Model Free Prediction with Uncertainty Assessment
- URL: http://arxiv.org/abs/2405.12684v3
- Date: Sun, 16 Jun 2024 05:30:25 GMT
- Title: Model Free Prediction with Uncertainty Assessment
- Authors: Yuling Jiao, Lican Kang, Jin Liu, Heng Peng, Heng Zuo,
- Abstract summary: We propose a novel framework that transforms the deep estimation paradigm into a platform conducive to conditional mean estimation.
We develop an end-to-end convergence rate for the conditional diffusion model and establish the normality of the generated samples.
Through numerical experiments, we empirically validate the efficacy of our proposed methodology.
- Score: 7.524024486998338
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Deep nonparametric regression, characterized by the utilization of deep neural networks to learn target functions, has emerged as a focus of research attention in recent years. Despite considerable progress in understanding convergence rates, the absence of asymptotic properties hinders rigorous statistical inference. To address this gap, we propose a novel framework that transforms the deep estimation paradigm into a platform conducive to conditional mean estimation, leveraging the conditional diffusion model. Theoretically, we develop an end-to-end convergence rate for the conditional diffusion model and establish the asymptotic normality of the generated samples. Consequently, we are equipped to construct confidence regions, facilitating robust statistical inference. Furthermore, through numerical experiments, we empirically validate the efficacy of our proposed methodology.
Related papers
- Deep Evidential Learning for Dose Prediction [0.0]
We present a novel application of an uncertainty-quantification framework called Deep Evidential Learning in the domain of radiotherapy dose prediction.
We found that this model can be effectively harnessed to yield uncertainty estimates that inherited correlations with prediction errors upon completion of network training.
arXiv Detail & Related papers (2024-04-26T02:43:45Z) - Unveil Conditional Diffusion Models with Classifier-free Guidance: A Sharp Statistical Theory [87.00653989457834]
Conditional diffusion models serve as the foundation of modern image synthesis and find extensive application in fields like computational biology and reinforcement learning.
Despite the empirical success, theory of conditional diffusion models is largely missing.
This paper bridges the gap by presenting a sharp statistical theory of distribution estimation using conditional diffusion models.
arXiv Detail & Related papers (2024-03-18T17:08:24Z) - Semi-Parametric Inference for Doubly Stochastic Spatial Point Processes: An Approximate Penalized Poisson Likelihood Approach [3.085995273374333]
Doubly-stochastic point processes model the occurrence of events over a spatial domain as an inhomogeneous process conditioned on the realization of a random intensity function.
Existing implementations of doubly-stochastic spatial models are computationally demanding, often have limited theoretical guarantee, and/or rely on restrictive assumptions.
arXiv Detail & Related papers (2023-06-11T19:48:39Z) - 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) - Communication-Efficient Distributed Estimation and Inference for Cox's Model [4.731404257629232]
We develop communication-efficient iterative distributed algorithms for estimation and inference in the high-dimensional sparse Cox proportional hazards model.
To construct confidence intervals for linear combinations of high-dimensional hazard regression coefficients, we introduce a novel debiased method.
We provide valid and powerful distributed hypothesis tests for any coordinate element based on a decorrelated score test.
arXiv Detail & Related papers (2023-02-23T15:50:17Z) - The Implicit Delta Method [61.36121543728134]
In this paper, we propose an alternative, the implicit delta method, which works by infinitesimally regularizing the training loss of uncertainty.
We show that the change in the evaluation due to regularization is consistent for the variance of the evaluation estimator, even when the infinitesimal change is approximated by a finite difference.
arXiv Detail & Related papers (2022-11-11T19:34:17Z) - Uncertainty Quantification for Traffic Forecasting: A Unified Approach [21.556559649467328]
Uncertainty is an essential consideration for time series forecasting tasks.
In this work, we focus on quantifying the uncertainty of traffic forecasting.
We develop Deep S-Temporal Uncertainty Quantification (STUQ), which can estimate both aleatoric and relational uncertainty.
arXiv Detail & Related papers (2022-08-11T15:21:53Z) - Conditional-Flow NeRF: Accurate 3D Modelling with Reliable Uncertainty
Quantification [44.598503284186336]
Conditional-Flow NeRF (CF-NeRF) is a novel probabilistic framework to incorporate uncertainty quantification into NeRF-based approaches.
CF-NeRF learns a distribution over all possible radiance fields modelling which is used to quantify the uncertainty associated with the modelled scene.
arXiv Detail & Related papers (2022-03-18T23:26:20Z) - Divergence Frontiers for Generative Models: Sample Complexity,
Quantization Level, and Frontier Integral [58.434753643798224]
Divergence frontiers have been proposed as an evaluation framework for generative models.
We establish non-asymptotic bounds on the sample complexity of the plug-in estimator of divergence frontiers.
We also augment the divergence frontier framework by investigating the statistical performance of smoothed distribution estimators.
arXiv Detail & Related papers (2021-06-15T06:26:25Z) - Leveraging Global Parameters for Flow-based Neural Posterior Estimation [90.21090932619695]
Inferring the parameters of a model based on experimental observations is central to the scientific method.
A particularly challenging setting is when the model is strongly indeterminate, i.e., when distinct sets of parameters yield identical observations.
We present a method for cracking such indeterminacy by exploiting additional information conveyed by an auxiliary set of observations sharing global parameters.
arXiv Detail & Related papers (2021-02-12T12:23:13Z) - Unlabelled Data Improves Bayesian Uncertainty Calibration under
Covariate Shift [100.52588638477862]
We develop an approximate Bayesian inference scheme based on posterior regularisation.
We demonstrate the utility of our method in the context of transferring prognostic models of prostate cancer across globally diverse populations.
arXiv Detail & Related papers (2020-06-26T13:50:19Z)
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.