# Approximate Bayesian Computation with the Sliced-Wasserstein Distance

@article{Nadjahi2019ApproximateBC, title={Approximate Bayesian Computation with the Sliced-Wasserstein Distance}, author={Kimia Nadjahi and Valentin De Bortoli and Alain Durmus and Roland Badeau and Umut Simsekli}, journal={ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)}, year={2019}, pages={5470-5474} }

Approximate Bayesian Computation (ABC) is a popular method for approximate inference in generative models with intractable but easy-to-sample likelihood. It constructs an approximate posterior distribution by finding parameters for which the simulated data are close to the observations in terms of summary statistics. These statistics are defined beforehand and might induce a loss of information, which has been shown to deteriorate the quality of the approximation. To overcome this problem…

## 11 Citations

### Fast Approximation of the Sliced-Wasserstein Distance Using Concentration of Random Projections

- Computer ScienceNeurIPS
- 2021

This work adopts a new perspective to approximate SW by making use of the concentration of measure phenomenon, and develops a simple deterministic approximation that is both accurate and easy to use compared to the usual Monte Carlo approximation.

### Shedding a PAC-Bayesian Light on Adaptive Sliced-Wasserstein Distances

- Computer ScienceArXiv
- 2022

The PAC-Bayesian theory and the central observation that SW actually hinges on a slice-distribution-dependent Gibbs risk are leveraged to bring new contributions to this line of research.

### Statistical, Robustness, and Computational Guarantees for Sliced Wasserstein Distances

- Computer ScienceArXiv
- 2022

This work quantifies sliced Wasserstein distances scalability from three key aspects: empirical convergence rates; robustness to data contamination; and efficient computational methods; and characterize minimax optimal, dimension-free robust estimation risks, and show an equivalence between robust 1-Wasserstein estimation and robust mean estimation.

### Minimax confidence intervals for the Sliced Wasserstein distance

- Computer ScienceElectronic Journal of Statistics
- 2022

Confidence intervals for the Sliced Wasserstein distance are constructed which have finite-sample validity under no assumptions or under mild moment assumptions and are adaptive in length to the regularity of the underlying distributions.

### Discrepancy-based Inference for Intractable Generative Models using Quasi-Monte Carlo

- Computer Science
- 2021

Results are sample complexity bounds which demonstrate that, under smoothness conditions on the generator, QMC can signiﬁcantly reduce the number of samples required to obtain a given level of accuracy when using three of the most common discrepancies: the maximum mean discrepancy, the Wasserstein distance, and the Sinkhorn divergence.

### Fast Approximation of the Generalized Sliced-Wasserstein Distance

- Computer ScienceArXiv
- 2022

This work proposes to form deterministic and fast approximations of the generalized sliced Wasserstein distance by using the concentration of random projections when the deﬁning functions are polynomial function, circular function, and neural network type function.

### Generalized Sliced Distances for Probability Distributions

- Computer ScienceArXiv
- 2020

A broad family of probability metrics, coined as Generalized Sliced Probability Metrics (GSPMs), that are deeply rooted in the generalized Radon transform are introduced and it is shown that under mild assumptions, the gradient flow converges to the global optimum.

### Hierarchical Sliced Wasserstein Distance

- Computer ScienceArXiv
- 2022

The metricity of Hierarchical Sliced Wasserstein (HSW) distance is derived by proving the injectivity of HRT and investigating the theoretical properties of HSW including its connection to SW variants and its computational and sample complexities.

### Revisiting Sliced Wasserstein on Images: From Vectorization to Convolution

- Computer ScienceArXiv
- 2022

Convolution sliced Wasserstein (CSW) is derived via incorporating stride, dilation, and non-linear activation function into the convolution operators and is demonstrated to have favorable performance in comparing probability measures over images and in training deep generative modeling on images.

### On Transportation of Mini-batches: A Hierarchical Approach

- Computer ScienceICML
- 2022

This work proposes a novel mini-batch scheme for optimal transport, named Batch of Mini-batches Optimal Transport (BoMb-OT), that satisfies the optimal coupling between mini-batched and it can be seen as an approximation to a well-deﬁned distance on the space of probability measures.

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- 2019

A central limit theorem is proved, which characterizes the asymptotic distribution of the estimators and establishes a convergence rate of $\sqrt{n}$, where $n$ denotes the number of observed data points.

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This study proposes a novel parameter-free algorithm for learning the underlying distributions of complicated datasets and sampling from them based on a functional optimization problem, which aims at finding a measure that is close to the data distribution as much as possible and also expressive enough for generative modeling purposes.

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- Computer ScienceNeurIPS
- 2019

The generalized Radon transform is utilized to define a new family of distances for probability measures, which are called generalized sliced-Wasserstein (GSW) distances, and it is shown that, similar to the SW distance, the GSW distance can be extended to a maximum GSW (max- GSW) distance.

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This work considers an alternative formulation for generative modeling based on random projections which, in its simplest form, results in a single objective rather than a saddle-point formulation and finds its approach to be significantly more stable compared to even the improved Wasserstein GAN.

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