зеркало из
https://github.com/docxology/cognitive.git
synced 2025-10-30 20:56:04 +02:00
138 строки
4.2 KiB
Markdown
138 строки
4.2 KiB
Markdown
# 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|Core Concepts]]
|
|
- [[../guides/implementation_guides|Implementation Guides]]
|
|
- [[../api/api_documentation|API Documentation]]
|
|
- [[../examples/usage_examples|Usage Examples]]
|
|
|
|
## References
|
|
- [[friston_2017]] - Active Inference
|
|
- [[da_costa_2020]] - Active Inference POMDP
|
|
- [[parr_2019]] - Free Energy Theory
|
|
- [[buckley_2017]] - Tutorial Paper |