cognitive/docs/research/research_documentation.md

Research Documentation

---

title: Research Documentation type: index status: stable created: 2024-02-06 tags:

• research
• theory
• mathematics
• statistics semantic_relations:
• type: implements links: ../concepts/cognitive_modeling_concepts
• type: relates links:
  • ../concepts/cognitive_modeling_concepts
  • knowledge_base/mathematics/active_inference_pomdp

---

Overview

This directory contains research documentation focusing on theoretical foundations, mathematical frameworks, and statistical methods in cognitive modeling.

Theoretical Foundations

POMDP Framework

• active_inference_pomdp - Active Inference POMDP formulation
• belief_updating - Belief update mechanisms
• state_estimation - State estimation methods
• policy_selection - Policy selection theory

Statistical Theory

• variational_methods - Variational inference methods
• information_theory - Information theoretic foundations
• game_theory - Game theoretic principles
• statistical_foundations - Core statistical concepts

Mathematical Components

Matrix Operations

• A_matrix - Observation model
• B_matrix - Transition dynamics
• C_matrix - Preferences
• D_matrix - Prior beliefs
• E_matrix - Action distribution

Free Energy Formulations

• variational_free_energy - VFE computation
• expected_free_energy - EFE formulation
• efe_components - EFE decomposition
• free_energy_principle - Theoretical foundation

Information Measures

• epistemic_value - Information gain
• pragmatic_value - Goal-directed value
• expected_free_energy_update - EFE updates
• compute_efe - EFE computation

Implementation Theory

Core Algorithms

• belief_propagation - Message passing algorithms
• variational_inference - Variational methods
• monte_carlo_methods - Sampling approaches
• gradient_descent - Optimization techniques

State Space Models

• state_spaces - State space theory
• markov_models - Markov processes
• hidden_states - Hidden state inference
• observation_models - Observation modeling

Policy Optimization

• policy_optimization - Policy improvement
• action_selection - Action selection methods
• exploration_exploitation - Exploration strategies
• temperature_parameter - Temperature scaling

Validation Framework

Statistical Tests

• hypothesis_testing - Statistical testing
• model_comparison - Model evaluation
• parameter_estimation - Parameter inference
• goodness_of_fit - Fit measures

Performance Metrics

• information_metrics - Information measures
• prediction_error - Error metrics
• convergence_analysis - Convergence studies
• stability_analysis - Stability measures

Research Methods

Experimental Design

• experiment_design - Design principles
• control_variables - Control methods
• sampling_strategies - Sampling approaches
• power_analysis - Statistical power

Data Analysis

• statistical_analysis - Analysis methods
• bayesian_analysis - Bayesian approaches
• frequentist_analysis - Frequentist methods
• causal_analysis - Causality studies

Visualization

• data_visualization - Visualization methods
• belief_evolution - Belief trajectories
• free_energy_landscape - Energy landscapes
• policy_visualization - Policy analysis

Integration Points

Theory Integration

• active_inference_theory - Active inference
• predictive_coding - Predictive processing
• optimal_control - Control theory
• reinforcement_learning - RL connections

Implementation Links

• model_implementation - Implementation guides
• numerical_methods - Numerical approaches
• optimization_methods - Optimization techniques
• validation_methods - Validation approaches

Related Documentation

• ../concepts/cognitive_modeling_concepts
• ../guides/implementation_guides
• ../api/api_documentation
• ../examples/usage_examples

References

• friston_2017 - Active Inference
• da_costa_2020 - Active Inference POMDP
• parr_2019 - Free Energy Theory
• buckley_2017 - Tutorial Paper