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Feature Driven and Point Process Approaches for Popularity Prediction

Swapnil Mishra, Marian-Andrei Rizoiu, Lexing Xie

arXiv:1608.04862v2cs.SIphysics.soc-ph

TL;DR

Popularity prediction lacks a common comparison across feature-driven and generative approaches, despite its relevance to information overload and collective behavior. The paper combines a Hawkes cascade model with a predictive layer, benchmarks it with feature-based methods, and finds that hybrid modeling performs best across the evaluated tasks.

  • Problem

    Popularity prediction is important for understanding collective behavior and managing information overload, but the strengths, weaknesses, and generalization of feature-driven and generative approaches remain insufficiently compared.

  • Method

    The paper models retweet cascades with a Hawkes self-exciting process capturing user influence, social memory, and tweet quality, then adds a predictive layer and compares it with feature-based prediction.

  • Results

    Both proposed generative and feature-driven methods outperform the current state-of-the-art predictor across total-size and cascade-doubling tasks, while combining them further improves performance.

  • Takeaways & Limitations

    Popularity modeling should compare feature-driven and generative approaches across classification and regression, and leverage their complementary strengths through hybrid prediction.

  • Takeaways & Limitations

    The model currently omits content-specific network behavior, time-varying user influence distributions, and explicit interactions among related cascades.

Abstract

from arXiv · show

Predicting popularity, or the total volume of information outbreaks, is an important subproblem for understanding collective behavior in networks. Each of the two main types of recent approaches to the problem, feature-driven and generative models, have desired qualities and clear limitations. This paper bridges the gap between these solutions with a new hybrid approach and a new performance benchmark. We model each social cascade with a marked Hawkes self-exciting point process, and estimate the content virality, memory decay, and user influence. We then learn a predictive layer for popularity prediction using a collection of cascade history. To our surprise, Hawkes process with a predictive overlay outperform recent feature-driven and generative approaches on existing tweet data [43] and a new public benchmark on news tweets. We also found that a basic set of user features and event time summary statistics performs competitively in both classification and regression tasks, and that adding point process information to the feature set further improves predictions. From these observations, we argue that future work on popularity prediction should compare across feature-driven and generative modeling approaches in both classification and regression tasks.

1. INTRODUCTION

Popularity prediction matters for managing information overload and improving content dissemination, but feature-driven and generative approaches leave gaps in coverage and comparability. This paper proposes hybrid prediction, public benchmarking, and features usable across tasks.

  • Popularity prediction can help consumers cope with information overload and producers identify trends and disseminate useful content faster.
  • Feature-driven methods summarize network, user, and event history, whereas generative methods use fine-grained timing but make stronger diffusion assumptions.
  • The paper builds Hawkes-based generative and feature-driven predictors, then combines them in a hybrid predictor for final retweet-cascade size.
  • The feature-based predictor uses message content, basic user profiles, user features, and temporal activity features, supporting both regression and classification.
  • After observing 10 minutes of retweet activity, the feature-based predictor reduces mean absolute relative error by more than 200% versus the current state-of-the-art model.
  • The paper contributes a comparative benchmark and a public news-tweet cascade dataset with code for evaluating feature-driven and generative approaches.

2. RELATED WORK

Related work divides popularity prediction into feature-driven and generative approaches. Feature-driven methods learn from extensive features, while generative point-process models represent diffusion mechanisms and timing but often require prediction-specific corrections.

  • Feature-driven approaches: Feature-driven models treat popularity as a nondecomposable process and use machine learning to connect item popularity with extensive feature sets.
  • Feature-driven approaches: Many feature proposals are data-source-specific or depend on information that is not publicly accessible outside their original contexts.
  • Generative approaches: Generative models fit parametric representations of observed phenomena and have been applied across neuroscience, economics, physics, criminology, and social media.
  • Generative approaches: Social-media point-process models capture popularity bursts, decay, rich-get-richer effects, and social contagion, with some estimating total retweet-cascade size.
  • Generative approaches: SEISMIC is described as the current state-of-the-art popularity-prediction model and is used as a comparison baseline.
  • Generative approaches: Generative models are typically designed to explain popularity rather than predict it, motivating a Hawkes predictive model that separates modeling from prediction.

