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138 строки
4.2 KiB
Markdown
138 строки
4.2 KiB
Markdown
# Research Documentation
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---
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title: Research Documentation
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type: index
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status: stable
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created: 2024-02-06
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tags:
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- research
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- theory
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- mathematics
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- statistics
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semantic_relations:
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- type: implements
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links: [[../concepts/cognitive_modeling_concepts]]
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- type: relates
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links:
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- [[../concepts/cognitive_modeling_concepts]]
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- [[knowledge_base/mathematics/active_inference_pomdp]]
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---
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## Overview
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This directory contains research documentation focusing on theoretical foundations, mathematical frameworks, and statistical methods in cognitive modeling.
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## Theoretical Foundations
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### POMDP Framework
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- [[active_inference_pomdp]] - Active Inference POMDP formulation
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- [[belief_updating]] - Belief update mechanisms
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- [[state_estimation]] - State estimation methods
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- [[policy_selection]] - Policy selection theory
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### Statistical Theory
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- [[variational_methods]] - Variational inference methods
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- [[information_theory]] - Information theoretic foundations
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- [[game_theory]] - Game theoretic principles
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- [[statistical_foundations]] - Core statistical concepts
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## Mathematical Components
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### Matrix Operations
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- [[A_matrix]] - Observation model
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- [[B_matrix]] - Transition dynamics
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- [[C_matrix]] - Preferences
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- [[D_matrix]] - Prior beliefs
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- [[E_matrix]] - Action distribution
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### Free Energy Formulations
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- [[variational_free_energy]] - VFE computation
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- [[expected_free_energy]] - EFE formulation
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- [[efe_components]] - EFE decomposition
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- [[free_energy_principle]] - Theoretical foundation
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### Information Measures
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- [[epistemic_value]] - Information gain
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- [[pragmatic_value]] - Goal-directed value
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- [[expected_free_energy_update]] - EFE updates
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- [[compute_efe]] - EFE computation
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## Implementation Theory
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### Core Algorithms
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- [[belief_propagation]] - Message passing algorithms
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- [[variational_inference]] - Variational methods
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- [[monte_carlo_methods]] - Sampling approaches
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- [[gradient_descent]] - Optimization techniques
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### State Space Models
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- [[state_spaces]] - State space theory
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- [[markov_models]] - Markov processes
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- [[hidden_states]] - Hidden state inference
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- [[observation_models]] - Observation modeling
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### Policy Optimization
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- [[policy_optimization]] - Policy improvement
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- [[action_selection]] - Action selection methods
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- [[exploration_exploitation]] - Exploration strategies
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- [[temperature_parameter]] - Temperature scaling
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## Validation Framework
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### Statistical Tests
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- [[hypothesis_testing]] - Statistical testing
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- [[model_comparison]] - Model evaluation
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- [[parameter_estimation]] - Parameter inference
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- [[goodness_of_fit]] - Fit measures
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### Performance Metrics
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- [[information_metrics]] - Information measures
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- [[prediction_error]] - Error metrics
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- [[convergence_analysis]] - Convergence studies
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- [[stability_analysis]] - Stability measures
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## Research Methods
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### Experimental Design
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- [[experiment_design]] - Design principles
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- [[control_variables]] - Control methods
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- [[sampling_strategies]] - Sampling approaches
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- [[power_analysis]] - Statistical power
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### Data Analysis
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- [[statistical_analysis]] - Analysis methods
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- [[bayesian_analysis]] - Bayesian approaches
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- [[frequentist_analysis]] - Frequentist methods
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- [[causal_analysis]] - Causality studies
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### Visualization
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- [[data_visualization]] - Visualization methods
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- [[belief_evolution]] - Belief trajectories
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- [[free_energy_landscape]] - Energy landscapes
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- [[policy_visualization]] - Policy analysis
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## Integration Points
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### Theory Integration
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- [[active_inference_theory]] - Active inference
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- [[predictive_coding]] - Predictive processing
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- [[optimal_control]] - Control theory
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- [[reinforcement_learning]] - RL connections
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### Implementation Links
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- [[model_implementation]] - Implementation guides
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- [[numerical_methods]] - Numerical approaches
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- [[optimization_methods]] - Optimization techniques
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- [[validation_methods]] - Validation approaches
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## Related Documentation
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- [[../concepts/cognitive_modeling_concepts|Core Concepts]]
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- [[../guides/implementation_guides|Implementation Guides]]
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- [[../api/api_documentation|API Documentation]]
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- [[../examples/usage_examples|Usage Examples]]
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## References
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- [[friston_2017]] - Active Inference
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- [[da_costa_2020]] - Active Inference POMDP
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- [[parr_2019]] - Free Energy Theory
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- [[buckley_2017]] - Tutorial Paper |