ArXiv

Structured Dimension-Matched Joint Variational Transdimensional Inference

2026-08-06 · 05:06 UTC ·Pingping Yin, Xiyun Jiao ·1 min read
Authors
Pingping Yin, Xiyun Jiao
Categories
stat.CO, stat.ME, stat.ML
arXiv
https://arxiv.org/abs/2608.05607v1
PDF
https://arxiv.org/pdf/2608.05607v1

Brief

SM-VTI (Structured Dimension-Matched Variational Transdimensional Inference) addresses Bayesian model selection by representing models as sequences of local stop/child edits on a rooted construction graph; typed edges implement exact native-coordinate dimension-matching lifts while edge-conditioned flows learn residual continuous transport. The paper derives the construction path density, trains by minimizing joint reverse-KL, and demonstrates improved early model-mass recovery and competitive final joint accuracy versus AVTI on 15- and 128-model benchmarks.

Why it matters

SM-VTI (Structured Dimension-Matched Variational Transdimensional Inference) builds a single joint variational distribution over discrete model indicators and model-specific continuous parameters using a rooted construction graph and edge-conditioned flows, avoiding embedding every model in a saturated maximum-dimensional surrogate.

Key details

  • The authors derive an exact path density for the construction-graph generative process and train local policies plus conditional flows by optimizing the joint reverse-KL objective.
  • Empirical results: SM-VTI-Joint accurately recovers terminal masses, local actions, and nonlinear conditional geometry on a controlled 15-model target; on a 128-model misspecified robust variable-selection benchmark (10-dataset, nearly parameter-matched affine comparison) it shows stronger early model-mass recovery and competitive final joint accuracy versus AVTI under the same target-evaluation budget.
Source evidence

Abstract

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.