3. RETWEETING AS A POINT PROCESS

The paper models retweet cascades as marked Hawkes self-exciting point processes, using parameters for content virality, user influence, and temporal memory, then estimates cascade popularity from the fitted model. It defines the branching factor and maximum-likelihood estimation procedure, and illustrates how fitted parameters distinguish cascades with similar sizes but different diffusion dynamics.

  • 3.1 A self-exciting point processes: A marked Hawkes process models each retweet as a stochastic event whose rate depends on previously observed events.The initial tweet is the only exogenous event in the cascade model; subsequent events are generated through a triggering kernel.
  • 3.1 A self-exciting point processes: The model separates content virality, user influence, and memory over time through κ, β, c, and θ.κ scales the subsequent retweet rate, β warps follower-based influence, and (τ + c)^−(1+θ) models temporal decay.
  • 3.1 A self-exciting point processes: The power-law memory kernel consistently outperformed exponential and Rayleigh kernels in the paper’s experimental setting.The authors therefore report detailed results only for the power-law kernel.
  • 3.2 The branching factor: The branching factor n∗ is the expected number of directly spawned child events and serves as a cascade-virality descriptor and prediction quantity.It is also used as a constraint during model estimation.
  • 3.2 The branching factor: For n∗<1, the process is subcritical, with bounded expected cascade size and an event rate that decays to zero.When n∗>1, the process is supercritical and the total number of retweets is unbounded.
  • 3.3 Estimating the Hawkes process: The model parameters {κ, β, c, θ} are estimated by maximizing the nonlinear point-process log-likelihood under positivity and branching-factor constraints.Direct optimization avoids the quadratic number of latent branching variables used by expectation-maximization approaches.
  • 3.4 Interpreting the generative model: Two similarly sized cascades, with observed popularities 224 and 219, exhibited markedly different diffusion speeds and fitted parameter values.The first cascade lasted four days, whereas the second lasted 12.5 minutes, reflecting different interactions between memory and user influence.
  • 3.4 Interpreting the generative model: Across 17,146 News cascades, most fitted cascades had low κ and low n∗ values, consistent with long-tailed content quality and cascade virality.The fitted θ and κ distributions are visualized in Figure 2.

4. PREDICTING POPULARITY

The paper estimates future cascade size from a fitted point process by organizing simulated events into generations, then corrects this theoretical prediction with a learned predictive layer. The correction reduces prediction error and addresses limitations of generative assumptions.

  • 4.1 The expected number of future events: The method estimates expected future events by grouping simulated cascade events according to their parent generation.Generation1 contains events spawned by observed events; later generations contain events spawned by the preceding generation.
  • 4.1 The expected number of future events: The theoretical total cascade size N∞ is computed by combining the observed-event contribution with expected events across subsequent generations.For generations i > 1, Ai is estimated recursively from the previous generation using n∗, assuming n∗ < 1 for convergence.
  • 4.1 The expected number of future events: A1 is estimated using the observed magnitudes of parent events, providing a more precise estimate than applying the recursive approximation directly.The paper then substitutes the resulting generation estimates into the total-event expression.
  • 4.2 Predicting total popularity: Generative prediction can be sub-optimal because point processes explain observed histories while relying on simplifying assumptions that limit prediction.The paper identifies approximate user influence, changing network conditions, supercritical cascades, and local minima as specific limitations.
  • 4.2 Predicting total popularity: The predictive layer trains a Random Forest to output a scaling factor ω that corrects the expected number of future events.The cascade is represented using c, θ, A1, and n∗, selected for their correlation with theoretical prediction error.
  • 4.2 Predicting total popularity: Error reduction generally increases with A1, while its relationship with n∗ has maxima near the 40th and 95th percentiles.The theoretical prediction also tends to overestimate cascade sizes, consistent with competition among content items for finite human attention.

