Bayesian Non-Parametric Model to Target Gamification Notifications Using Big Data

46 Pages Posted: 14 Nov 2016

See all articles by Meisam Hejazi Nia

Meisam Hejazi Nia

University of Texas at Dallas, Naveen Jindal School of Management

Brian T. Ratchford

University of Texas at Dallas

Date Written: November 3, 2015

Abstract

User generated content (UGC) is the cornerstone of social and online marketing. However, the key challenge for online marketers to leverage UGC is to encourage users to generate more quality content. To overcome this burden, practitioners have started to use video game concepts such as badges, leaderboard, and points to encourage users, under the umbrella of an approach called Gamification. Online marketers require a data driven approach to target users based on their response to gamification elements. Knowing the response of individual users to various game elements can help the online marketer to emphasize various content generating tasks in its personal messaging, to maximize the total number of user generated contents. For example, knowing that a user reduces its content contribution after receiving a badge, an online marketer can create a diversified list of content generating tasks for user in a customized message, to make badge earning more difficult. Moreover, knowing that a user increases its content contribution after earning more points, the online marketer can create a targeted list of content generating tasks for users in a customized message, to make badge earning simpler.

Online marketers can leverage their massive data sets of users’ content generations to create more customized targeted messages. This big data usually consists of several little data sets for each user, but its key advantage relative to the classic data sets is that it has more information about the tail of the distribution of customer response. This tail is relevant for targeting. Of course, a model can accommodate capturing the behavior on tail, if it allows the number of parameters to grow with the size of the data set. A useful method shall not through away these data by sampling, but it shall be flexible to not to misfit.

Hierarchical Bayesian (HB) approaches are well known for their estimation of individual specific parameters, and for allowing for unobserved heterogeneity, while sharing statistical strength across individual parameters. However, to be flexible, an HB model shall deviate from the normal prior on the consumer response parameters to the mixture normal structure, to capture behavior parameter of users in tail. Furthermore, a suitable method for Big Data shall be not only scalable, but also fast, to allow an online marketer to target its users in timely manner. In summary, a suitable approach shall create a computationally tractable solution for the computationally hard gamified targeting problem for big data.

The current proposed model uses hierarchical Bayesian sparse modeling approach for users’ content generating choices to allow for users’ unobserved heterogeneity. It exercises a mixed logit model, with individual specific random effects that control for self-selection. To address scalability and flexibility concerns, I used a version of stochastic optimization approach called mini-batch gradient descend. Unlike the batch approach that uses complete data set to update the parameters, the mini-batch approach iteratively and randomly samples data to create a noisy measure of gradient and hessian of the objective function. Studies show that under regularity conditions the mini-batch approach can converge to the batch optimization approach. However, the advantage of the mini-batch approach is that it uses less memory, and it is computationally faster. In addition, the proposed approach estimates the mixed logit model in two steps. In the first step, it uses the observed data to identify the segment membership of each user. The BIC measure identifies the number of segments. Then, in the second step, conditional on the segment membership the model, it optimizes a-posteriori of the parameters. In summery, the current approach sets the number of segments exogenously, using BIC measure.

Although the mentioned approach is not wrong, a better approach involves endogenizing the number of segments. A realistic approach should not even assume the number of segments, rather it shall assume that the world is infinitely complex, so it shall allow the model to automatically select the finite number of segments observed in the finite data set. This way the approach can be general enough to update the number of segments as firm observes more data. As a result, the learning of an online marketer from its big data is not limited anymore, and the marketer learns more about its users, as it observes more data. In fact a good approach should allow the firm to update its segmentation based on latent information set that it has captured from the streaming data. This segmentation might also evolve across time as users’ latent motivation state changes. Therefore, an online marketer requires a dynamic segmentation technique. This way the online marketers’ posterior belief about parameters evolves, as the marketer updates its belief conditioning on the latest information.

In fact, big data makes offline model selection computationally intractable because estimating a non-linear model over a big data for a specific model structure is time consuming. Non-parametric Bayesian provides tools for this computationally hard automatic model structure selection problem. The new approach I have planned to use falls into non-parametric Bayesian approaches category. In particular, to model users’ latent motivation I use infinite Hidden Markov Model (iHMM). In this approach, I assume that users have various latent motivation states that are time varying. These latent time varying motivation states define users’ response parameters to gamification elements, in choosing whether to contribute content or not. In this structure, the transition probability between states is modeled as a Hierarchical Dirichlet Process (HDP), and the emission probability is modeled as ordered logit model of users’ content contribution choice given the latent state motivation and the users’ gamification earnings (i.e. badges, rank on the leaderboard, reputation points).

To control for unobserved heterogeneity across users, further I use a Dirichlet Process (DP) on the parameters of the ordered logit emission probability model. As a result the model has two building blocks of iHMM and DP to allow automatic model structure selection over big data, by endogenizing the number of user segments and states. These approaches are scalable, flexible, realistic, and machine learning literature shows that they improve prediction; however, their estimation with MCMC method suffers from slow convergence, and slow mixing problem. Therefore, to allow an online marketer to learn parameter of users responses in timely manner to target them, conditional on the latest information, I use a combination of Particle Learning (PL) and Variational Bayesian (VB). These approaches help to speed up the estimation. To estimate the iHMM model, I will use PL. PL is a Sequential Monte Carlo (SMC) method that uses simulation based on discrete approximation of a random cloud of particle to estimate the targeted posterior density. Its advantage is that it allows belief updating over parameters based on the latest observed information set in a computationally tractable way. I parallelize the PL process to speed up estimation. To speed up estimation of the DP over users specific parameters, I use a Variational Bayesian (VB) approach. This approach maximizes the evidence lower bound for the K-L divergence of parameters to approximate the parameters of the factorized variational distribution of user specific parameters.

All in all, I suggest an approach that helps the online marketers to target their gamification elements to users by modifying the order of the list of tasks that they send to users. It is more realistic and flexible as it allows the model to learn more parameters when the online marketers collect more data. The targeting approach is scalable and quick, and it can be used over streaming data.

Keywords: Bayesian non parametric, infinite hidden Markov model, infinite mixture model, variational Bayesian, particle learning

Suggested Citation

Hejazi Nia, Meisam and Ratchford, Brian T., Bayesian Non-Parametric Model to Target Gamification Notifications Using Big Data (November 3, 2015). Available at SSRN: https://ssrn.com/abstract=2864189 or http://dx.doi.org/10.2139/ssrn.2864189

Meisam Hejazi Nia (Contact Author)

University of Texas at Dallas, Naveen Jindal School of Management ( email )

P.O. Box 830688
Richardson, TX 75083-0688
United States

HOME PAGE: http://www.hejazinia.com

Brian T. Ratchford

University of Texas at Dallas ( email )

2601 North Floyd Road
Richardson, TX 75083
United States

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