# Structured Dimension-Matched Joint Variational Transdimensional Inference

arXiv: https://arxiv.org/abs/2608.05607 · HTML: https://mlsanity.com/paper/2608.05607/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 8 references that are in the map.
- First posted on arXiv 6 Aug 2026.

## Builds on (most cited first, 3 of 3)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Transport Reversible Jump Proposals](https://mlsanity.com/paper/2210.12572/) (2022)
- [Variational Transdimensional Inference](https://mlsanity.com/paper/2506.04749/) (2025)

## Abstract (arXiv)

Bayesian model selection couples a discrete model indicator with a model-specific continuous parameter space. We introduce structured dimension-matched variational transdimensional inference (SM-VTI) for finite enumerable model spaces. A rooted construction graph expresses a model as a sequence of local stop/child decisions. Each typed edge compiles a declared scientific parent-child edit into an exact native-coordinate dimension-matching lifting; an edge-conditioned flow then learns the residual continuous transport. The resulting local policy and conditional flow define one direct joint variational distribution, without embedding every model in a saturated maximum-dimensional surrogate. We derive its exact path density and optimize the joint reverse-KL objective. On a controlled 15-model target, SM-VTI-Joint recovers terminal masses, local actions, and nonlinear conditional geometry. On a 128-model misspecified robust variable-selection problem, a 10-data-set nearly parameter-matched affine comparison with AVTI shows stronger early model-mass recovery and competitive final joint accuracy under the same target-evaluation budget.