sppcax
latest
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
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Documentation Improvements
Code Contributions
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Troubleshooting
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Changelog
Version 0.1
sppcax
sppcax package
sppcax.metrics package
View page source
sppcax.metrics package
Submodules
sppcax.metrics.kl_divergence module
Module contents