Monte Carlo inference for semiparametric Bayesian regression

• URL: http://arxiv.org/abs/2306.05498v2
• Date: Mon, 29 Jul 2024 18:12:09 GMT
• Title: Monte Carlo inference for semiparametric Bayesian regression
• Authors: Daniel R. Kowal, Bohan Wu,
• Abstract summary: This paper introduces a simple, general, and efficient strategy for joint posterior inference of an unknown transformation and all regression model parameters. It delivers (1) joint posterior consistency under general conditions, including multiple model misspecifications, and (2) efficient Monte Carlo (not Markov chain Monte Carlo) inference for the transformation and all parameters for important special cases.
• Score: 5.488491124945426
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Data transformations are essential for broad applicability of parametric regression models. However, for Bayesian analysis, joint inference of the transformation and model parameters typically involves restrictive parametric transformations or nonparametric representations that are computationally inefficient and cumbersome for implementation and theoretical analysis, which limits their usability in practice. This paper introduces a simple, general, and efficient strategy for joint posterior inference of an unknown transformation and all regression model parameters. The proposed approach directly targets the posterior distribution of the transformation by linking it with the marginal distributions of the independent and dependent variables, and then deploys a Bayesian nonparametric model via the Bayesian bootstrap. Crucially, this approach delivers (1) joint posterior consistency under general conditions, including multiple model misspecifications, and (2) efficient Monte Carlo (not Markov chain Monte Carlo) inference for the transformation and all parameters for important special cases. These tools apply across a variety of data domains, including real-valued, positive, and compactly-supported data. Simulation studies and an empirical application demonstrate the effectiveness and efficiency of this strategy for semiparametric Bayesian analysis with linear models, quantile regression, and Gaussian processes. The R package SeBR is available on CRAN.

Related papers

• von Mises Quasi-Processes for Bayesian Circular Regression [57.88921637944379]
  We explore a family of expressive and interpretable distributions over circle-valued random functions. The resulting probability model has connections with continuous spin models in statistical physics. For posterior inference, we introduce a new Stratonovich-like augmentation that lends itself to fast Markov Chain Monte Carlo sampling.
  arXiv  Detail & Related papers  (2024-06-19T01:57:21Z)
• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  This paper presents a succinct derivation of the training and generalization performance of a variety of high-dimensional ridge regression models. We provide an introduction and review of recent results on these topics, aimed at readers with backgrounds in physics and deep learning.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• Variational Bayesian surrogate modelling with application to robust design optimisation [0.9626666671366836]
  Surrogate models provide a quick-to-evaluate approximation to complex computational models. We consider Bayesian inference for constructing statistical surrogates with input uncertainties and dimensionality reduction. We demonstrate intrinsic and robust structural optimisation problems where cost functions depend on a weighted sum of the mean and standard deviation of model outputs.
  arXiv  Detail & Related papers  (2024-04-23T09:22:35Z)
• Fusion of Gaussian Processes Predictions with Monte Carlo Sampling [61.31380086717422]
  In science and engineering, we often work with models designed for accurate prediction of variables of interest. Recognizing that these models are approximations of reality, it becomes desirable to apply multiple models to the same data and integrate their outcomes.
  arXiv  Detail & Related papers  (2024-03-03T04:21:21Z)
• Gradient-flow adaptive importance sampling for Bayesian leave one out cross-validation with application to sigmoidal classification models [0.9895793818721335]
  gradient-flow-guided adaptive importance sampling (IS) transformations for stabilizing Monte-Carlo approximations of leave-one-out predictions. We derive closed-form exact formulae for Jacobian determinants with respect to the model Hessian.
  arXiv  Detail & Related papers  (2024-02-13T01:03:39Z)
• Conformal inference for regression on Riemannian Manifolds [49.7719149179179]
  We investigate prediction sets for regression scenarios when the response variable, denoted by $Y$, resides in a manifold, and the covariable, denoted by X, lies in Euclidean space. We prove the almost sure convergence of the empirical version of these regions on the manifold to their population counterparts.
  arXiv  Detail & Related papers  (2023-10-12T10:56:25Z)
• Sparse high-dimensional linear regression with a partitioned empirical Bayes ECM algorithm [62.997667081978825]
  We propose a computationally efficient and powerful Bayesian approach for sparse high-dimensional linear regression. Minimal prior assumptions on the parameters are used through the use of plug-in empirical Bayes estimates. The proposed approach is implemented in the R package probe.
  arXiv  Detail & Related papers  (2022-09-16T19:15:50Z)
• Nonparametric Functional Analysis of Generalized Linear Models Under Nonlinear Constraints [0.0]
  This article introduces a novel nonparametric methodology for Generalized Linear Models. It combines the strengths of the binary regression and latent variable formulations for categorical data. It extends recently published parametric versions of the methodology and generalizes it.
  arXiv  Detail & Related papers  (2021-10-11T04:49:59Z)
• Convex Latent Effect Logit Model via Sparse and Low-rank Decomposition [2.1915057426589746]
  We propose a convexparametric convexparametric formulation for learning logistic regression model (logit) with latent heterogeneous effect on sub-population. Despite its popularity, the mixed logit approach for learning individual heterogeneity has several downsides.
  arXiv  Detail & Related papers  (2021-08-22T22:23:39Z)
• Statistical Guarantees for Transformation Based Models with Applications to Implicit Variational Inference [8.333191406788423]
  We provide theoretical justification for the use of non-linear latent variable models (NL-LVMs) in non-parametric inference. We use the NL-LVMs to construct an implicit family of variational distributions, deemed GP-IVI. To the best of our knowledge, this is the first work on providing theoretical guarantees for implicit variational inference.
  arXiv  Detail & Related papers  (2020-10-23T21:06:29Z)
• Understanding Implicit Regularization in Over-Parameterized Single Index Model [55.41685740015095]
  We design regularization-free algorithms for the high-dimensional single index model. We provide theoretical guarantees for the induced implicit regularization phenomenon.
  arXiv  Detail & Related papers  (2020-07-16T13:27:47Z)

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.