Post-Inference Model Chaining: A Problem Statement and a Model-based Bootstrap for Training End-to-End Digital Twins
Lukas Madenach, Timo Bailer, Tobias Eilert
AI 速览：作者指出，在端到端数字孪生中，将完整预测抽样沿各阶段模型链式前向传递的常用Monte Carlo方案会导致区间与覆盖率膨胀，并提出一种基于模型的Bootstrap来改善末端预测。
End-to-end digital twins can be constructed by fitting separate stage models and connecting them after inference. We investigate the Frequentist prediction properties of a commonly used Monte Carlo simulation scheme that forwards complete predictive draws through such a chain when measured stage outputs contain independent normal errors, but the latent stage means are deterministic. Analytical two-stage examples show persistent asymptotic interval and coverage inflation and, with quadratic propagation, mean bias dependent on the parameters to be estimated. Simulations of four- and eight-stage linear-quadratic univariate chains with 7, 15 or 30 training runs demonstrate pronounced input-dependent distortions. A diagnostic using error-free latent training predictors shows that the effect is mainly not attributable to errors in variables, but to the MCSim approach even showing underestimation of coverage. We propose a model-based bootstrap: an initial chain forwards fitted means, bootstrap chains are refitted on fixed-center bootstrap data while forwarding their mean prediction, and a target-stage future error enters a studentized prediction root. Across the investigated scenarios, relative mean bias is substantially reduced, and coverage is closer to the nominal 90%. At sample size 30, the eight-stage bootstrap has mean width ratios of 1.16-1.42 relative to the known-parameter normal reference, compared with 4.11-4.97 for observed-to-observed MCSim. These results support improved endpoint prediction in the tested setting. Further investigations of the bootstrap scheme in the supplement for a bivariate 6-stage process show similar satisfactory results.
Lei Huang, Chuan Qiu, Kuan-Jui Su, Anqi Liu, Yun Gong, Weiqiang Lin, Lindong Jiang, Chen Zhao 等 16 位作者
Genotype imputation enables dense variant coverage for genome-wide association and risk-prediction studies, yet conventional reference-panel methods remain limited by ancestry bias and reduced rare-variant accuracy. We present Genotype Bidirectional Encoder Representations from Transformers (GenoBERT), a transformer-based, reference-free framework that tokenizes phased genotypes and uses a self-attention mechanism to capture both short- and long-range linkage disequilibrium (LD) dependencies. Benchmarking on two independent datasets including the Louisiana Osteoporosis Study (LOS) and the 1000 Genomes Project (1KGP) across ancestry groups and multiple genotype missingness levels (5-50%) shows that GenoBERT achieves the highest overall accuracy compared to four baseline methods (Beagle5.4, SCDA, BiU-Net, and STICI). At practical sparsity levels (up to 25% missing), GenoBERT attains high overall imputation accuracy ($r^2 approx 0.98$) across datasets, and maintains robust performance ($r^2 > 0.90$) even at 50% missingness. Experimental results across different ancestries confirm consistent gains across datasets, with resilience to small sample sizes and weak LD. A 128-SNP (single-nucleotide polymorphism) context window (approximately 100 Kb) is validated through LD-decay analyses as sufficient to capture local correlation structures. By eliminating reference-panel dependence while preserving high accuracy, GenoBERT provides a scalable and robust solution for genotype imputation and a foundation for downstream genomic modeling.
Optimizing expected rewards and reachability probabilities in parametric Markov chains (pMCs) is central to the analysis and synthesis of probabilistic systems with loops. While traditional symbolic synthesis approaches--such as parameter lifting and rational function generation--suffer from scalability bottlenecks, gradient-based optimization emerges as an effective alternative. However, existing gradient-based techniques still rely on symbolic gradient computation--such as solving large linear systems--over the global state space, inheriting scalability limits. Finite-horizon approximation is possible but introduces uncontrollable bias. In this paper, we introduce a scalable Monte Carlo gradient estimator based on a measure-theoretic generalization of the log-derivative trick. We prove that our estimator provides unbiased gradient estimates under almost-sure termination and standard regularity conditions. Crucially, our method avoids global state-space materialization and linear system solving entirely: it operates purely along sampled trajectories, requiring only black-box evaluations of local transition probabilities (or densities) and their derivatives. Unlike existing pMC techniques that are fundamentally restricted to finite discrete systems, our measure-theoretic framework naturally extends to continuous and general $σ$-finite state spaces. Empirical evaluations on synthetic discrete pMCs and continuous-state case studies demonstrate that our method scales to state spaces far beyond the reach of existing solvers, significantly reducing execution time without introducing bias.