5. DATA AND FEATURES FOR PREDICTION

The experiments use Tweet-1Mo and a newly constructed News dataset, alongside feature sets based on user, temporal, volume, and historical-success information. The paper emphasizes an open, domain-specific benchmark and features requiring only free Twitter data access.

  • 5. DATA AND FEATURES FOR PREDICTION: The study evaluates prediction on Tweet-1Mo and News datasets, then constructs features for its feature-driven approach.Tweet-1Mo contains cascades sampled over one month and filtered to lengths greater than 50; News covers tweets from April to July 2015.
  • 5. DATA AND FEATURES FOR PREDICTION: The News dataset adds friends, posted-status, and account-creation information for users in each retweet cascade.These fields are required by the feature-driven method and are unavailable for Tweet-1Mo experiments.
  • 5. DATA AND FEATURES FOR PREDICTION: The News dataset is presented as an open-access, domain-specific benchmark intended to improve reproducibility over prior restricted datasets.Earlier benchmarks were difficult to replicate because of proprietary network measurements, privileged API access, or restricted non-English data.
  • 5.2 Features for popularity prediction: The feature-driven predictor uses basic user, temporal, volume, and past-user-success features selected from recent popularity-prediction research.The design targets features obtainable through free access to Twitter data.
  • 5.2 Features for popularity prediction: Basic user features summarize follower, friend, status, and account-age distributions across observed cascade participants.Each feature is represented using minimum, median, maximum, 25th-percentile, and 75th-percentile values.
  • 5.2 Features for popularity prediction: Past user success measures the average size of cascades previously started by participating users.It requires substantial historical data and applies only to users with prior cascade history.

6. EXPERIMENTS

The experiments compare generative, feature-driven, and hybrid predictors across regression and classification tasks for retweet-cascade popularity. Hawkes generally outperforms Seismic, while Hybrid achieves the strongest regression performance on the News benchmark.

  • Experimental setup: Experiments evaluate cascade-size regression and cascade-doubling classification across Tweet-1Mo and News datasets.Cascades are observed for fixed time prefixes in regression and fixed retweet counts in classification.
  • Cascade-size regression: Hawkes consistently achieves lower mean ARE than Seismic on both Tweet-1Mo and News.Hawkes also produces predictions for more cascades; on News after 5 minutes, it covers 873 more cascades than Seismic.
  • Cascade-size regression: Hawkes has median ARE at most 0.19 at 5 minutes on News, compared with Seismic’s best median ARE of 0.24 at 1 hour.The comparison is reported for the News-data results summarized in Fig. 5.
  • Feature-driven versus generative: Hybrid performs best on the News July’15 regression benchmark, improving mean APE by 42% from 0.17 to 0.11 at 1 hour.The Hybrid differences from the other approaches are statistically significant, and the authors attribute complementarity to uncorrelated errors.
  • Error by popularity: Prediction errors are lowest for most middle-popularity cascades, while extreme popularity percentiles are harder because ARE amplifies small errors or reflects intrinsic difficulty.Figure 7 reports this distribution after observing cascades for 10 minutes.
  • Cascade-doubling classification: Feature-Driven has the best accuracy for predicting whether a cascade will double, while combining its features with HawkesC does not significantly improve performance.HawkesC nevertheless improves substantially over majority-class random guessing.

7. CONCLUSION

The paper establishes a common benchmark and compares feature-driven and generative approaches for cascade-size regression and cascade-doubling classification. Both proposed methods outperform the prior state-of-the-art predictor, and combining them further improves performance.

  • CONCLUSION: The benchmark enables comparisons between feature-driven and generative approaches across multiple popularity-prediction problem variants.The paper targets settings with limited access to network and user information by selecting features available through free-access services.
  • CONCLUSION: The Hawkes model represents user influence, social memory, and content quality, then applies a predictive layer learned from historical cascades.This separates cascade modeling from prediction while retaining interpretable diffusion factors.
  • CONCLUSION: Both the proposed Hawkes and Feature-Driven methods outperform the current state-of-the-art predictor across the evaluated popularity tasks.The tasks are predicting total retweet-cascade size and whether a cascade will double its size.
  • CONCLUSION: Hybrid further improves performance, supporting the conclusion that popularity modeling should combine complementary feature-driven and generative information.The paper evaluates this conclusion on a benchmark dataset and a news-tweet dataset.
  • CONCLUSION: Future extensions include content-specific network behavior, time-varying user influence distributions, and explicit interactions between related cascades.These factors are identified as planned additions rather than components of the current model.

