# Statistical Inference for Autoencoder-based Anomaly Detection after Representation Learning-based Domain Adaptation

arXiv: https://arxiv.org/abs/2508.07049 · HTML: https://mlsanity.com/paper/2508.07049/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 48 references that are in the map.
- First posted on arXiv 9 Aug 2025.

## Builds on (most cited first, 27 of 27)

- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Exact post-selection inference, with application to the lasso](https://mlsanity.com/paper/1311.6238/) (2013)
- [Optimal Inference After Model Selection](https://mlsanity.com/paper/1410.2597/) (2014)
- [Exact Post-Selection Inference for Sequential Regression Procedures](https://mlsanity.com/paper/1401.3889/) (2014)
- [Selective Inference for Hierarchical Clustering](https://mlsanity.com/paper/2012.02936/) (2020)
- [A Review of Vibration-Based Damage Detection in Civil Structures: From Traditional Methods to Machine Learning and Deep Learning Applications](https://mlsanity.com/paper/2004.04373/) (2020)
- [Testing for a Change in Mean After Changepoint Detection](https://mlsanity.com/paper/1910.04291/) (2019)
- [Computing Valid p-value for Optimal Changepoint by Selective Inference using Dynamic Programming](https://mlsanity.com/paper/2002.09132/) (2020)
- [More Powerful Conditional Selective Inference for Generalized Lasso by Parametric Programming](https://mlsanity.com/paper/2105.04920/) (2021)
- [Computing Valid p-values for Image Segmentation by Selective Inference](https://mlsanity.com/paper/1906.00629/) (2019)
- [More powerful post-selection inference, with application to the Lasso](https://mlsanity.com/paper/1801.09037/) (2018)
- [Selective inference for k-means clustering](https://mlsanity.com/paper/2203.15267/) (2022)
- [Selective Inference for Group-Sparse Linear Models](https://mlsanity.com/paper/1607.08211/) (2016)
- [Quantifying Statistical Significance of Neural Network-based Image Segmentation by Selective Inference](https://mlsanity.com/paper/2010.01823/) (2020)
- [Post-Selection Inference for Changepoint Detection Algorithms with Application to Copy Number Variation Data](https://mlsanity.com/paper/1812.03644/) (2018)
- [A significance test for forward stepwise model selection](https://mlsanity.com/paper/1405.3920/) (2014)
- [Selective Sequential Model Selection](https://mlsanity.com/paper/1512.02565/) (2015)
- [Valid P-Value for Deep Learning-Driven Salient Region](https://mlsanity.com/paper/2301.02437/) (2023)
- [Fast and More Powerful Selective Inference for Sparse High-order Interaction Model](https://mlsanity.com/paper/2106.04929/) (2021)
- [Tree-Values: selective inference for regression trees](https://mlsanity.com/paper/2106.07816/) (2021)
- [Post Selection Inference with Kernels](https://mlsanity.com/paper/1610.03725/) (2016)
- [Selective Inference for Change Point Detection in Multi-dimensional Sequences](https://mlsanity.com/paper/1706.00514/) (2017)
- [Valid and Exact Statistical Inference for Multi-dimensional Multiple Change-Points by Selective Inference](https://mlsanity.com/paper/2110.08989/) (2021)
- [CAD-DA: Controllable Anomaly Detection after Domain Adaptation by Statistical Inference](https://mlsanity.com/paper/2310.14608/) (2023)
- [Exact Statistical Inference for the Wasserstein Distance by Selective Inference](https://mlsanity.com/paper/2109.14206/) (2021)
- [More Powerful and General Selective Inference for Stepwise Feature Selection using the Homotopy Continuation Approach](https://mlsanity.com/paper/2012.13545/) (2020)
- [si4onnx: A Python package for Selective Inference in Deep Learning Models](https://mlsanity.com/paper/2501.17415/) (2025)

## Built on by (most cited first, 2 of 2)

- [GCA: Global Centroid Alignment in Federated Learning](https://mlsanity.com/paper/2608.22593/) (2026)
- [Post-Anomaly Detection Inference for Deep SVDD](https://mlsanity.com/paper/2609.37935/) (2026)

## Abstract (arXiv)

Anomaly detection (AD) plays a vital role across a wide range of domains, but its performance might deteriorate when applied to target domains with limited data. Domain Adaptation (DA) offers a solution by transferring knowledge from a related source domain with abundant data. However, this adaptation process can introduce additional uncertainty, making it difficult to draw statistically valid conclusions from AD results. In this paper, we propose STAND-DA -- a novel framework for statistically rigorous Autoencoder-based AD after Representation Learning-based DA. Built on the Selective Inference (SI) framework, STAND-DA computes valid p-values for detected anomalies and rigorously controls the false positive rate below a pre-specified level α (e.g., 0.05). To address the computational challenges of applying SI to deep learning models, we develop the GPU-accelerated SI implementation, significantly enhancing both scalability and runtime performance. This advancement makes SI practically feasible for modern, large-scale deep architectures. Extensive experiments on synthetic and real-world datasets validate the theoretical results and computational efficiency of the proposed STAND-DA method.