Finite-Sample Sensitivity of Kernel Metrics for Generative Evaluation

Tomasz Radzikowski; Mateusz Modrzejewski

Home/Archive/arXiv

arXiv · 2610.34477

Finite-Sample Sensitivity of Kernel Metrics for Generative Evaluation

Tomasz Radzikowski·Mateusz Modrzejewski

View original source ↗Read source document ↗Export metadata ↓

Abstract

Kernel distances such as the Kernel Inception Distance (KID) and the Kernel Audio Distance (KAD) compare generated and reference samples in an embedding space, and model comparisons rest on their values. Each ships with one fixed kernel, and a reported value does not say which changes that kernel detects at the sample size used. We run each default as a permutation two-sample test on real embeddings of symbolic music, audio and images, comparing a sample with an independent sample changed by a mean shift, an isotropic contraction, or a rotation that keeps the mean and the covariance trace and is matched to the shift in transport distance. At 780 samples per side, both defaults rarely detect the rotations in five evaluation spaces, while they detect the shifts in every run. The median-bandwidth Gaussian kernel of KAD detects the contraction and regains power against rotations on image embeddings with an order of magnitude more samples. The cubic kernel of KID contains second- and third-moment information but misses the contraction in most runs, and our experiments do not establish a high-power rotation regime for it over the tested sample sizes. Narrower Gaussian bandwidths restore sensitivity in music and audio, an $\ell_1$ Laplace kernel does so for images, and aggregated tests combine both at nominal level. We recommend that a reported kernel distance state its sample budget and the changes its configuration detects at that budget.

Explore related subjects

cs.LG cs.SD

Keep this discovery

Explore connections, maps & timelines

BibTeX RIS

Tomasz Radzikowski, Mateusz Modrzejewski. 2026-10-25. Finite-Sample Sensitivity of Kernel Metrics for Generative Evaluation. https://arxiv.org/abs/2610.34477

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

InfoDiffusion: Representation Learning Using Information Maximizing Diffusion Models

While diffusion models excel at generating high-quality samples, their latent variables typically lack semantic meaning and are not suitable for representation learning. Here, we propose InfoDiffusion, an algorithm that augments diffusion models with low-dimensional latent variables that capture high-level factors of variation in the data. InfoDiffusion relies on a learning objective regularized with the mutual information between observed and hidden variables, which is designed to improve latent space quality and to prevent the latents from being ignored by expressive diffusion-based decoders. Empirically, we find that InfoDiffusion learns disentangled and human-interpretable latent representations that are competitive with state-of-the-art generative and contrastive methods, while retaining the high sample quality of diffusion models. Our method enables manipulating the attributes of generated images and has the potential to assist tasks that require exploring a learned latent space to generate quality samples, e.g., generative design.

cs.LG↗

arXiv2026

Discovering and Reasoning of Causality in the Hidden World with Large Language Models

Revealing hidden causal variables alongside the underlying causal mechanisms is essential to the development of science. Despite the progress in the past decades, existing practice in causal discovery (CD) heavily relies on high-quality measured variables, which are usually given by human experts. In fact, the lack of well-defined high-level variables behind unstructured data has been a longstanding roadblock to a broader real-world application of CD. This procedure can naturally benefit from an automated process that can suggest potential hidden variables in the system. Interestingly, Large language models (LLMs) are trained on massive observations of the world and have demonstrated great capability in processing unstructured data. To leverage the power of LLMs, we develop a new framework termed Causal representatiOn AssistanT (COAT) that incorporates the rich world knowledge of LLMs to propose useful measured variables for CD with respect to high-value target variables on their paired unstructured data. Instead of directly inferring causality with LLMs, COAT constructs feedback from intermediate CD results to LLMs to refine the proposed variables. Given the target variable and the paired unstructured data, we first develop COAT-MB that leverages the predictivity of the proposed variables to iteratively uncover the Markov Blanket of the target variable. Built upon COAT-MB, COAT-PAG further extends to uncover a more complete causal graph, i.e., Partial Ancestral Graph, by iterating over the target variables and actively seeking new high-level variables. Moreover, the reliable CD capabilities of COAT also extend the debiased causal inference to unstructured data by discovering an adjustment set. We establish theoretical guarantees for the CD results and verify their efficiency and reliability across realistic benchmarks and real-world case studies.

cs.LG↗

arXiv2026

Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weights

Long-term treatment effect estimation is a significant but challenging problem in many applications. Existing methods rely on ideal assumptions, such as no unobserved confounders or binary treatment, to estimate long-term average treatment effects. However, in numerous real-world applications, these assumptions could be violated, and average treatment effects are insufficient for personalized decision-making. In this paper, we address a more general problem of estimating long-term Heterogeneous Dose-Response Curve (HDRC) while accounting for unobserved confounders and continuous treatment. Specifically, to remove the unobserved confounders in the long-term observational data, we introduce an optimal transport weighting framework to align the long-term observational data to an auxiliary short-term experimental data. Furthermore, to accurately predict the heterogeneous effects of continuous treatment, we establish a generalization bound on counterfactual prediction error by leveraging the reweighted distribution induced by optimal transport. Finally, we develop a long-term HDRC estimator building upon the above theoretical foundations. Extensive experiments on synthetic and semi-synthetic datasets demonstrate the effectiveness of our approach.

cs.LG↗