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Stein’s Method for Practical Machine Learning
Stein's method, due to
Charles M. Stein,
is a set of
remarkably powerful
theoretical techniques for
proving approximation and limit theorems in probability theory.
It has been mostly known to theoretical statisticians.
Recently, however,
it has been shown that some of the key ideas from Stein's method
can be naturally adopted to solve computational and statistical challenges in practical machine learning.
This project aims to harness Stein’s method for practical purposes,
with a focus on
develop new and efficient practical algorithms for
learning, inference and model evaluation of highly complex probabilistic graphical models and deep learning models.
Kernelized Stein Discrepancy
Kernelized Stein discrepancy (KSD), based on combining the classical Stein discrepancy with reproducing kernel Hilbert space (RKHS), allows us to access the compatibility between empirical data and probabilistic distributions, and provides a powerful tool for developing algorithms for model evaluation (goodness-of-fit test), as well as learning and inference in general. Unlike the traditional divergence measures (such as KL, Chi-square divergence), KSD does not require to evaluate the normalization constant of the distribution, and can be applied even for the intractable, unnormalized distributions widely used in modern machine learning.
- A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation
Liu, Lee, Jordan; ICML, 2016,
[A short note],
[code: matlab, R ]
[See more details here>>].
Stein Variational Gradient Descent
Based on exploiting an interesting connection between Stein discrepancy and KL divergence,
we derive a new form of variational inference algorithm, called Stein variational gradient descent (SVGD),
that mixes the advantages of variational inference, Monte Carlo, quasi Monte Carl and gradient descent (for MAP).
SVGD provides a new powerful tool for attacking the inference and learning challenges in graphical models and probabilistic deep learning, especially when there is a need for getting diverse outputs
to capture the posterior uncertainty in the Bayesian framework.
- Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm
Liu, Wang; NeurIPS, 2016 [code]
- Stein Variational Gradient Descent as Gradient Flow
Liu; NeurIPS, 2017
- Stein Variational Gradient Descent as Moment Matching
Liu; NeurIPS, 2018
[See more details here>>].
Slides
Probabilistic Learning and Inference Using Stein's Method [slides, slides]
A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation
[ICML2016 slides]
Papers
- A Kernelized Stein Discrepancy for Goodness-of-fit Tests and Model Evaluation
Liu, Lee, Jordan; ICML, 2016
[code: matlab, R ]
- Stein Variational Gradient Descent: A General Purpose Bayesian Inference Algorithm
Liu, Wang; NeurIPS, 2016 [code]
- Learning to Draw Samples: With Application to Amortized MLE for Generative Adversarial Learning
Wang, Liu; preprint 2016
[code]
- Two methods for Wild Variational Inference
Liu, Feng; preprint, 2016
- Black-box Importance Sampling
Liu, Lee; AISTATS, 2017
- Learning Deep Energy Models: Contrastive Divergence vs. Amortized MLE
Liu, Wang, 2017
- Learning to Draw Samples with Amortized Stein Variational Gradient Descent
Feng et al. UAI 2017
- Stein Variational Gradient Descent as Gradient Flow
Liu; NeurIPS, 2017
- Stein Variational Policy Gradient
Yang et al. UAI. 2017
- Stein Variational Gradient Descent as Moment Matching
Liu; NeurIPS, 2018
- Stein Variational Gradient Descent Without Gradient
Han, Liu; ICML, 2018
- Stein variational gradient descent with matrix-valued kernels
Wang, Tang, Bajaj, Liu, NeurIPS, 2019
- Nonlinear Stein Variational Gradient Descent for Learning Diversified Mixture Models
Wang, Liu, ICML, 2019
- Learning Self-Imitating Diverse Policies
Gangwani et al. ICLR. 2019
- Stein Variational Inference for Discrete Distributions
Han, et al. AISTATS, 2020
- Profiling Pareto Front With Multi-Objective Stein Variational Gradient Descent
Liu et al. NeurIPS 2021
- Sampling with Trustworthy Constraints: A Variational Gradient Framework
Liu et al. NeurIPS 2021
- Sampling in Constrained Domains with Orthogonal-Space Variational Gradient Descent
Zhang et al. NeurIPS 2022
- Goodness-of-Fit Testing for Discrete Distributions via Stein Discrepancy
Yang et al. ICML 2018
- Stein’s Method Meets Computational Statistics: A Review of Some Recent Developments
Anastasiou et al. 2022
Informal Notes & Misc
- A Short Note on Kernelized Stein Discrepancy
Liu, 2016
- Stein Variational Gradient Descent: Theory and Applications
Liu, NeurIPS Workshop on Advances in Approximate Bayesian Inference, 2016
- Learning to Sample Using Stein Discrepancy
Wang, Feng, Liu, NeurIPS Workshop on Bayesian Deep Learning, 2016
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