommended. Due to the simiarity in functionaity of the recommended apps, a user hardy has an incentive to downoad mutipe apps isted on the same screen. Given that a mobie user coud easiy press mutipe downoad buttons from the same 1

2 mobie screen if they see severa reevant apps, such a recommendation mechanism coud miss out on a ot of opportunities. Motivated by this, we shoud not ony consider the probabiity of downoading an app individuay when making recommendations, but aso take into consideration the effect that apps have on each other. The recommended ist of apps shoud be optimized as a whoe to maximize the number of apps that a user downoads. We are working with one of the biggest Android apps markets (with around 100 miion users) in China, and heping them design an app recommendation system whose goa is to maximize the number of apps users downoad considering that apps on the recommendation ist can infuence each other. To the best of our knowedge, this probem has not been studied in either the mobie app recommendation iterature or the recommendation iterature in genera. In addition, we wi be abe to conduct experiments on their patform once the recommendation system is deveoped. Probem Formuation and Approach For a specific mobie user, the apps market tracks a the apps she has downoaded. Based on the downoad history, the user s rating for each app can be inferred by appying we-deveoped recommendation techniques such as coaborative fitering and matrix factorization. In addition, apps viewed during current browsing session may aso hep to identify the apps the user coud potentiay be interested in downoading. Given the user s rating for each app and her behavior in the current browsing session, we want to find the recommendation ist that has the maximum expectation of the tota number of downoads. This recommended ist of apps wi appear at the end of the screen of the app the user is currenty browsing. Let n be the number of apps in the apps market, m be the number of apps viewed in current browsing session, be the number of apps on the recommendation ist. Let C = {C1, C2 Cm} refer to the apps a specific user viewed in the current browsing session ordered by time viewed. 2

3 Each app Ck viewed in the current session has a binary downoad status Dk. Dk = 1 means that Ck has been downoaded during this session, and Dk = 0 indicates that Ck was just viewed by the user. C1 is the most recenty viewed app, and normay the recommended ist of apps wi appear at the end of the screen of the information page of C1. Let R = {R1, R2 R} denote the recommended apps ordered by the position on the recommendation ist. Each recommended app Ri has a rating RTi for the given user (which was computed previousy based on a users downoad history). Let S = {S1, S2 S} be the binary downoad status of the apps in the recommendation ist. Si = 1 means that the recommended Ri is downoaded by the user, and Si = 0 indicates that the user did not downoad Ri. Given C, the objective function is to find an optima R that maximizes the expectation of the summation of Si, i.e. R = argmax {E( i=1 S i C, R)} R To sove this probem, we first need to mode the probabiity distribution over S conditioning on C and R. We introduce a conditiona random fied mode, which is shown in Figure 1, to represent the conditiona probabiity distribution. C, R S 1 S 2... S n Figure 1. The conditiona random fied mode The factors function of the mode and their expanations are as foows. 1. The rating RTi refects the preference of the user towards app Ri, thus it woud infuence the downoad status Si. Aso the position i of Ri in the recommendation ist woud aso infuence 3

4 Si. We use ogistic regression to mode the reationship between ratings, position and downoad status. Factor f(si Ri) is introduced to capture the infuence of Ri on Si. (g (RT f(s i R i ) = { i, i)) α, S i = 1 (1 g (RT i, i)) α, otherwise where g(rti, i) is the ogistic function that returns a vaue within [0, 1], and α is a parameter that contros the decine rate. 2. Each Ck viewed in the current session has impact on the downoad status Si of Ri. Based on the downoad and browsing history of a users, we wi be abe to compute the associations between a pair of apps. Let A and B refer to any two given apps, and SA and SB are the downoad status of app A and B. Generay, probabiity of A s downoad status being SA given that A is viewed can be derived as foows. P(S A A) = # of sessions where A appears and its downoad status is S A # of session where A appears When the other app B is viewed previousy, the probabiity of A s downoad status SA might be infuenced by the fact that B is viewed and its downoad status SB. Let P(SA A, B, SB) denotes the probabiity of A s downoad status being SA given that A and B are viewed in the same session and B s downoad status is SB. P(S A A, B, S B ) = # of sessions where A and B both appear and their downoad status are S A and S B respectivey # of session where A and B both appear and B s downoad status is S B Now we specify app A to be Si and app B to be Ck. The ratio of P(Si Ri, Ck, Dk) over P(Si Ri) can be used to measure how much more or ess ikey Ri s downoad status wi be Si after Ck is viewed and Ck s downoad status is Dk. Aso we assume that the extent of infuence of Ck on Ri s downoad status Si decreases exponentiay as index k increases (i.e. more recenty browsed app has more infuence on Si). Factor g(si Ri, Ck) is introduced to capture this infuence of Ck on Ri s downoad status Si. g(s i R i, C k ) = ( P(S β i R i, C k, D k ) k ) P(S i R i ) 4

