Modeling and Predicting Popularity Dynamics via Reinforced Poisson Processes

Abstract: An ability to predict the popularity dynamics of individual items within a complex evolving system has important implications in an array of areas. Here we propose a generative probabilistic framework using a reinforced Poisson process to model explicitly the process through which individual items gain their popularity. This model distinguishes itself from existing models via its capability of modeling the arrival process of popularity and its remarkable power at predicting the popularity of individual items. It possesses the flexibility of applying Bayesian treatment to further improve the predictive power using a conjugate prior. Extensive experiments on a longitudinal citation dataset demonstrate that this model consistently outperforms existing popularity prediction methods.

• The paper introduces a novel reinforced Poisson process framework incorporating intrinsic fitness, temporal aging, and reinforcement effects to model popularity dynamics.
• It employs a Bayesian approach with conjugate priors to mitigate overfitting and improve prediction accuracy for individual items.
• Experimental evaluations on citation data demonstrate its superior forecasting ability over traditional autoregressive and linear models.

Modeling and Predicting Popularity Dynamics via Reinforced Poisson Processes

The paper introduces a novel framework for modeling and predicting the popularity dynamics of individual items within evolving systems using reinforced Poisson processes. This model aims to address the limitations of existing methods by directly modeling the stochastic arrival process of popularity and improving predictive power through Bayesian techniques. The proposed approach incorporates key factors like intrinsic attractiveness, temporal aging effects, and reinforcement mechanisms to capture popularity dynamics comprehensively.

Introduction to Popularity Dynamics

The study of popularity dynamics is motivated by its crucial role in understanding attention economies and implications for areas such as marketing and policy-making. Traditional models typically focus on aggregated statistical analyses or deterministic time series methods, falling short in predicting individual item popularity over time. The paper argues for a probabilistic framework, as existing deterministic models fail to capture the stochastic nature of individual attention processes crucial for accurate prediction.

Reinforced Poisson Process Framework

Model Formulation

The reinforced Poisson process (RPP) adapts classic stochastic process theory to model popularity acquisition through:

• Fitness of an Item: Quantified by $\lambda_d$, which denotes intrinsic attractiveness.
• Aging Effect: Modeled using a temporal relaxation function $f_d(t;\theta_d)$.
• Reinforcement Mechanism: Captures the "rich-get-richer" phenomenon in popularity dynamics.

The rate function $x_d(t)$, detailing the arrival of attention, is crucial in defining the probabilistic nature of the model. The likelihood of observing a popularity sequence is derived, enabling parameter estimation and prediction based on established statistical principles.

Parameter Estimation and Bayesian Treatment

For robustness, the model incorporates a Bayesian approach by introducing a conjugate prior, thereby enhancing prediction accuracy, especially for items with limited attention data. The posterior distribution of fitness parameters $\lambda_d$ is leveraged to make Bayesian predictions, mitigating traditional overfitting risks associated with maximum likelihood estimation.

Experimental Evaluation

Dataset and Relaxation Functions

The model is validated using an extensive longitudinal citation dataset from American Physical Society journals. A log-normal relaxation function effectively captures citation dynamics, optimizing parameters through likelihood maximization. The relaxation function is crucial in defining the temporal inhomogeneity of item attractiveness.

Comparison and Results

The RPP model is benchmarked against autoregressive and linear models utilizing MAPE and accuracy metrics. Results demonstrate consistent outperformance in predictive capabilities, particularly in long-term forecasts post-training period. This is attributed to the RPP model's methodological advantages in capturing stochastic dynamics and temporal correlations.

Influential Factors

Analysis of training period lengths, conceived attention numbers, and citation distribution across decades highlights model robustness and adaptability. The sensitivity to prior parameters and effective attention numbers further illuminate the role of reinforcement mechanisms in driving popularity disparities.

Related Work

Existing literature spans areas such as social contagion and diffusion models, yet often lacks predictive precision for individual popularity trajectories. The paper contrasts the proposed probabilistic approach with descriptive models and deterministic time series analyses, highlighting the necessity for an explicit stochastic framework.

Conclusion

The reinforced Poisson process framework offers a promising avenue for advancing popularity prediction models. Its ability to integrate diverse domain-specific factors through flexible relaxation functions underscores its potential applicability across various fields. Future research could refine relaxation function identification and explore the integration of additional domain factors to enrich predictive power and theoretical insights into popularity dynamics. Such developments may substantially enhance our understanding of complex attention-driven systems.