Cross-Block Conditioning in Deep Boltzmann Machines for Statistical Data Fusion

• URL: http://arxiv.org/abs/2609.14934v1
• Date: Mon, 14 Sep 2026 02:26:16 GMT
• Title: Cross-Block Conditioning in Deep Boltzmann Machines for Statistical Data Fusion
• Abstract summary: We propose observed-block multi-prediction, which restricts the multi-prediction objective to targets drawn from what each row actually observes.<n>Having a discriminative criterion that survives the setting lets us ask whether the joint model is needed at all.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Statistical data fusion combines two panels that share a block of covariates but observe disjoint outcome blocks, and in its traditional form no row observes both outcomes at once. That rules out the discriminative criterion one would rather train a Deep Boltzmann Machine with, since multi-prediction training needs ground truth for whatever it holds out. We propose observed-block multi-prediction, which restricts the multi-prediction objective to targets drawn from what each row actually observes. It is well defined for any missingness pattern and reduces to the original criterion when rows are complete. Having a discriminative criterion that survives the setting lets us ask whether the joint model is needed at all, by separating what it contributes into a representation part and an inference part. On two consumer panels, on grids over sample size and covariate width spanning 35 cells and 875 runs, the fine-tuned DBM is the best of fifteen methods in every cell; but almost none of that advantage comes from generative pre-training, which is confined to the smallest sample size on one dataset and absent on the other. It comes from conditioning on one outcome block when predicting the other. This term amounts to +0.19 and +0.07 percentage points, is positive in all 35 cells, and, unlike every other contribution we measure, neither decays as the panels grow, nor requires a second hidden layer, nor requires more inference. Permuting one outcome block to destroy its association with the other removes the gain entirely, which is what the account predicts. The margins are small. But a small effect that does not decay is a different object from one that does, because it rests on evidence that no model mapping covariates to outcomes can accept.

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