Semi-supervised Regression Analysis with Model Misspecification and High-dimensional Data

• URL: http://arxiv.org/abs/2406.13906v1
• Date: Thu, 20 Jun 2024 00:34:54 GMT
• Title: Semi-supervised Regression Analysis with Model Misspecification and High-dimensional Data
• Authors: Ye Tian, Peng Wu, Zhiqiang Tan,
• Abstract summary: We present an inference framework for estimating regression coefficients in conditional mean models. We develop an augmented inverse probability weighted (AIPW) method, employing regularized estimators for both propensity score (PS) and outcome regression (OR) models. Our theoretical findings are verified through extensive simulation studies and a real-world data application.
• Score: 8.619243141968886
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The accessibility of vast volumes of unlabeled data has sparked growing interest in semi-supervised learning (SSL) and covariate shift transfer learning (CSTL). In this paper, we present an inference framework for estimating regression coefficients in conditional mean models within both SSL and CSTL settings, while allowing for the misspecification of conditional mean models. We develop an augmented inverse probability weighted (AIPW) method, employing regularized calibrated estimators for both propensity score (PS) and outcome regression (OR) nuisance models, with PS and OR models being sequentially dependent. We show that when the PS model is correctly specified, the proposed estimator achieves consistency, asymptotic normality, and valid confidence intervals, even with possible OR model misspecification and high-dimensional data. Moreover, by suppressing detailed technical choices, we demonstrate that previous methods can be unified within our AIPW framework. Our theoretical findings are verified through extensive simulation studies and a real-world data application.

Related papers

• On conditional diffusion models for PDE simulations [53.01911265639582]
  We study score-based diffusion models for forecasting and assimilation of sparse observations. We propose an autoregressive sampling approach that significantly improves performance in forecasting. We also propose a new training strategy for conditional score-based models that achieves stable performance over a range of history lengths.
  arXiv  Detail & Related papers  (2024-10-21T18:31:04Z)
• Towards Theoretical Understandings of Self-Consuming Generative Models [56.84592466204185]
  This paper tackles the emerging challenge of training generative models within a self-consuming loop. We construct a theoretical framework to rigorously evaluate how this training procedure impacts the data distributions learned by future models. We present results for kernel density estimation, delivering nuanced insights such as the impact of mixed data training on error propagation.
  arXiv  Detail & Related papers  (2024-02-19T02:08:09Z)
• Online Variational Sequential Monte Carlo [49.97673761305336]
  We build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference. Online VSMC is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation.
  arXiv  Detail & Related papers  (2023-12-19T21:45:38Z)
• A PAC-Bayesian Perspective on the Interpolating Information Criterion [54.548058449535155]
  We show how a PAC-Bayes bound is obtained for a general class of models, characterizing factors which influence performance in the interpolating regime. We quantify how the test error for overparameterized models achieving effectively zero training error depends on the quality of the implicit regularization imposed by e.g. the combination of model, parameter-initialization scheme.
  arXiv  Detail & Related papers  (2023-11-13T01:48:08Z)
• Kalman Filter for Online Classification of Non-Stationary Data [101.26838049872651]
  In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. We introduce a probabilistic Bayesian online learning model by using a neural representation and a state space model over the linear predictor weights. In experiments in multi-class classification we demonstrate the predictive ability of the model and its flexibility to capture non-stationarity.
  arXiv  Detail & Related papers  (2023-06-14T11:41:42Z)
• Benign-Overfitting in Conditional Average Treatment Effect Prediction with Linear Regression [14.493176427999028]
  We study the benign overfitting theory in the prediction of the conditional average treatment effect (CATE) with linear regression models. We show that the T-learner fails to achieve the consistency except the random assignment, while the IPW-learner converges the risk to zero if the propensity score is known.
  arXiv  Detail & Related papers  (2022-02-10T18:51:52Z)
• Optimal regularizations for data generation with probabilistic graphical models [0.0]
  Empirically, well-chosen regularization schemes dramatically improve the quality of the inferred models. We consider the particular case of L 2 and L 1 regularizations in the Maximum A Posteriori (MAP) inference of generative pairwise graphical models.
  arXiv  Detail & Related papers  (2021-12-02T14:45:16Z)
• Identification of Latent Variables From Graphical Model Residuals [0.0]
  We present a novel method to control for the latent space when estimating a DAG by iteratively deriving proxies for the latent space from the residuals of the inferred model. We show that any improvement of prediction of an outcome is intrinsically capped and cannot rise beyond a certain limit as compared to the confounded model.
  arXiv  Detail & Related papers  (2021-01-07T02:28:49Z)
• Learning Consistent Deep Generative Models from Sparse Data via Prediction Constraints [16.48824312904122]
  We develop a new framework for learning variational autoencoders and other deep generative models. We show that these two contributions -- prediction constraints and consistency constraints -- lead to promising image classification performance.
  arXiv  Detail & Related papers  (2020-12-12T04:18:50Z)
• Autoregressive Score Matching [113.4502004812927]
  We propose autoregressive conditional score models (AR-CSM) where we parameterize the joint distribution in terms of the derivatives of univariable log-conditionals (scores) For AR-CSM models, this divergence between data and model distributions can be computed and optimized efficiently, requiring no expensive sampling or adversarial training. We show with extensive experimental results that it can be applied to density estimation on synthetic data, image generation, image denoising, and training latent variable models with implicit encoders.
  arXiv  Detail & Related papers  (2020-10-24T07:01:24Z)

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.