Dynamical Factor Models (DFM) Implementation (GSOC 2025) (#446)

* Added new file DFM.py for GSOC 2025 Dynamical Factor Models

* Add initial notebook on custom DFM implementation

* Update of DFM draft implementation

In the notebook a comparison between the custom DFM and the implemented DFM (which has an hardcoded version of make_symbolic_graph, that work just in this case)

* Aligning the order of vector state with statsmodel and updating the test

* Added test_DFM_update_matches_statsmodels and small corrections to DFM.py

* Updating test following test_ETS.py and small adjustment for exog variables in DFM.py

* Added support for joint VAR modelling (error_var=True)

* Adding a first implemntation of exogeneous variable support based on pymc_extras/statespace/models/structural/components/regression.py

* Completing the implementation of exogeneous varibales support

* Small adjustments and improvements in DFM.py

* Small adjustments and improvements in DFM.py

* Adjustments after Jesse review

* Adjustments following Jesse suggestions and added tests for exog support

* Added new DFM example notebook and deleted an old version of custom DFM example

* Add tests for names/dims/coords

* De-duplicate exogenous dim between DFM and SARIMAX

* Small adjustments and refactoring after code review

* Allow exogenous regressors in `BayesianVARMAX` (#567)

* First pass on exogenous variables in VARMA

* Adjust state names for API consistency

* Allow exogenous variables in BayesianVARMAX

* Eagerly simplify model where possible

* Typo fix

* Small adjustments in the tests after review

* Harmonizing names for EXOG dimension between DFM and VARMAX

* Corrections in the notebook and add a small comment in DFM.py

* Add deterministic advi (#564)

* Add first version of deterministic ADVI

* Update API

* Add a notebook example

* Add to API and add a docstring

* Change import in notebook

* Add jax to dependencies

* Add pytensor version

* Fix handling of pymc model

* Add (probably suboptimal) handling of the two backends

* Add transformation

* Follow Ricardo's advice to simplify the transformation step

* Fix naming bug

* Document and clean up

* Fix example

* Update pymc_extras/inference/deterministic_advi/dadvi.py

Co-authored-by: Ricardo Vieira <[email protected]>

* Respond to comments

* Fix with pre commit checks

* Update pymc_extras/inference/deterministic_advi/dadvi.py

Co-authored-by: Jesse Grabowski <[email protected]>

* Implement suggestions

* Rename parameter because it's duplicated otherwise

* Rename to be consistent in use of dadvi

* Rename to `optimizer_method` and drop jac=True

* Add jac=True back in since trust-ncg complained

* Make hessp and jac optional

* Harmonize naming with existing code

* Fix example

* Switch to `better_optimize`

* Replace with pt.split

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Co-authored-by: Martin Ingram <[email protected]>
Co-authored-by: Ricardo Vieira <[email protected]>
Co-authored-by: Jesse Grabowski <[email protected]>

* Small adjustments in the notebook

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Co-authored-by: jessegrabowski <[email protected]>
Co-authored-by: Jesse Grabowski <[email protected]>
Co-authored-by: Martin Ingram <[email protected]>
Co-authored-by: Martin Ingram <[email protected]>
Co-authored-by: Ricardo Vieira <[email protected]>

Author: 5 people