Probabilistic Modeling of User Interaction Patterns in Controlled Web Application Sessions : Transforming Web Sessions into Interpretable Behavioral Models

Sammanfattning

Background : Understanding user interaction behavior in web applications requires modeling sequences of actions rather than isolated events. User sessions often contain structural patterns such as repeated navigation paths and transition dependencies between actions. However, access to large-scale interaction datasets is frequently restricted due to privacy and organizational limitations, making it difficult to study realistic behavioral patterns. This creates a need for lightweight and interpretable approaches that can model user behavior effectively under limited data conditions. Objectives: This thesis investigates how effectively first-order and second-order Markov models can represent user navigation behavior in controlled web application sessions, what accuracy–robustness trade-offs arise under small-scale data conditions, and whether Markov-generated synthetic sessions can reproduce structural patterns observed in real sessions. Methods: A controlled web application was developed and instrumented to collect structured interaction data from 49 user sessions consisting of sequences of 10–20 distinct action types. The collected logs were transformed into ordered session-based action sequences suitable for probabilistic modeling. Two probabilistic sequence models were implemented: a first-order Markov model and a second-order Markov model. Transition probabilities were estimated using Laplace smoothing to reduce sparsity and avoid zero-probability transitions. Model evaluation was performed using 5-fold cross-validation with metrics including log-likelihood, perplexity, and Kullback–Leibler divergence. In addition, 500 synthetic sessions were generated through probabilistic sampling from the learned transition distributions. The generated sessions were compared with real interaction data using transition analysis, session-length distributions, and behavioral pattern extraction. Results: The second-order Markov model achieved higher predictive performance, with improved log-likelihood (−90.14 vs −99.28) and lower perplexity (7.10 vs 7.28) compared to the first-order model. Both values are well below the uniform baselineperplexity of 19, confirming that both models learn non-trivial sequential structure. However, the second-order model also showed significantly higher divergence from real transition distributions (KL divergence: 61.12 vs 21.52), indicating greater sensitivity to sparse observations and increased risk of overfitting. Synthetic session analysis showed that the second-order model captured sequential dependencies more effectively, reducing transition divergence by approximately 3.4% compared to the first-order model. It should be noted that both absolute JSD values (0.51 and 0.53) are near the theoretical maximum of ln2 ≈ 0.693 nats, meaning this reduction occurs within a regime of poor overall fidelity. Analysis of real interaction sessions revealed strong navigation-oriented behavior, relatively short sessions (mean length 9.4), and recurring transition loops such as: home_view → view_cart → home_view These results demonstrate that even small-scale controlled datasets contain identifiable structural interaction patterns that can be modeled probabilistically. Conclusions: The findings demonstrate a clear trade-off between model complexity and robustness in small-scale datasets. While second-order Markov models capture richer sequential dependencies and improve predictive accuracy, they are more vulnerable to sparsity, instability, and overfitting. First-order models, although simpler, provide more stable and reliable estimates under limited data conditions. Overall, the study shows that probabilistic Markov modeling can successfully identify meaningful user interaction patterns in controlled small-scale environments. Synthetic sessions show limited local realism but are not sufficiently faithful to replace real session data for behavioral analysis. The results highlight the importance of balancing model complexity with available data when modeling user behavior and generating synthetic interaction sessions.