1 Technical details about the optimization procedure

The supplementary material derives the Hawkes log-likelihood and its partial derivatives, which are used to fit model parameters through numerical optimization.

  • Log-likelihood derivation: The supplement derives the Hawkes-process log-likelihood for marked event sequences.The likelihood is written as L(κ, β, c, θ) = log P({(m_i, t_i), i = 1, . . . , n}).
  • Log-likelihood derivation: The derivation computes the integral term Λ before substituting the Hawkes intensity expression into the likelihood.Subsequent equations rewrite the likelihood using this integral.
  • Optimization: Partial derivatives with respect to κ, β, c, and θ support optimization of the Hawkes model parameters.The derivatives are used by the Ipopt function-optimization procedure to fit each cascade’s model.
  • Supplementary analyses: The supplementary material includes density-distribution graphics for branching factor n* and related Hawkes parameters.Figure 8 reports distributions for β, n*, and c on News cascades.

2 Additional density distribution graphics

The additional density analyses characterize Hawkes parameters across News cascades. They show a low typical branching factor, fast-decaying excitation, and highly reactive early diffusion for most cascades.

  • Parameter distributions: The β density has a dominant local maximum near 0.079 and a smaller peak near the boundary associated with n*=1.The secondary peak results from optimization terminating at the nonlinear constraint n*=1.
  • Parameter distributions: The branching factor n* represents the expected number of events spawned by one event, with a distribution maximum around 0.022 and a smaller local maximum around 1.Low n* values indicate a fast-decaying self-exciting process that produces small, short-lived cascades.
  • Parameter distributions: The cutoff parameter c controls initial diffusion reactivity, with smaller values corresponding to earlier first retweets and larger values to longer waiting times.Its distribution is long-tailed, and the median value is c = 111 seconds.

3 Goodness of Fit

The goodness-of-fit analysis evaluates unseen cascade data after fitting models on observed cascade prefixes, comparing Hawkes with Seismic. Hawkes fits slightly worse than Seismic on unseen data in this analysis, despite stronger predictive power in the main text.

  • Evaluation setup: Unseen-data fit is evaluated by fitting each model through time t_N and estimating log-likelihood through the cascade end time t_M.The unseen-data likelihood is obtained from the observed prefix and the full cascade likelihood.
  • Hawkes and Seismic evaluation: For Hawkes, the unseen-data log-likelihood can be calculated from the model’s equations for both the observed prefix and full cascade.The calculation uses Equation 16 for the seen and complete cascades.
  • Hawkes and Seismic evaluation: For Seismic, unseen-data evaluation requires a separate derivation because its model does not explicitly provide the log-likelihood.The derivation uses the model’s infectiousness formulation and assumes estimated infectiousness remains constant after t_N.
  • Goodness-of-fit result: On a 100-cascade News subsample, Seismic fits slightly better to unseen data than Hawkes, although Hawkes has better predictive power in the main text.The comparison uses unconstrained parameter optimization for Hawkes against Seismic.

4 More Results

Statistical testing on the News dataset finds that the Hybrid model generally improves significantly over the alternatives, while Hawkes and Feature-Driven are usually better than Seismic but not significantly different from each other.

  • Statistical significance: The Hybrid model shows statistically significant improvement over the other approaches almost every time on the News dataset.The analysis uses a strict p-value cutoff of 0.01.
  • Statistical significance: Hawkes and Feature-Driven models generally outperform Seismic, but their differences are statistically insignificant relative to each other.Table 6 marks comparisons without statistically significant differences as draws.
  • Testing procedure: The testing compares Seismic, Hawkes, Feature-Driven, and Hybrid models using majority lower error values plus p-value confirmation.A comparison is counted as a win only when both criteria support it.
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