# Anchor-based Maximum Discrepancy for Relative Similarity Testing

arXiv: https://arxiv.org/abs/2510.10477 · HTML: https://mlsanity.com/paper/2510.10477/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 61 references that are in the map.
- First posted on arXiv 12 Oct 2025.

## Builds on (most cited first, 30 of 32)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Unsupervised Domain Adaptation with Residual Transfer Networks](https://mlsanity.com/paper/1602.04433/) (2016)
- [Revisiting Classifier Two-Sample Tests](https://mlsanity.com/paper/1610.06545/) (2016)
- [Data Augmentation Can Improve Robustness](https://mlsanity.com/paper/2111.05328/) (2021)
- [Learning Deep Kernels for Non-Parametric Two-Sample Tests](https://mlsanity.com/paper/2002.09116/) (2020)
- [Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy](https://mlsanity.com/paper/1611.04488/) (2016)
- [MMD Aggregated Two-Sample Test](https://mlsanity.com/paper/2110.15073/) (2021)
- [Interpretable Distribution Features with Maximum Testing Power](https://mlsanity.com/paper/1605.06796/) (2016)
- [Fast Two-Sample Testing with Analytic Representations of Probability Measures](https://mlsanity.com/paper/1506.04725/) (2015)
- [Maximum Mean Discrepancy Test is Aware of Adversarial Attacks](https://mlsanity.com/paper/2010.11415/) (2020)
- [Classification accuracy as a proxy for two sample testing](https://mlsanity.com/paper/1602.02210/) (2016)
- [Unveiling Causal Reasoning in Large Language Models: Reality or Mirage?](https://mlsanity.com/paper/2506.21215/) (2025)
- [MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting](https://mlsanity.com/paper/2306.08777/) (2023)
- [A Kernel Two-Sample Test for Functional Data](https://mlsanity.com/paper/2008.11095/) (2020)
- [Efficient Aggregated Kernel Tests using Incomplete U-statistics](https://mlsanity.com/paper/2206.09194/) (2022)
- [Classification Logit Two-sample Testing by Neural Networks](https://mlsanity.com/paper/1909.11298/) (2019)
- [A Test of Relative Similarity For Model Selection in Generative Models](https://mlsanity.com/paper/1511.04581/) (2015)
- [A Permutation-free Kernel Two-Sample Test](https://mlsanity.com/paper/2211.14908/) (2022)
- [AutoML Two-Sample Test](https://mlsanity.com/paper/2206.08843/) (2022)
- [Detecting Adversarial Data by Probing Multiple Perturbations Using Expected Perturbation Score](https://mlsanity.com/paper/2305.16035/) (2023)
- [Detecting Machine-Generated Texts by Multi-Population Aware Optimization for Maximum Mean Discrepancy](https://mlsanity.com/paper/2402.16041/) (2024)
- [A Kernel Stein Test for Comparing Latent Variable Models](https://mlsanity.com/paper/1907.00586/) (2019)
- [Meta Two-Sample Testing: Learning Kernels for Testing with Limited Data](https://mlsanity.com/paper/2106.07636/) (2021)
- [TOHAN: A One-step Approach towards Few-shot Hypothesis Adaptation](https://mlsanity.com/paper/2106.06326/) (2021)
- [On the Use of Random Forest for Two-Sample Testing](https://mlsanity.com/paper/1903.06287/) (2019)
- [Informative Features for Model Comparison](https://mlsanity.com/paper/1810.11630/) (2018)
- [Kernel Stein Tests for Multiple Model Comparison](https://mlsanity.com/paper/1910.12252/) (2019)
- [A kernel Stein test of goodness of fit for sequential models](https://mlsanity.com/paper/2210.10741/) (2022)
- [A Unified Data Representation Learning for Non-parametric Two-sample Testing](https://mlsanity.com/paper/2412.00613/) (2024)

## Built on by (most cited first, 1 of 1)

- [LOTTERY: Learning from Reference-Only Samples in Two-Sample Testing under Size Asymmetry](https://mlsanity.com/paper/2606.08460/) (2026)

## Abstract (arXiv)

The relative similarity testing aims to determine which of the distributions, P or Q, is closer to an anchor distribution U. Existing kernel-based approaches often test the relative similarity with a fixed kernel in a manually specified alternative hypothesis, e.g., Q is closer to U than P. Although kernel selection is known to be important to kernel-based testing methods, the manually specified hypothesis poses a significant challenge for kernel selection in relative similarity testing: Once the hypothesis is specified first, we can always find a kernel such that the hypothesis is rejected. This challenge makes relative similarity testing ill-defined when we want to select a good kernel after the hypothesis is specified. In this paper, we cope with this challenge via learning a proper hypothesis and a kernel simultaneously, instead of learning a kernel after manually specifying the hypothesis. We propose an anchor-based maximum discrepancy (AMD), which defines the relative similarity as the maximum discrepancy between the distances of (U, P) and (U, Q) in a space of deep kernels. Based on AMD, our testing incorporates two phases. In Phase I, we estimate the AMD over the deep kernel space and infer the potential hypothesis. In Phase II, we assess the statistical significance of the potential hypothesis, where we propose a unified testing framework to derive thresholds for tests over different possible hypotheses from Phase I. Lastly, we validate our method theoretically and demonstrate its effectiveness via extensive experiments on benchmark datasets. Codes are publicly available at: https://github.com/zhijianzhouml/AMD.