# Stein Points

@inproceedings{Chen2018SteinP, title={Stein Points}, author={Wilson Ye Chen and Lester W. Mackey and Jackson Gorham and François-Xavier Briol and Chris. J. Oates}, booktitle={ICML}, year={2018} }

An important task in computational statistics and machine learning is to approximate a posterior distribution $p(x)$ with an empirical measure supported on a set of representative points $\{x_i\}_{i=1}^n. [... ] Key Result The idea is to exploit either a greedy or a conditional gradient method to iteratively minimise a kernel Stein discrepancy between the empirical measure and $p(x)$. Our empirical results demonstrate that Stein Points enable accurate approximation of the posterior at modest computational cost… Expand

## 61 Citations

### Stein Point Markov Chain Monte Carlo

- Computer ScienceICML
- 2019

This paper removes the need to solve this optimisation problem by selecting each new point based on a Markov chain sample path, which significantly reduces the computational cost of Stein Points and leads to a suite of algorithms that are straightforward to implement.

### On the geometry of Stein variational gradient descent

- Computer Science, MathematicsArXiv
- 2019

This paper focuses on the recently introduced Stein variational gradient descent methodology, a class of algorithms that rely on iterated steepest descent steps with respect to a reproducing kernel Hilbert space norm, and considers certain nondifferentiable kernels with adjusted tails.

### Optimal thinning of MCMC output

- Computer ScienceJournal of the Royal Statistical Society: Series B (Statistical Methodology)
- 2022

A novel method is proposed, based on greedy minimisation of a kernel Stein discrepancy, that is suitable for problems where heavy compression is required and its effectiveness is demonstrated in the challenging context of parameter inference for ordinary differential equations.

### Gradient-Free Kernel Stein Discrepancy

- Mathematics
- 2022

Stein discrepancies have emerged as a powerful statistical tool, being applied to fundamental statistical problems including parameter inference, goodness-of-ﬁt testing, and sampling. The canonical…

### Bayesian Posterior Approximation via Greedy Particle Optimization

- Computer ScienceAAAI
- 2019

A novel method named maximum mean discrepancy minimization by the Frank-Wolfe algorithm (MMD-FW), which minimizes MMD in a greedy way by the FW algorithm is proposed and it is shown that its finite sample convergence bound is in a linear order in finite dimensions.

### The reproducing Stein kernel approach for post-hoc corrected sampling

- Mathematics
- 2020

Stein importance sampling is a widely applicable technique based on kernelized Stein discrepancy, which corrects the output of approximate sampling algorithms by reweighting the empirical…

### Projected Stein Variational Gradient Descent

- Computer ScienceNeurIPS
- 2020

This work proposes a projected Stein variational gradient descent (pSVGD) method to overcome the curse of dimensionality by exploiting the fundamental property of intrinsic low dimensionality of the data informed subspace stemming from ill-posedness of such problems.

### Model Inference with Stein Density Ratio Estimation

- Computer ScienceArXiv
- 2018

The estimated density ratio allows us to compute the likelihood ratio function which is a surrogate to the actual Kullback-Leibler divergence from model to data, and can perform model fitting and inference from either frequentist or Bayesian point of view.

### Kernel Stein Discrepancy Descent

- Computer ScienceICML
- 2021

The convergence properties of KSD Descent are studied and its practical relevance is demonstrated, but failure cases are highlighted by showing that the algorithm can get stuck in spurious local minima.

### A Riemann–Stein kernel method

- MathematicsBernoulli
- 2022

This paper proposes and studies a numerical method for approximation of posterior expectations based on interpolation with a Stein reproducing kernel. Finite-sample-size bounds on the approximation…

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