发表机构
University of Washington; University of Texas at Austin（华盛顿大学; 德克萨斯大学奥斯汀分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对FID估计的有限样本偏差问题，提出RTD算法与高阶外推法，实现O(d/ε²)的最优样本复杂度，并在ImageNet上验证了高效性。
AI 中文摘要
Fréchet Inception Distance (FID) 被广泛用于评估生成模型，但其经验插件估计器存在有限样本偏差 [BSAG18, CF20]。我们研究了在已知一个分布的情况下，估计均值和协方差有界的 d 维高斯分布之间的 FID 到误差 ε 所需的样本复杂度 n。我们的贡献有三方面。(1) 我们为经验插件估计器建立了紧的有限样本偏差界 Θ(d²/n) 和方差界 Θ(d/n + d²/n²)，确立了 ≳ d² 的样本复杂度。(2) 为了对经验插件估计器去偏，我们将 [CF20] 的 FID_∞ 估计器推广到任意阶 k 的外推方法。我们进一步证明了在我们的框架下，任意 k 阶外推的偏差和方差界分别为 Θ(d^{k+2}/n^{k+1}) 和 Θ(d/n + d²/n²)。(3) 我们引入了相对泰勒去偏 (RTD)，一种新的、计算高效的 FID 估计算法，使用受 U-统计量启发的去偏技术。我们证明 RTD 达到 O(d/ε²) 的样本复杂度，并证明这是最优的。我们对新估计器提供了补充的实证评估。我们在合成高斯上的实验验证了预测的残差偏差，并支持我们界的紧性。在带有 Inception 嵌入的 ImageNet 上，RTD 在标准 50K 样本预算下达到最低的平均估计误差，而我们的二阶方差感知外推估计器 (VALE₂) 仅使用 10K 样本即可达到与 50K 样本的 FID_∞ 相当的精度。
英文摘要
The Fréchet Inception Distance (FID) is widely used to evaluate generative models, but its empirical plug-in estimator suffers from finite-sample bias [BSAG18, CF20]. We study the sample complexity $n$ of estimating FID to error $ε$ between $d$-dimensional Gaussians with bounded mean distance and covariances, when one distribution is known. Our contributions are threefold. (1) We establish tight finite-sample $Θ(\frac{d^2}{n})$ bias and $Θ(\frac{d}{n} + \frac {d^2} {n^2})$ variance bounds for the empirical plug-in estimator, establishing a $\gtrsim d^2$ sample complexity. (2) To debias the empirical plug-in estimator, we generalize the ${\rm FID}_\infty$ estimator of [CF20] to extrapolation methods of arbitrary order $k$. We further prove tight bias and variance bounds of $Θ(\frac{d^{k + 2}}{n^{k + 1}})$ and $Θ(\frac d n + \frac{d^2}{n^2})$ for any order-$k$ extrapolation under our framework. (3) We introduce Relative Taylor Debiasing (RTD), a new, computationally efficient FID estimation algorithm using debiasing techniques inspired by U-statistics. We show that RTD achieves an $O(\frac d {ε^2})$ sample complexity, and prove that this is optimal. We provide a complementary empirical evaluation of our new estimators. Our experiments on synthetic Gaussians validate the predicted residual bias and support the tightness of our bounds. On ImageNet with Inception embeddings, RTD achieves the lowest mean estimation error at the standard 50K sample budget, while our second-order variance-aware extrapolation estimator (VALE$_2$) uses only 10K samples to achieve accuracy comparable to FID$_\infty$ at 50K samples.
CommentsOur code is available at https://github.com/zys996/sample-optimal-fid-estimation
