Refereeing the Referees: Evaluating Two-Sample Tests for Validating Generators in Precision Sciences

• URL: http://arxiv.org/abs/2409.16336v1
• Date: Tue, 24 Sep 2024 13:58:46 GMT
• Title: Refereeing the Referees: Evaluating Two-Sample Tests for Validating Generators in Precision Sciences
• Authors: Samuele Grossi, Marco Letizia, Riccardo Torre,
• Abstract summary: One-dimensional tests provide a level of sensitivity comparable to other multivariate metrics, but with significantly lower computational cost. This methodology offers an efficient, standardized tool for model comparison and can serve as a benchmark for more advanced tests.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We propose a robust methodology to evaluate the performance and computational efficiency of non-parametric two-sample tests, specifically designed for high-dimensional generative models in scientific applications such as in particle physics. The study focuses on tests built from univariate integral probability measures: the sliced Wasserstein distance and the mean of the Kolmogorov-Smirnov statistics, already discussed in the literature, and the novel sliced Kolmogorov-Smirnov statistic. These metrics can be evaluated in parallel, allowing for fast and reliable estimates of their distribution under the null hypothesis. We also compare these metrics with the recently proposed unbiased Fr\'echet Gaussian Distance and the unbiased quadratic Maximum Mean Discrepancy, computed with a quartic polynomial kernel. We evaluate the proposed tests on various distributions, focusing on their sensitivity to deformations parameterized by a single parameter $\epsilon$. Our experiments include correlated Gaussians and mixtures of Gaussians in 5, 20, and 100 dimensions, and a particle physics dataset of gluon jets from the JetNet dataset, considering both jet- and particle-level features. Our results demonstrate that one-dimensional-based tests provide a level of sensitivity comparable to other multivariate metrics, but with significantly lower computational cost, making them ideal for evaluating generative models in high-dimensional settings. This methodology offers an efficient, standardized tool for model comparison and can serve as a benchmark for more advanced tests, including machine-learning-based approaches.

Related papers

• A Kernel-Based Conditional Two-Sample Test Using Nearest Neighbors (with Applications to Calibration, Regression Curves, and Simulation-Based Inference) [3.622435665395788]
  We introduce a kernel-based measure for detecting differences between two conditional distributions. When the two conditional distributions are the same, the estimate has a Gaussian limit and its variance has a simple form that can be easily estimated from the data. We also provide a resampling based test using our estimate that applies to the conditional goodness-of-fit problem.
  arXiv  Detail & Related papers  (2024-07-23T15:04:38Z)
• Diffusion posterior sampling for simulation-based inference in tall data settings [53.17563688225137]
  Simulation-based inference ( SBI) is capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
  arXiv  Detail & Related papers  (2024-04-11T09:23:36Z)
• Boosting the Power of Kernel Two-Sample Tests [4.07125466598411]
  A kernel two-sample test based on the maximum mean discrepancy (MMD) is one of the most popular methods for detecting differences between two distributions over general metric spaces. We propose a method to boost the power of the kernel test by combining MMD estimates over multiple kernels using their Mahalanobis distance.
  arXiv  Detail & Related papers  (2023-02-21T14:14:30Z)
• Learning Gaussian Mixtures Using the Wasserstein-Fisher-Rao Gradient Flow [12.455057637445174]
  We propose a new algorithm to compute the nonparametric maximum likelihood estimator (NPMLE) in a Gaussian mixture model. Our method is based on gradient descent over the space of probability measures equipped with the Wasserstein-Fisher-Rao geometry. We conduct extensive numerical experiments to confirm the effectiveness of the proposed algorithm.
  arXiv  Detail & Related papers  (2023-01-04T18:59:35Z)
• Evaluating generative models in high energy physics [7.545095780512178]
  We present the first systematic review and investigation into evaluation metrics and their sensitivity to failure modes of generative models. We propose two new metrics, the Fr'echet and kernel physics distances (FPD and KPD, respectively), and perform a variety of experiments measuring their performance. We demonstrate the efficacy of these proposed metrics in evaluating and comparing a novel attention-based generative adversarial particle transformer to the state-of-the-art message-passing generative adversarial network jet simulation model.
  arXiv  Detail & Related papers  (2022-11-18T15:36:28Z)
• Test Set Sizing Via Random Matrix Theory [91.3755431537592]
  This paper uses techniques from Random Matrix Theory to find the ideal training-testing data split for a simple linear regression. It defines "ideal" as satisfying the integrity metric, i.e. the empirical model error is the actual measurement noise. This paper is the first to solve for the training and test size for any model in a way that is truly optimal.
  arXiv  Detail & Related papers  (2021-12-11T13:18:33Z)
• Doubly Robust Semiparametric Difference-in-Differences Estimators with High-Dimensional Data [15.27393561231633]
  We propose a doubly robust two-stage semiparametric difference-in-difference estimator for estimating heterogeneous treatment effects. The first stage allows a general set of machine learning methods to be used to estimate the propensity score. In the second stage, we derive the rates of convergence for both the parametric parameter and the unknown function.
  arXiv  Detail & Related papers  (2020-09-07T15:14:29Z)
• Good Classifiers are Abundant in the Interpolating Regime [64.72044662855612]
  We develop a methodology to compute precisely the full distribution of test errors among interpolating classifiers. We find that test errors tend to concentrate around a small typical value $varepsilon*$, which deviates substantially from the test error of worst-case interpolating model. Our results show that the usual style of analysis in statistical learning theory may not be fine-grained enough to capture the good generalization performance observed in practice.
  arXiv  Detail & Related papers  (2020-06-22T21:12:31Z)
• Instability, Computational Efficiency and Statistical Accuracy [101.32305022521024]
  We develop a framework that yields statistical accuracy based on interplay between the deterministic convergence rate of the algorithm at the population level, and its degree of (instability) when applied to an empirical object based on $n$ samples. We provide applications of our general results to several concrete classes of models, including Gaussian mixture estimation, non-linear regression models, and informative non-response models.
  arXiv  Detail & Related papers  (2020-05-22T22:30:52Z)
• Nonparametric Score Estimators [49.42469547970041]
  Estimating the score from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models. We provide a unifying view of these estimators under the framework of regularized nonparametric regression. We propose score estimators based on iterative regularization that enjoy computational benefits from curl-free kernels and fast convergence.
  arXiv  Detail & Related papers  (2020-05-20T15:01:03Z)
• Machine learning for causal inference: on the use of cross-fit estimators [77.34726150561087]
  Doubly-robust cross-fit estimators have been proposed to yield better statistical properties. We conducted a simulation study to assess the performance of several estimators for the average causal effect (ACE) When used with machine learning, the doubly-robust cross-fit estimators substantially outperformed all of the other estimators in terms of bias, variance, and confidence interval coverage.
  arXiv  Detail & Related papers  (2020-04-21T23:09:55Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.