Statistical Inference via Generative Models: Flow Matching and Causal Inference

• URL: http://arxiv.org/abs/2603.09009v1
• Date: Mon, 09 Mar 2026 22:56:02 GMT
• Title: Statistical Inference via Generative Models: Flow Matching and Causal Inference
• Abstract summary: Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque.<n>This book reinterprets generative AI in the language of statistics, using flow matching as a central example.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Generative AI has achieved remarkable empirical success, but from the perspective of statistics it often remains opaque: its predictions may be accurate, yet the underlying mechanism is difficult to interpret, analyze, and trust. This book reinterprets generative AI in the language of statistics, using flow matching as a central example. The key idea is that generative models should be understood not merely as devices for producing plausible data, but as methods for the nonparametric learning of high-dimensional probability distributions. From this viewpoint, missing-data imputation becomes principled sampling from learned conditional distributions, counterfactual analysis becomes the estimation of intervention distributions, and distributional dynamics become statistically analyzable objects. Mathematically, flow matching represents distributional deformation through the continuity equation and a time-dependent velocity field, thereby extending score matching from the learning of static score fields to the learning of transport paths themselves. Building on this foundation, the book develops a statistical framework in which generative models are used to estimate nuisance components while inferential validity is maintained through orthogonalization and cross-fitting in the spirit of double/debiased machine learning. Applications to survival analysis, censoring, missingness, and causal inference show how generative models can be integrated into statistical inference for structured high-dimensional problems.

Related papers

• Robust Estimation for Kernel Exponential Families with Smoothed Total Variation Distances [2.317910166616341]
  In statistical inference, we commonly assume that samples are independent and identically distributed from a probability distribution. In this paper, we explore the application of GAN-like estimators to a general class of statistical models.
  arXiv  Detail & Related papers  (2024-10-28T05:50:47Z)
• Quantifying Distribution Shifts and Uncertainties for Enhanced Model Robustness in Machine Learning Applications [0.0]
  This study explores model adaptation and generalization by utilizing synthetic data. We employ quantitative measures such as Kullback-Leibler divergence, Jensen-Shannon distance, and Mahalanobis distance to assess data similarity. Our findings suggest that utilizing statistical measures, such as the Mahalanobis distance, to determine whether model predictions fall within the low-error "interpolation regime" or the high-error "extrapolation regime" provides a complementary method for assessing distribution shift and model uncertainty.
  arXiv  Detail & Related papers  (2024-05-03T10:05:31Z)
• Model-agnostic variable importance for predictive uncertainty: an entropy-based approach [1.912429179274357]
  We show how existing methods in explainability can be extended to uncertainty-aware models. We demonstrate the utility of these approaches to understand both the sources of uncertainty and their impact on model performance.
  arXiv  Detail & Related papers  (2023-10-19T15:51:23Z)
• Quantification of Predictive Uncertainty via Inference-Time Sampling [57.749601811982096]
  We propose a post-hoc sampling strategy for estimating predictive uncertainty accounting for data ambiguity. The method can generate different plausible outputs for a given input and does not assume parametric forms of predictive distributions.
  arXiv  Detail & Related papers  (2023-08-03T12:43:21Z)
• Advancing Counterfactual Inference through Nonlinear Quantile Regression [77.28323341329461]
  We propose a framework for efficient and effective counterfactual inference implemented with neural networks. The proposed approach enhances the capacity to generalize estimated counterfactual outcomes to unseen data. Empirical results conducted on multiple datasets offer compelling support for our theoretical assertions.
  arXiv  Detail & Related papers  (2023-06-09T08:30:51Z)
• MAUVE Scores for Generative Models: Theory and Practice [95.86006777961182]
  We present MAUVE, a family of comparison measures between pairs of distributions such as those encountered in the generative modeling of text or images. We find that MAUVE can quantify the gaps between the distributions of human-written text and those of modern neural language models. We demonstrate in the vision domain that MAUVE can identify known properties of generated images on par with or better than existing metrics.
  arXiv  Detail & Related papers  (2022-12-30T07:37:40Z)
• Discriminative and Generative Learning for Linear Estimation of Random Signals [Lecture Notes] [40.38581446579124]
  Inference tasks in signal processing are often characterized by reliable statistical modeling with missing instance-specific parameters. One conventional approach uses data to estimate these missing parameters and then infers based on the estimated model. This lecture note introduces the concepts of generative and discriminative learning for inference with a partially-known statistical model.
  arXiv  Detail & Related papers  (2022-06-09T11:39:41Z)
• Bias-inducing geometries: an exactly solvable data model with fairness implications [12.532003449620607]
  We introduce an exactly solvable high-dimensional model of data imbalance.<n>We analytically unpack the typical properties of learning models trained in this synthetic framework.<n>We obtain exact predictions for the observables that are commonly employed for fairness assessment.
  arXiv  Detail & Related papers  (2022-05-31T16:27:57Z)
• Causality and Generalizability: Identifiability and Learning Methods [0.0]
  This thesis contributes to the research areas concerning the estimation of causal effects, causal structure learning, and distributionally robust prediction methods. We present novel and consistent linear and non-linear causal effects estimators in instrumental variable settings that employ data-dependent mean squared prediction error regularization. We propose a general framework for distributional robustness with respect to intervention-induced distributions.
  arXiv  Detail & Related papers  (2021-10-04T13:12:11Z)
• Trust but Verify: Assigning Prediction Credibility by Counterfactual Constrained Learning [123.3472310767721]
  Prediction credibility measures are fundamental in statistics and machine learning. These measures should account for the wide variety of models used in practice. The framework developed in this work expresses the credibility as a risk-fit trade-off.
  arXiv  Detail & Related papers  (2020-11-24T19:52:38Z)
• General stochastic separation theorems with optimal bounds [68.8204255655161]
  Phenomenon of separability was revealed and used in machine learning to correct errors of Artificial Intelligence (AI) systems and analyze AI instabilities. Errors or clusters of errors can be separated from the rest of the data. The ability to correct an AI system also opens up the possibility of an attack on it, and the high dimensionality induces vulnerabilities caused by the same separability.
  arXiv  Detail & Related papers  (2020-10-11T13:12:41Z)
• Good Classifiers are Abundant in the Interpolating Regime [64.72044662855612]
  We develop a methodology to compute precisely the full distribution of test errors among interpolating classifiers. We find that test errors tend to concentrate around a small typical value $varepsilon*$, which deviates substantially from the test error of worst-case interpolating model. Our results show that the usual style of analysis in statistical learning theory may not be fine-grained enough to capture the good generalization performance observed in practice.
  arXiv  Detail & Related papers  (2020-06-22T21:12:31Z)
• Balance-Subsampled Stable Prediction [55.13512328954456]
  We propose a novel balance-subsampled stable prediction (BSSP) algorithm based on the theory of fractional factorial design. A design-theoretic analysis shows that the proposed method can reduce the confounding effects among predictors induced by the distribution shift. Numerical experiments on both synthetic and real-world data sets demonstrate that our BSSP algorithm significantly outperforms the baseline methods for stable prediction across unknown test data.
  arXiv  Detail & Related papers  (2020-06-08T07:01:38Z)

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.