Generative models for decision-making under distributional shift

• URL: http://arxiv.org/abs/2604.04342v1
• Date: Mon, 06 Apr 2026 01:35:13 GMT
• Title: Generative models for decision-making under distributional shift
• Abstract summary: This tutorial presents modern generative models, particularly flow- and score-based methods, as mathematical tools for constructing decision-relevant distributions.<n>We present a unified framework based on pushforward maps, continuity, Fokker-Planck equations, Wasserstein geometry, and optimization in probability space.
• Score: 19.065806786298534
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Many data-driven decision problems are formulated using a nominal distribution estimated from historical data, while performance is ultimately determined by a deployment distribution that may be shifted, context-dependent, partially observed, or stress-induced. This tutorial presents modern generative models, particularly flow- and score-based methods, as mathematical tools for constructing decision-relevant distributions. From an operations research perspective, their primary value lies not in unconstrained sample synthesis but in representing and transforming distributions through transport maps, velocity fields, score fields, and guided stochastic dynamics. We present a unified framework based on pushforward maps, continuity, Fokker-Planck equations, Wasserstein geometry, and optimization in probability space. Within this framework, generative models can be used to learn nominal uncertainty, construct stressed or least-favorable distributions for robustness, and produce conditional or posterior distributions under side information and partial observation. We also highlight representative theoretical guarantees, including forward-reverse convergence for iterative flow models, first-order minimax analysis in transport-map space, and error-transfer bounds for posterior sampling with generative priors. The tutorial provides a principled introduction to using generative models for scenario generation, robust decision-making, uncertainty quantification, and related problems under distributional shift.

Related papers

• A Unified Measure-Theoretic View of Diffusion, Score-Based, and Flow Matching Generative Models [0.3222802562733787]
  We survey continuous-time generative modeling methods based on transporting a simple reference distribution to a data distribution via deterministic dynamics.<n>We present a unified framework in which diffusion models, score-based generative models, and flow matching are instances of learning a time-dependent vector field.
  arXiv  Detail & Related papers  (2026-05-07T18:32:15Z)
• An Elementary Approach to Scheduling in Generative Diffusion Models [55.171367482496755]
  An elementary approach to characterizing the impact of noise scheduling and time discretization in generative diffusion models is developed.<n> Experiments across different datasets and pretrained models demonstrate that the time discretization strategy selected by our approach consistently outperforms baseline and search-based strategies.
  arXiv  Detail & Related papers  (2026-01-20T05:06:26Z)
• Worst-case generation via minimax optimization in Wasserstein space [19.645939141861543]
  Worst-case generation plays a critical role in evaluating robustness and stress-testing systems under distribution shifts.<n>We develop a generative modeling framework for worst-case generation for a pre-specified risk.
  arXiv  Detail & Related papers  (2025-12-09T02:11:08Z)
• Bridging the Last Mile of Prediction: Enhancing Time Series Forecasting with Conditional Guided Flow Matching [9.465542901469815]
  Conditional Guided Flow Matching (CGFM) is a model-agnostic framework that extends flow matching by integrating outputs from an auxiliary predictive model.<n>CGFM incorporates historical data as both conditions and guidance, uses two-sided conditional paths, and employs affine paths to expand the path space.<n> Experiments across datasets and baselines show CGFM consistently outperforms state-of-the-art models, advancing forecasting.
  arXiv  Detail & Related papers  (2025-07-09T18:03:31Z)
• Partial Transportability for Domain Generalization [56.37032680901525]
  Building on the theory of partial identification and transportability, this paper introduces new results for bounding the value of a functional of the target distribution.<n>Our contribution is to provide the first general estimation technique for transportability problems.<n>We propose a gradient-based optimization scheme for making scalable inferences in practice.
  arXiv  Detail & Related papers  (2025-03-30T22:06:37Z)
• Distributed Markov Chain Monte Carlo Sampling based on the Alternating Direction Method of Multipliers [143.6249073384419]
  In this paper, we propose a distributed sampling scheme based on the alternating direction method of multipliers. We provide both theoretical guarantees of our algorithm's convergence and experimental evidence of its superiority to the state-of-the-art. In simulation, we deploy our algorithm on linear and logistic regression tasks and illustrate its fast convergence compared to existing gradient-based methods.
  arXiv  Detail & Related papers  (2024-01-29T02:08:40Z)
• Performative Prediction with Bandit Feedback: Learning through Reparameterization [23.039885534575966]
  performative prediction is a framework for studying social prediction in which the data distribution itself changes in response to the deployment of a model. We develop a reparametization that reparametrizes the performative prediction objective as a function of induced data distribution.
  arXiv  Detail & Related papers  (2023-05-01T21:31:29Z)
• An Energy-Based Prior for Generative Saliency [62.79775297611203]
  We propose a novel generative saliency prediction framework that adopts an informative energy-based model as a prior distribution. With the generative saliency model, we can obtain a pixel-wise uncertainty map from an image, indicating model confidence in the saliency prediction. Experimental results show that our generative saliency model with an energy-based prior can achieve not only accurate saliency predictions but also reliable uncertainty maps consistent with human perception.
  arXiv  Detail & Related papers  (2022-04-19T10:51:00Z)
• Which Invariance Should We Transfer? A Causal Minimax Learning Approach [18.71316951734806]
  We present a comprehensive minimax analysis from a causal perspective. We propose an efficient algorithm to search for the subset with minimal worst-case risk. The effectiveness and efficiency of our methods are demonstrated on synthetic data and the diagnosis of Alzheimer's disease.
  arXiv  Detail & Related papers  (2021-07-05T09:07:29Z)
• Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks: Theory, Methods, and Algorithms [2.266704469122763]
  This paper proposes a new methodology for performing Bayesian inference in imaging inverse problems where the prior knowledge is available in the form of training data. We establish the existence and well-posedness of the associated posterior moments under easily verifiable conditions. A model accuracy analysis suggests that the Bayesian probability probabilities reported by the data-driven models are also remarkably accurate under a frequentist definition.
  arXiv  Detail & Related papers  (2021-03-18T11:34:08Z)
• Generative Model without Prior Distribution Matching [26.91643368299913]
  Variational Autoencoder (VAE) and its variations are classic generative models by learning a low-dimensional latent representation to satisfy some prior distribution. We propose to let the prior match the embedding distribution rather than imposing the latent variables to fit the prior.
  arXiv  Detail & Related papers  (2020-09-23T09:33:24Z)
• Accounting for Unobserved Confounding in Domain Generalization [107.0464488046289]
  This paper investigates the problem of learning robust, generalizable prediction models from a combination of datasets. Part of the challenge of learning robust models lies in the influence of unobserved confounders. We demonstrate the empirical performance of our approach on healthcare data from different modalities.
  arXiv  Detail & Related papers  (2020-07-21T08:18:06Z)
• Decision-Making with Auto-Encoding Variational Bayes [71.44735417472043]
  We show that a posterior approximation distinct from the variational distribution should be used for making decisions. Motivated by these theoretical results, we propose learning several approximate proposals for the best model. In addition to toy examples, we present a full-fledged case study of single-cell RNA sequencing.
  arXiv  Detail & Related papers  (2020-02-17T19:23:36Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.