This project implements a discrete-time Markov chain to model user behavior in a content consumption platform. It simulates user transitions between engagement states and analyzes both empirical and theoretical behavior using probability theory and linear algebra.
The system includes:
- Monte Carlo simulation of user sessions
- Transition-based recommendation system
- Greedy and stochastic recommendation strategies
- Graph-based visualization of state transitions
- Mathematical analysis using eigenvalues and stationary distributions
The system is modeled as a Markov chain in which each state represents a level of user engagement:
- Watching
- Browsing
- Disengaged
- Engaged
- Off_platform (absorbing state)
State transitions are governed by a stochastic matrix ( P ), where:
[ P_{ij} = P(X_{t+1} = j \mid X_t = i) ]
Each row of the matrix sums to 1:
[ \sum_j P_{ij} = 1 ]
The long-term behavior of the system is described by the stationary distribution:
[ \pi P = \pi ]
Where:
- ( \pi ) is the stationary distribution
- ( \pi ) is an eigenvector of ( P^T )
- The corresponding eigenvalue is 1
This distribution represents the equilibrium state of user behavior over time.
- Simulates 1,000 user sessions using Monte Carlo sampling
- Each session follows transition probabilities defined by the Markov chain
- State frequency distribution
- Session length statistics
- Drop-off analysis
- Transition frequency matrix
- Greedy recommendation based on highest-probability next state
- Stochastic recommendation based on probabilistic sampling
- Deterministic path generation using highest-probability transitions
- Full Markov chain graph
- Most likely user journey visualization
- Stationary distribution computed via eigen decomposition
- Validation of stochastic matrix properties
├── main.py ├── states.py ├── transitions.py ├── simulation.py ├── analytics.py ├── recommendation.py ├── visualization.py ├── requirements.txt └── README.md
This project can be applied to:
- Content recommendation systems
- User engagement modeling
- Session abandonment prediction
- Behavioral analysis in digital platforms
This project demonstrates how Markov chains can be used to model user behavior, simulate realistic sessions, and generate recommendations based on probabilistic transitions. It combines mathematical theory (eigenvalues and stationary distributions) with practical implementation and visualization.
Markov Chains, Stochastic Processes, Linear Algebra, Eigenvalues, Eigenvectors, Probability Theory, Recommendation Systems, User Behavior Modeling, Monte Carlo Simulation, Graph Theory
Bethlehem Negussie