结构化维度匹配联合变分跨维推理
Structured Dimension-Matched Joint Variational Transdimensional Inference
AI总结：
针对有限可枚举模型空间，提出SM-VTI方法，通过构造图与条件流定义联合变分分布，在15模型受控任务及128模型变量选择任务中，其模型质量恢复与联合精度表现优于或媲美对比方法。
AI中文摘要：
贝叶斯模型选择将离散模型指示符与特定模型的连续参数空间耦合。针对有限可枚举模型空间，我们提出结构化维度匹配变分跨维推理（SM-VTI）。带根的构造图将模型表示为一系列局部停止/子节点决策；每条带类型的边将声明的科学父子编辑编译为精确的原生坐标维度匹配提升；边条件化流则学习剩余连续传输。所得局部策略与条件流定义了一个直接联合变分分布，无需将每个模型嵌入饱和的最大维代理。我们推导其精确路径密度并优化联合反向KL目标。在受控15个模型的目标上，SM-VTI-Joint恢复了终端质量、局部动作和非线性条件几何；在128个模型的误设定鲁棒变量选择问题中，与AVTI进行的10个数据集近参数匹配仿射比较显示，在相同目标评估预算下，SM-VTI-Joint的早期模型质量恢复更强，最终联合精度具有竞争力。
英文摘要：
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.
