2 research outputs found
Minimax Confidence Intervals for the Sliced Wasserstein Distance
Motivated by the growing popularity of variants of the Wasserstein distance
in statistics and machine learning, we study statistical inference for the
Sliced Wasserstein distance--an easily computable variant of the Wasserstein
distance. Specifically, we construct confidence intervals for the Sliced
Wasserstein distance which have finite-sample validity under no assumptions or
under mild moment assumptions. These intervals are adaptive in length to the
regularity of the underlying distributions. We also bound the minimax risk of
estimating the Sliced Wasserstein distance, and as a consequence establish that
the lengths of our proposed confidence intervals are minimax optimal over
appropriate distribution classes. To motivate the choice of these classes, we
also study minimax rates of estimating a distribution under the Sliced
Wasserstein distance. These theoretical findings are complemented with a
simulation study demonstrating the deficiencies of the classical bootstrap, and
the advantages of our proposed methods. We also show strong correspondences
between our theoretical predictions and the adaptivity of our confidence
interval lengths in simulations. We conclude by demonstrating the use of our
confidence intervals in the setting of simulator-based likelihood-free
inference. In this setting, contrasting popular approximate Bayesian
computation methods, we develop uncertainty quantification methods with
rigorous frequentist coverage guarantees
Benchmarking Simulation-Based Inference
Recent advances in probabilistic modelling have led to a large number of
simulation-based inference algorithms which do not require numerical evaluation
of likelihoods. However, a public benchmark with appropriate performance
metrics for such 'likelihood-free' algorithms has been lacking. This has made
it difficult to compare algorithms and identify their strengths and weaknesses.
We set out to fill this gap: We provide a benchmark with inference tasks and
suitable performance metrics, with an initial selection of algorithms including
recent approaches employing neural networks and classical Approximate Bayesian
Computation methods. We found that the choice of performance metric is
critical, that even state-of-the-art algorithms have substantial room for
improvement, and that sequential estimation improves sample efficiency. Neural
network-based approaches generally exhibit better performance, but there is no
uniformly best algorithm. We provide practical advice and highlight the
potential of the benchmark to diagnose problems and improve algorithms. The
results can be explored interactively on a companion website. All code is open
source, making it possible to contribute further benchmark tasks and inference
algorithms.Comment: In AISTATS 202