MSS-PAE: Saving Autoencoder-based Outlier Detection from Unexpected Reconstruction

TL;DR

This work tackles unexpected reconstruction and overconfidence in autoencoder-based outlier detection by (1) introducing a probabilistic autoencoder (PAE) that models per-dimension uncertainty with $\bm{\mu}$ and $\bm{\sigma}^2$ and by (2) weighting the reconstruction loss with Weighted Negative Log Likelihood (WNLL). To address the neglect of local data structure, it proposes Mean-Shift Scoring (MSS), which uses mean-shifted inputs $\mathbf{x}^{MS}(m,k)$ to compute more robust outlier scores via MSS-MSE or MSS-WNLL. Experiments on 32 real-world tabular OD datasets show that WNLL substantially improves detection performance over standard MSE-based AE, and MSS further boosts robustness by reducing false inliers, with MSS-PAE achieving the best overall results and outperforming eight non-AE baselines by a large margin. The results demonstrate that combining uncertainty-aware reconstruction with local-structure information yields practical, transferable improvements for OD in real-world settings.

Abstract

AutoEncoders (AEs) are commonly used for machine learning tasks due to their intrinsic learning ability. This unique characteristic can be capitalized for Outlier Detection (OD). However conventional AE-based methods face the issue of overconfident decisions and unexpected reconstruction results of outliers, limiting their performance in OD. To mitigate these issues, the Mean Squared Error (MSE) and Negative Logarithmic Likelihood (NLL) were firstly analyzed, and the importance of incorporating aleatoric uncertainty to AE-based OD was elucidated. Then the Weighted Negative Logarithmic Likelihood (WNLL) was proposed to adjust for the effect of uncertainty for different OD scenarios. Moreover, the Mean-Shift Scoring (MSS) method was proposed to utilize the local relationship of data to reduce the issue of false inliers caused by AE. Experiments on 32 real-world OD datasets proved the effectiveness of the proposed methods. The combination of WNLL and MSS achieved 41% relative performance improvement compared to the best baseline. In addition, MSS improved the detection performance of multiple AE-based outlier detectors by an average of 20%. The proposed methods have the potential to advance AE's development in OD.

Figures (11)

• Figure 1: An illustration of how this work will improve AE-based OD methods. WNLL incorporates the aleatoric uncertainty to alleviate the overconfidence issue of AE, and MSS introduces the local relationship to detect well-reconstructed outliers.
• Figure 2: The typical structure of the AE and PAE. AE has a symmetrical structure and the size of the latent vector is much smaller than the input layer, while PAE has an output layer twice the size of its input layer.
• Figure 3: The first case contained a group of sinusoidal-shaped data with different Gaussian noise in different regions. (a) showed that the reconstruction results of AE were seriously affected by the noisy data. (b) showed that MSE scores computed from AE demonstrated the irregularity after reconstruction. (c) and (d) showed that the reconstruction results of PAE were smooth and essentially fit the original curve. (e) showed that PAE output high aleatoric uncertainty in the region between (-0.5,0.5) along horizontal axis. (f) showed that PAE assigned low NLL scores to the regions where data exist, but relatively high scores in the noisy regions. "Ori." and "Rec." in the figures denote "Original" and "Reconstruction" respectively.
• Figure 4: The second case contained two groups of sinusoidal-shaped data with equal density. (a) and (d) showed that AE and PAE both reconstructed the original data well. (b) and (c) showed that some regions between the two groups were also reconstructed well. (e) showed that PAE output low aleatoric uncertainty in the blank area between two groups. (f) showed that PAE only assigned low NLL scores to regions near the data.
• Figure 5: The third cases included a large group of semicircular-shaped inliers and a small group of arcuate-shaped outliers, with an overlapping range on horizontal axis. (a) and (c) showed that AE mistakenly fit the outliers, resulting in bad OD performance. (b) and (d) showed that the reconstruction results of PAE did not deviate a lot from the inliers manifold. (e) showed that PAE outputs high aleatoric uncertainty around outliers, making outliers easier to be discriminated. (f) to (h) showed that PAE achieved better OD performance with smaller $\alpha$ in WNLL.