5 where β is a parameter that that contros g factor s effect to the whoe mode. 3. Any two apps on the same recommendation ist coud affect the downoad status of each other. Let A and B refer to any two given apps, and SA and SB are the downoad status of apps A and B. The joint probabiity of A s downoad status being SA and B s downoad status being SB given that A and B are viewed can be derived as foows. P(S A, S B A, B) = # of sessions where A and B both appear and their downoad status are S A and S B respectivey # of session where A and B both appear If the downoad status SA and SB are independent when A and B are viewed in the same session, the expected probabiity of A s downoad status being SA and B s downoad status being SB given that A and B are viewed is P(SA A) P(SB B). Now we specify app A to be Si and app B to be Sj. The ratio of P(Si, Sj Ri, Rj) over P(Si Ri) P(Sj Rj) can be used to measure how much more or ess ikey Ri s downoad status wi be Si and Rj s downoad status wi be Sj when Si and Sj are viewed simutaneousy. Factor h(si, Sj Ri, Rj) is introduced to capture this interaction. h(s i, S j R i, R j ) = ( P(S γ i, S j R i, R j ) P(S i R i ) P(S j R j ) ) where γ is a parameter that contros h factor s effect to the whoe mode. The joint conditiona probabiity P(S R, C) can be derived from the conditiona random fied mode. 1 P(S R, C) = Z(θ R, C) f(s i R i ) g(s i R i, C k ) h(s i, S j R i, R j ) i=1 where Z(θ R, C) is the partition function. m i=1 k=1 i=1 j=1,j i m Z(θ R, C) = f(s i R i ) g(s i R i, C k ) h(s i, S j R i, R j ) S 1 S 2 S i=1 i=1 k=1 i=1 j=1 5

6 Since the size of the recommendation ist is usuay quite sma, i.e. not bigger than 10, we can use the direct enumerating method to sove the inference probem of the mode. We use the maximum ikeihood estimation to earn a the parameters in the mode. A gradient ascent method is used to iterativey find the optima parameters given data. With the conditiona probabiity distribution, we can then proceed to find the soution for the objective function. We can use a greedy method to quicky generate the recommendation ist by picking the best apps one at a time sequentiay. We first determine the best R1, and then determine the best R2 given R1, and so on so forth. When picking Ri, the apps appear before it on the ist R1, R2 Ri-1 have aready been chosen. At this step, we set the ength of the recommendation ist to i, and find the optima Ri that makes the recommendation ist (Ri, Ri Ri-1, Ri) have the maximum expectation of tota downoads. Expected contributions We are designing a mobie app recommendation system aiming to maximize the number of apps users downoad considering that apps on the recommendation ist can infuence each other. To the best of our knowedge, this probem has not been studied before. Moreover, our dataset was coected from one of the biggest Android apps market in China. We have a very detaied data to support our experiments. Once fuy deveoped and verified both theoreticay and computationay, our method wi be depoyed on this apps market, and we wi be abe to run controed experiments in rea production to measure how much better our method performs compared to the system currenty in pace at the apps market and other aternative methods. Very few pubished research on recommendation system has the opportunity to run experiments on a rea recommendation patform. Current status of the manuscript 6

7 The mode based on conditiona Markov random fied has been designed, and we are in the process of evauating this mode first based on offine data we have to first see whether incorporating interactions between recommended apps provides vaue. Once this is verified, we wi first use the initia greedy based agorithm to find the best apps to recommend. Then we wi fine tune our agorithm using arge scae data, and then depoy on the apps market to conduct controed experiments. 7