Gibbs sampler and coordinate ascent variational inference: A set-theoretical review

@article{Lee2021GibbsSA,
  title={Gibbs sampler and coordinate ascent variational inference: A set-theoretical review},
  author={Se Yoon Lee},
  journal={Communications in Statistics - Theory and Methods},
  year={2021},
  volume={51},
  pages={1549 - 1568}
}
  • Se Yoon Lee
  • Published 3 August 2020
  • Computer Science
  • Communications in Statistics - Theory and Methods
Abstract One of the fundamental problems in Bayesian statistics is the approximation of the posterior distribution. Gibbs sampler and coordinate ascent variational inference are renownedly utilized approximation techniques that rely on stochastic and deterministic approximations. In this paper, we define fundamental sets of densities frequently used in Bayesian inference. We shall be concerned with the clarification of the two schemes from the set-theoretical point of view. This new way… 
Effects of Multi-Omics Characteristics on Identification of Driver Genes Using Machine Learning Algorithms
TLDR
This study presents a framework to analyze the effects of multi-omics characteristics on the identification of cancer driver genes and provides a more comprehensive understanding of cancer mechanisms.
Regularization for Wasserstein Distributionally Robust Optimization
TLDR
This paper derives a general strong duality result of regularized Wasserstein distributionally robust problems in the case of entropic regularization and provides an approximation result when the regularization parameters vanish.
Bayesian Nonlinear Models for Repeated Measurement Data: An Overview, Implementation, and Applications
TLDR
This article presents an overview of the formulation, interpretation, and implementation of Bayesian nonlinear mixed effects models and surveys recent advances and applications.
Contractual Supply Chain Governance, Relational Supply Chain Governance and Performance Of Agro Processing Firms In Kenya
Agro processing industry establishes the biggest bit of 38% of Kenya manufacturing sector, but has untapped potential to contribute to employment and gross domestic product growth. The sector is
Inferring Parsimonious Coupling Statistics in Nonlinear Dynamics with Variational Gaussian Processes
TLDR
This work determines a posteriori the hyperparameter distribution conditioned on the data by the use of variational Bayesian methods with mean approximations on the posterior distribution of thehyperparameters, thus introducing the variational form of Gaussian process convergent cross-mapping (VGP-CCM).
Improving MC-Dropout Uncertainty Estimates with Calibration Error-based Optimization
TLDR
This study proposes two new loss functions by combining cross entropy with Expected Calibration Error (ECE) and Predictive Entropy (PE) and shows that the new proposed loss functions lead to having a calibrated MC-Dropout method.

References

SHOWING 1-10 OF 61 REFERENCES
Probability and Measure
Probability. Measure. Integration. Random Variables and Expected Values. Convergence of Distributions. Derivatives and Conditional Probability. Stochastic Processes. Appendix. Notes on the Problems.
Variational Inference: A Review for Statisticians
TLDR
Variational inference (VI), a method from machine learning that approximates probability densities through optimization, is reviewed and a variant that uses stochastic optimization to scale up to massive data is derived.
Explaining Variational Approximations
Variational approximations facilitate approximate inference for the parameters in complex statistical models and provide fast, deterministic alternatives to Monte Carlo methods. However, much of the
Information Theory and Statistics: A Tutorial
TLDR
This tutorial is concerned with applications of information theory concepts in statistics, in the finite alphabet setting, and an introduction is provided to the theory of universal coding, and to statistical inference via the minimum description length principle motivated by that theory.
Concentration inequalities and model selection, volume
  • 2007
On Variational Bayes Estimation and Variational Information Criteria for Linear Regression Models
TLDR
It is proved that under mild regularity conditions, VB based estimators enjoy some desirable frequentist properties such as consistency and can be used to obtain asymptotically valid standard errors.
Memoir on the Probability of the Causes of Events
Translated from the original French by S. M. Stigler, University of Chicago. Originally published as "Memoire sur la probabilite des causes par les evenemens," par M. de la Place, Professeur a
...
...