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A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
Multiple Imputation Guided by Full Law and Target Law Ide...
[Submitted on 24 Oct 2024 (v1), last revised 27 Aug 2026 (this v · 2024-10-24 · via stat updates on arXiv.org

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Abstract:The central challenges in missing data models concern the identifiability of two distributions: the target law and the full law. The target law refers to the joint distribution of the data variables, whereas the full law refers to the joint distribution of the data variables and their corresponding response indicators. However, the relationship between the identifiability of these two distributions and the feasibility of multiple imputation has not been clearly established when the data are missing not at random (MNAR). We present a procedure in which the choice of imputation method is guided by identifiability considerations. The identifiability of the full law implies the applicability of conditionally complete imputation methods that draw imputations for all missing data patterns. By contrast, the non-identifiability of the full law implies that any multiple imputation method aiming to implement conditionally complete imputation will produce biased estimates, thereby also restricting the options for estimating the target law. We demonstrate that alternative imputation strategies can sometimes enable the estimation of the target law in such cases. Specifically, we introduce factorizable imputation where certain observed values are also imputed and the imputed data are weighted in the analysis.

Submission history

From: Juha Karvanen [view email]
[v1] Thu, 24 Oct 2024 12:33:58 UTC (9 KB)
[v2] Fri, 31 Jan 2025 13:31:16 UTC (12 KB)
[v3] Tue, 6 May 2025 07:12:36 UTC (12 KB)
[v4] Tue, 28 Oct 2025 18:42:20 UTC (17 KB)
[v5] Wed, 24 Jun 2026 06:55:19 UTC (28 KB)
[v6] Thu, 27 Aug 2026 08:33:56 UTC (31 KB)