Performance Prediction Module Abstract

High-level Purpose and Responsibility

The performance prediction module implements mathematical models for forecasting learning performance and optimization schedules based on empirical learning curves. It provides curve-fitting algorithms, trajectory analysis, and schedule optimization to predict future learning outcomes and optimize training interventions.

Key Data Structures and Relationships

  • PerformanceCurve: Mathematical models representing learning performance over time or practice
  • PowerLawModel: Power law learning curves with asymptotic performance predictions
  • ExponentialModel: Exponential approach to mastery with rate parameter estimation
  • LogisticModel: S-shaped learning curves with initial learning phase and plateau
  • BiExponentialModel: Dual-phase learning with distinct fast and slow learning components
  • CurveParameters: Fitted parameters for learning curve models with uncertainty estimates
  • PredictionInterval: Confidence and prediction intervals for future performance forecasts

Main Data Flows and Transformations

  1. Data Preparation: Learning performance history → Time series organization → Model fitting preparation
  2. Curve Fitting: Performance data → Parameter estimation → Fitted learning curve models
  3. Model Selection: Multiple curve fits → Information criteria comparison → Optimal model selection
  4. Performance Forecasting: Fitted models + Future time points → Performance predictions + Uncertainty
  5. Schedule Optimization: Performance predictions → Optimal training schedules → Intervention timing

External Dependencies and Interfaces

  • Statistics Module: Parameter estimation, model fitting, and statistical inference procedures
  • Learning Module: Integration with learner performance data and proficiency tracking
  • Experiments Module: Predictive modeling for experimental outcome forecasting
  • Validation Module: Model validation and goodness-of-fit assessment

State Management Patterns

  • Fitted Model Storage: Maintains fitted curve parameters for prediction and analysis
  • Prediction Cache: Performance optimization for repeated predictions with same parameters
  • Model Comparison State: Tracks model selection results and performance comparisons
  • Parameter Uncertainty Tracking: Maintains uncertainty estimates for robust prediction

Core Algorithms or Business Logic Abstractions

  • Non-Linear Curve Fitting: Levenberg-Marquardt and other optimization algorithms for parameter estimation
  • Model Selection Criteria: AIC, BIC, and cross-validation for learning curve model comparison
  • Extrapolation Methods: Robust prediction beyond observed data with uncertainty quantification
  • Multi-Model Ensemble: Combining predictions from multiple curve models for improved accuracy
  • Schedule Optimization: Mathematical optimization of training schedules based on predicted learning curves
  • Change Point Detection: Identification of transitions between different learning phases or regimes