sppcax
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  • Overview
    • Installation
    • Note
  • Installation
    • Requirements
    • Stable Release
    • From Source
    • Development Installation
    • Install Test Dependencies
    • JAX Installation Notes
  • Usage
    • Basic Example
    • Factor Analysis vs. PPCA
    • Handling Missing Data (Partial Observations)
    • Bayesian Model Reduction
    • Advanced Usage
  • Mathematical Theory
    • Bayesian Dynamic Factor Analysis
      • Introduction
      • Model Definition
      • Prior Distributions
        • Emission Matrix and Noise
        • Dynamics Matrix
        • ARD Priors
        • Initial State
      • Variational Inference
        • VBE-Step
        • VBM-Step
        • ELBO
      • Factor Analysis and PCA as Special Cases
      • Training Pipeline
      • References
    • Inference Methods: EM, VBEM, and Gibbs
      • Introduction
      • Shared M-Step Pipeline
      • EM (Maximum A Posteriori)
        • E-Step
        • M-Step
      • VBEM (Variational Bayes EM)
        • E-Step
        • M-Step
      • Blocked Gibbs Sampling
        • E-Step: Forward Filtering Backward Sampling (FFBS)
        • M-Step: Sampling from Conditional Posteriors
      • Algorithm Summaries
      • See Also
      • References
    • Factor Analysis and PCA
      • Introduction
      • Model Definition
      • Prior Distributions
        • Latent Variables
        • Loading Matrix and Noise Precision
      • Variational Inference
      • Evidence Lower Bound (ELBO)
      • Update Equations
        • VBE-step:
        • VBM-step:
      • Handling Missing Data
      • References
    • Parameter Expansion for Dynamic Factor Analysis
      • Introduction
      • Parameter Expanded VBEM (PX-VBEM)
        • Rotation-Based Parameter Expansion for LGSSM
        • Standard VB-EM Updates
        • PX-VB Rotation Step
        • Finding the Optimal Rotation
        • Static Case Simplification
        • PX-VBEM Algorithm Summary
      • See Also
      • References
    • Bayesian Model Reduction
      • Introduction
      • Principle of Bayesian Model Reduction
      • Mathematical Formulation
      • Variational Approximation
      • Computing \(\Delta F\)
        • MVNIG Case (Loading Matrix)
        • MVN Case (Dynamics Matrix)
      • Gibbs Sampling with Indian Buffet Process Prior
        • Indian Buffet Process Prior
        • Gibbs Sampling Procedure
      • Posterior Correction After Pruning
        • MVNIG (Emissions)
        • MVN (Dynamics)
      • See Also
      • References
    • Examples
      • Testing PX-VBEM for Bayesian Factor Analysis
        • 1. Generate Synthetic FA Data
        • 2. Experiments Without BMR
        • 3. Experiments With BMR
        • 7. Summary
      • Testing PX-VBEM for Dynamic Factor Analysis
        • 1. Generate Synthetic DFA Data
        • 2. Experiments Without BMR
        • 3. Experiments With BMR
        • 7. Summary
      • Testing Observation Masking
      • Part 1: Factor Analysis (Static Mode)
        • 1.1 Regression test: mask=None vs mask=all-True
        • 1.2 FA: Masked training vs subset training
        • 1.3 FA with random masking (30% missing)
      • Part 2: Dynamic Factor Analysis (DFA)
        • 2.1 DFA regression test: mask=None vs mask=all-True
        • 2.2 DFA with random masking (70% missing)
        • 2.3 DFA with partial time-varying masking
        • 2.4 Compare masked vs full DFA training
  • Module Reference
    • Subpackages
      • sppcax.bmr package
        • Submodules
        • sppcax.bmr.delta_f module
        • sppcax.bmr.model_reduction module
        • Module contents
      • sppcax.distributions package
        • Submodules
        • sppcax.distributions.base module
        • sppcax.distributions.beta module
        • sppcax.distributions.categorical module
        • sppcax.distributions.delta module
        • sppcax.distributions.exponential_family module
        • sppcax.distributions.gamma module
        • sppcax.distributions.inverse_wishart module
        • sppcax.distributions.mean_field module
        • sppcax.distributions.mvn module
        • sppcax.distributions.mvn_gamma module
        • sppcax.distributions.normal module
        • sppcax.distributions.poisson module
        • sppcax.distributions.updates module
        • sppcax.distributions.utils module
        • Module contents
      • sppcax.inference package
        • Submodules
        • sppcax.inference.filtering module
        • sppcax.inference.smoothing module
        • sppcax.inference.utils module
        • Module contents
      • sppcax.metrics package
        • Submodules
        • sppcax.metrics.kl_divergence module
        • Module contents
      • sppcax.models package
        • Submodules
        • sppcax.models.dynamic_factor_analysis module
        • sppcax.models.factor_analysis module
        • sppcax.models.likelihood_utils module
        • sppcax.models.utils module
        • Module contents
      • sppcax.parameter_expansion package
        • Submodules
        • sppcax.parameter_expansion.rotation module
        • Module contents
    • Submodules
    • sppcax.types module
    • Module contents
  • Contributions & Help
    • Issue Reports
    • Documentation Improvements
    • Code Contributions
      • Submit an issue
      • Create an environment
      • Clone the repository
      • Implement your changes
      • Submit your contribution
      • Troubleshooting
    • Maintainer tasks
      • Releases
  • License
  • Authors
  • Changelog
    • Version 0.1
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