distributionally robust npe

This work addresses the issue of overconfident and unreliable posterior distributions commonly produced by Neural Posterior Estimation (NPE) under limited simulation budgets. To mitigate this, the authors propose DRO-NPE, a distributionally robust optimization framework that replaces the standard NPE objective with a worst-case loss over a Wasserstein ambiguity set. The method integrates normalizing flows with a parallel training strategy and introduces KL divergence–based metrics to quantify under-coverage and calibration error, effectively curbing overfitting and overconfidence. Experimental results demonstrate that DRO-NPE significantly improves posterior coverage and calibration across multiple simulation-based inference benchmarks, narrows the gap between empirical and population losses, and yields more reliable Bayesian inference—particularly in low-simulation regimes.

This work addresses the sensitivity of Bayesian optimization to model misspecification, which can lead to fragile out-of-sample decisions. The authors propose a distributionally robust optimization framework that formalizes and quantifies model robustness under perturbations to both parameters and likelihood through novel measures: posterior sensitivity and likelihood sensitivity. Theoretical analysis reveals that posterior sensitivity vanishes as variance decreases, whereas likelihood sensitivity persists; parameter learning mitigates the former but cannot eliminate the latter. By constructing an uncertainty set based on a bias-aware divergence measure, the method achieves a near-Pareto-optimal trade-off between expected performance and dual robustness. Empirical experiments validate the effectiveness of the proposed approach.

For high-dimensional simulator-based models with intractable likelihoods, this paper proposes an efficient and stable Sequential Neural Posterior Estimation (SNPE) method. The approach employs conditional neural density estimation within a sequential simulation framework, augmented by an adaptive calibration kernel mechanism—novelly introduced herein—to dynamically adjust kernel weights during inference. To further enhance stability and accelerate convergence, we integrate importance-weighted gradient variance reduction with Monte Carlo loss optimization. This combination effectively mitigates the inference bottlenecks inherent in high-dimensional settings while preserving posterior approximation accuracy. Extensive experiments on multiple benchmark simulators and real-world high-dimensional datasets demonstrate that our method achieves over a two-fold speedup in training time and reduces posterior approximation error by more than 30% compared to standard SNPE and other state-of-the-art approaches.

Sequential decision-making under model uncertainty remains challenging, particularly when prior knowledge is limited and posterior distributions are complex. Method: This paper proposes DRO-BAS, a distributionally robust optimization (DRO) framework grounded in Bayesian posterior inference. It constructs two novel ambiguity sets—posterior expectation–based and posterior predictive–based—enabling unified modeling across the entire conjugate exponential family. The framework leverages strong duality theory to ensure computational tractability and supports efficient single-stage optimization. Contributions/Results: DRO-BAS theoretically guarantees strong duality and finite-dimensional reformulation, yielding closed-form or convex optimization solutions. Empirically, it achieves Pareto dominance over existing Bayesian DRO methods on the Newsvendor problem and significantly accelerates computation—while maintaining comparable robustness—in portfolio optimization. All claims are validated on standard benchmarks, integrating distributionally robust optimization, Bayesian inference, and strong duality theory.

Neural Processes (NPs) suffer from underfitting in modeling function distributions due to suboptimal inference, limiting their performance in regression and image completion tasks. This work identifies a systematic bias in standard NPs when maximizing the log-likelihood of the meta-dataset and proposes a surrogate objective grounded in the Expectation-Maximization (EM) framework. We further introduce Self-Normalized Importance-weighted Neural Processes (SI-NP), the first NP variant with a theoretical guarantee of improved log-likelihood estimation. SI-NP integrates importance-weighted variational inference with an attention-enhanced NP architecture. Extensive experiments demonstrate significant improvements over existing NP methods across multiple function regression and image completion benchmarks, achieving state-of-the-art performance. The implementation is publicly available.

This work addresses the lack of finite-sample theoretical guarantees and systematic comparisons for existing robust learning methods under distribution shift between training and deployment environments. Focusing on Distributionally Robust Optimization (DRO) and Robust Satisficing (RS), the paper establishes, for the first time, dimension-free finite-sample generalization error bounds for the target domain and introduces an information-guided hyperparameter calibration strategy that leverages partial knowledge of the distributional shift. Theoretical analysis reveals a complementary relationship between DRO and RS under partial shift information, while empirical studies in inventory network planning demonstrate their distinct response mechanisms to positively shifted demand, thereby providing principled guidance for method selection in practice.

This work addresses the limitations of traditional predict-then-optimize approaches, which ignore prediction uncertainty, and existing distributionally robust optimization (DRO) methods that employ fixed-radius ambiguity sets ill-suited for dynamic risk environments. The authors propose a Learnable Prediction Ambiguity Set (LPAS), which jointly learns the center, state-dependent Wasserstein radius, and anisotropic metric of the ambiguity set. This is achieved through end-to-end joint optimization of a deep contextual model and the downstream decision layer, enhanced by conditional quantile calibration and scale regularization to enable state-adaptive robustness. Evaluated on S&P 500 portfolio optimization from 2018 to 2026, LPAS achieves an annualized return of 26.28%, a Sharpe ratio of 1.30, a terminal wealth of 1.61, lower tail risk, and a smaller average ambiguity set radius compared to benchmarks.

本文统一了保形预测和Wasserstein分布鲁棒优化两种方法，通过调整分位数估计器来解决有限数据下的不确定性量化问题。

This work addresses the vulnerability of probabilistic circuits to overfitting and poor generalization under data noise, limited samples, or distribution shifts. To mitigate this, the authors propose PeTeR, the first data-free post-training framework that enhances the robustness of pretrained probabilistic circuits to distributional shifts without requiring retraining. PeTeR leverages distributionally robust optimization by modeling worst-case distributions within a Wasserstein ball and introduces a data-agnostic parameter adjustment mechanism grounded in this principle. Empirical evaluations across multiple density estimation benchmarks demonstrate that PeTeR significantly improves model robustness against both random and adversarial perturbations, matching or outperforming existing data-dependent robust learning baselines.

本文针对Sinkhorn分布鲁棒假设检验问题，提出一种生成框架，通过学习最不利分布并利用Hyper Input Convex神经网络有效训练和端到端采样来解决大规模锥规划的可扩展性问题。