Partially factorized variational inference for high-dimensional mixed models

• URL: http://arxiv.org/abs/2312.13148v2
• Date: Sun, 01 Dec 2024 01:37:11 GMT
• Title: Partially factorized variational inference for high-dimensional mixed models
• Authors: Max Goplerud, Omiros Papaspiliopoulos, Giacomo Zanella,
• Abstract summary: Variational inference is a popular way to perform such computations, especially in the Bayesian context.<n>We show that standard mean-field variational inference dramatically underestimates posterior uncertainty in high-dimensions.<n>We then show how appropriately relaxing the mean-field assumption leads to methods whose uncertainty quantification does not deteriorate in high-dimensions.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: While generalized linear mixed models are a fundamental tool in applied statistics, many specifications, such as those involving categorical factors with many levels or interaction terms, can be computationally challenging to estimate due to the need to compute or approximate high-dimensional integrals. Variational inference is a popular way to perform such computations, especially in the Bayesian context. However, naive use of such methods can provide unreliable uncertainty quantification. We show that this is indeed the case for mixed models, proving that standard mean-field variational inference dramatically underestimates posterior uncertainty in high-dimensions. We then show how appropriately relaxing the mean-field assumption leads to methods whose uncertainty quantification does not deteriorate in high-dimensions, and whose total computational cost scales linearly with the number of parameters and observations. Our theoretical and numerical results focus on mixed models with Gaussian or binomial likelihoods, and rely on connections to random graph theory to obtain sharp high-dimensional asymptotic analysis. We also provide generic results, which are of independent interest, relating the accuracy of variational inference to the convergence rate of the corresponding coordinate ascent algorithm that is used to find it. Our proposed methodology is implemented in the R package, see https://github.com/mgoplerud/vglmer . Numerical results with simulated and real data examples illustrate the favourable computation cost versus accuracy trade-off of our approach compared to various alternatives.

