Variational Gibbs Inference for Statistical Model Estimation from Incomplete Data

• URL: http://arxiv.org/abs/2111.13180v4
• Date: Tue, 15 Aug 2023 08:57:59 GMT
• Title: Variational Gibbs Inference for Statistical Model Estimation from Incomplete Data
• Authors: Vaidotas Simkus, Benjamin Rhodes, Michael U. Gutmann
• Abstract summary: We introduce variational Gibbs inference (VGI), a new general-purpose method to estimate the parameters of statistical models from incomplete data. We validate VGI on a set of synthetic and real-world estimation tasks, estimating important machine learning models such as variational autoencoders and normalising flows from incomplete data.
• Score: 7.4250022679087495
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Statistical models are central to machine learning with broad applicability across a range of downstream tasks. The models are controlled by free parameters that are typically estimated from data by maximum-likelihood estimation or approximations thereof. However, when faced with real-world data sets many of the models run into a critical issue: they are formulated in terms of fully-observed data, whereas in practice the data sets are plagued with missing data. The theory of statistical model estimation from incomplete data is conceptually similar to the estimation of latent-variable models, where powerful tools such as variational inference (VI) exist. However, in contrast to standard latent-variable models, parameter estimation with incomplete data often requires estimating exponentially-many conditional distributions of the missing variables, hence making standard VI methods intractable. We address this gap by introducing variational Gibbs inference (VGI), a new general-purpose method to estimate the parameters of statistical models from incomplete data. We validate VGI on a set of synthetic and real-world estimation tasks, estimating important machine learning models such as variational autoencoders and normalising flows from incomplete data. The proposed method, whilst general-purpose, achieves competitive or better performance than existing model-specific estimation methods.

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)
• Influence Functions for Scalable Data Attribution in Diffusion Models [52.92223039302037]
  Diffusion models have led to significant advancements in generative modelling. Yet their widespread adoption poses challenges regarding data attribution and interpretability. In this paper, we aim to help address such challenges by developing an textitinfluence functions framework.
  arXiv  Detail & Related papers  (2024-10-17T17:59:02Z)
• Semi-supervised Regression Analysis with Model Misspecification and High-dimensional Data [8.619243141968886]
  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.
  arXiv  Detail & Related papers  (2024-06-20T00:34:54Z)
• 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)
• 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)
• Learning Robust Statistics for Simulation-based Inference under Model Misspecification [23.331522354991527]
  We propose the first general approach to handle model misspecification that works across different classes of simulation-based inference methods. We show that our method yields robust inference in misspecified scenarios, whilst still being accurate when the model is well-specified.
  arXiv  Detail & Related papers  (2023-05-25T09:06:26Z)
• Rigorous Assessment of Model Inference Accuracy using Language Cardinality [5.584832154027001]
  We develop a systematic approach that minimizes bias and uncertainty in model accuracy assessment by replacing statistical estimation with deterministic accuracy measures. We experimentally demonstrate the consistency and applicability of our approach by assessing the accuracy of models inferred by state-of-the-art inference tools.
  arXiv  Detail & Related papers  (2022-11-29T21:03:26Z)
• Learning Summary Statistics for Bayesian Inference with Autoencoders [58.720142291102135]
  We use the inner dimension of deep neural network based Autoencoders as summary statistics. To create an incentive for the encoder to encode all the parameter-related information but not the noise, we give the decoder access to explicit or implicit information that has been used to generate the training data.
  arXiv  Detail & Related papers  (2022-01-28T12:00:31Z)
• Training Deep Normalizing Flow Models in Highly Incomplete Data Scenarios with Prior Regularization [13.985534521589257]
  We propose a novel framework to facilitate the learning of data distributions in high paucity scenarios. The proposed framework naturally stems from posing the process of learning from incomplete data as a joint optimization task.
  arXiv  Detail & Related papers  (2021-04-03T20:57:57Z)
• Performance metrics for intervention-triggering prediction models do not reflect an expected reduction in outcomes from using the model [71.9860741092209]
  Clinical researchers often select among and evaluate risk prediction models. Standard metrics calculated from retrospective data are only related to model utility under certain assumptions. When predictions are delivered repeatedly throughout time, the relationship between standard metrics and utility is further complicated.
  arXiv  Detail & Related papers  (2020-06-02T16:26:49Z)
• TraDE: Transformers for Density Estimation [101.20137732920718]
  TraDE is a self-attention-based architecture for auto-regressive density estimation. We present a suite of tasks such as regression using generated samples, out-of-distribution detection, and robustness to noise in the training data.
  arXiv  Detail & Related papers  (2020-04-06T07:32:51Z)

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.