Related papers

• Multivariate root-n-consistent smoothing parameter free matching estimators and estimators of inverse density weighted expectations [51.000851088730684]
  We develop novel modifications of nearest-neighbor and matching estimators which converge at the parametric $sqrt n $-rate. We stress that our estimators do not involve nonparametric function estimators and in particular do not rely on sample-size dependent parameters smoothing.
  arXiv  Detail & Related papers  (2024-07-11T13:28:34Z)
• 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)
• Extending Mean-Field Variational Inference via Entropic Regularization: Theory and Computation [2.2656885622116394]
  Variational inference (VI) has emerged as a popular method for approximate inference for high-dimensional Bayesian models. We propose a novel VI method that extends the naive mean field via entropic regularization. We show that $Xi$-variational posteriors effectively recover the true posterior dependency.
  arXiv  Detail & Related papers  (2024-04-14T01:40:11Z)
• Efficient Training of Probabilistic Neural Networks for Survival Analysis [0.6437284704257459]
  Variational Inference (VI) is a commonly used technique for approximate Bayesian inference and uncertainty estimation in deep learning models. It comes at a computational cost, as it doubles the number of trainable parameters to represent uncertainty. We investigate how to train deep probabilistic survival models in large datasets without introducing additional overhead in model complexity.
  arXiv  Detail & Related papers  (2024-04-09T16:10:39Z)
• A Generalized Variable Importance Metric and Estimator for Black Box Machine Learning Models [0.21249247666376617]
  We define a population parameter, Generalized Variable Importance Metric (GVIM)'', to measure importance of predictors for black box machine learning methods. We extend previously published results to show that the defined GVIM can be represented as a function of the Conditional Average Treatment Effect (CATE) for any kind of a predictor.
  arXiv  Detail & Related papers  (2022-12-20T00:50:28Z)
• Manifold Gaussian Variational Bayes on the Precision Matrix [70.44024861252554]
  We propose an optimization algorithm for Variational Inference (VI) in complex models. We develop an efficient algorithm for Gaussian Variational Inference whose updates satisfy the positive definite constraint on the variational covariance matrix. Due to its black-box nature, MGVBP stands as a ready-to-use solution for VI in complex models.
  arXiv  Detail & Related papers  (2022-10-26T10:12:31Z)
• Posterior and Computational Uncertainty in Gaussian Processes [52.26904059556759]
  Gaussian processes scale prohibitively with the size of the dataset. Many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited computation, is entirely ignored when using the approximate posterior. We develop a new class of methods that provides consistent estimation of the combined uncertainty arising from both the finite number of data observed and the finite amount of computation expended.
  arXiv  Detail & Related papers  (2022-05-30T22:16:25Z)
• Efficient CDF Approximations for Normalizing Flows [64.60846767084877]
  We build upon the diffeomorphic properties of normalizing flows to estimate the cumulative distribution function (CDF) over a closed region. Our experiments on popular flow architectures and UCI datasets show a marked improvement in sample efficiency as compared to traditional estimators.
  arXiv  Detail & Related papers  (2022-02-23T06:11:49Z)
• Learning to Estimate Without Bias [57.82628598276623]
  Gauss theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via deep learning with bias constraints. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance.
  arXiv  Detail & Related papers  (2021-10-24T10:23:51Z)
• Efficient Semi-Implicit Variational Inference [65.07058307271329]
  We propose an efficient and scalable semi-implicit extrapolational (SIVI) Our method maps SIVI's evidence to a rigorous inference of lower gradient values.
  arXiv  Detail & Related papers  (2021-01-15T11:39:09Z)
• A similarity-based Bayesian mixture-of-experts model [0.5156484100374058]
  We present a new non-parametric mixture-of-experts model for multivariate regression problems. Using a conditionally specified model, predictions for out-of-sample inputs are based on similarities to each observed data point. Posterior inference is performed on the parameters of the mixture as well as the distance metric.
  arXiv  Detail & Related papers  (2020-12-03T18:08:30Z)
• Generalized Matrix Factorization: efficient algorithms for fitting generalized linear latent variable models to large data arrays [62.997667081978825]
  Generalized Linear Latent Variable models (GLLVMs) generalize such factor models to non-Gaussian responses. Current algorithms for estimating model parameters in GLLVMs require intensive computation and do not scale to large datasets. We propose a new approach for fitting GLLVMs to high-dimensional datasets, based on approximating the model using penalized quasi-likelihood.
  arXiv  Detail & Related papers  (2020-10-06T04:28:19Z)
• Instability, Computational Efficiency and Statistical Accuracy [101.32305022521024]
  We develop a framework that yields statistical accuracy based on interplay between the deterministic convergence rate of the algorithm at the population level, and its degree of (instability) when applied to an empirical object based on $n$ samples. We provide applications of our general results to several concrete classes of models, including Gaussian mixture estimation, non-linear regression models, and informative non-response models.
  arXiv  Detail & Related papers  (2020-05-22T22:30:52Z)
• Machine learning for causal inference: on the use of cross-fit estimators [77.34726150561087]
  Doubly-robust cross-fit estimators have been proposed to yield better statistical properties. We conducted a simulation study to assess the performance of several estimators for the average causal effect (ACE) When used with machine learning, the doubly-robust cross-fit estimators substantially outperformed all of the other estimators in terms of bias, variance, and confidence interval coverage.
  arXiv  Detail & Related papers  (2020-04-21T23:09:55Z)
• Asymptotic Analysis of an Ensemble of Randomly Projected Linear Discriminants [94.46276668068327]
  In [1], an ensemble of randomly projected linear discriminants is used to classify datasets. We develop a consistent estimator of the misclassification probability as an alternative to the computationally-costly cross-validation estimator. We also demonstrate the use of our estimator for tuning the projection dimension on both real and synthetic data.
  arXiv  Detail & Related papers  (2020-04-17T12:47:04Z)
• Maximum likelihood estimation and uncertainty quantification for Gaussian process approximation of deterministic functions [10.319367855067476]
  This article provides one of the first theoretical analyses in the context of Gaussian process regression with a noiseless dataset. We show that the maximum likelihood estimation of the scale parameter alone provides significant adaptation against misspecification of the Gaussian process model.
  arXiv  Detail & Related papers  (2020-01-29T17:20:21Z)

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.