PTAD: Prototype-Oriented Tabular Anomaly Detection via Mask Modeling
Tabular anomaly detection;Prototype learning;Mask modeling
Yes
No ethics review needed.
1. In line 139, what does the dimension $e$ represent, and how is $H^0$ constructed? Additionally, in Eq. (1), what is the dimension $h$, and why does stacking on axis $n$ yield a tensor with dimensions $N \times d \times e$? Clarifying these aspects would help in understanding the operations in Non-Parametric Transformers. 

2. What specific advantage does soft masking offer in the data space?
1. The paper proposed a new framework for tabular anomaly detection.

2. The experiments, including comprehensive ablation studies, are thorough and effectively demonstrate the method’s performance.
This paper aims to tackle two key challenges in tabular anomaly detection: representation entanglement and the lack of global information. It proposes a new framework that combines mask modeling with prototype learning, leveraging optimal transport to align data-adaptive masks with association prototypes. Extensive experiments on 20 tabular benchmarks demonstrate the effectiveness of the proposed approach.
1. I was wondering about the role of conducting masking strategy in the raw data space. Given that common tabular data features are unordered and lack the natural sequential or contextual relationships found in images or text, how does the masking strategy effectively capture meaningful correlations in tabular data? 

2. The writing and some notations could be improved for clarity. As I am not an expert in anomaly detection, I found certain sections, particularly the motivations behind key design choices, challenging to follow.
Yes
No ethics review needed.
Q1: The ODDS used contains over 30 pure table datasets, of which only 12 are used; ADBench contains 57 datasets, not just eight as used in this work (there are partial overlaps between the data sets, but this does not change the main problem). How were the data sets selected, why were the others not used and what is the performance of the other data sets? (Answering these questions could lead to further questions).

Q2: Why was a separate benchmark created instead of following previous work (which were used as baseline methods and are therefore known and could probably have been used directly) such as [1] and [2], which all use more data sets or well-known benchmarks?

Q3: Some models from the PyOD library were used as baselines. How were these models selected? Why were methods such as LUNAR, KPCA and GMM, which show strong results in papers such as [3], not used?


Despite the apparent weaknesses regarding evaluation and comparability, this work is well-written and interesting. I would put the marginal acceptance for now, but I will be happy to raise my score if my questions are answered appropriately and the results continue to be sustainable.


[1] Victor Livernoche, Vineet Jain, Yashar Hezaveh, and Siamak Ravanbakhsh. On diffusion modeling  for anomaly detection. In The Twelfth International Conference on Learning Representations, 2024. URL https://openreview.net/forum?id=lR3rk7ysXz.

[2] Hugo Thimonier, Fabrice Popineau, Arpad Rimmel, and Bich-Lien Doan. Beyond individual input for deep anomaly detection on tabular data. arXiv preprint arXiv:2305.15121, 2023.

[3] Roel Bouman, Zaharah Bukhsh, and Tom Heskes. Unsupervised anomaly detection algorithms on real-world data: how many do we need? Journal of Machine Learning Research, 25(105):1–34, 2024
- The manuscript is well-written and easy to follow. The maths is clearly set out, the individual parts justified and the influence demonstrated.
- The paper offers a new perspective and a novel optimization strategy for the application of mask modeling in combination with transformers in the field of anomaly detection.
- The proposed approach performs best in the existing setup compared to the chosen baselines.
The PTAD (Prototype-Oriented Tabular Anomaly Detection) model introduces advanced mask modeling and prototype learning techniques to enhance anomaly detection in tabular data. To address the issue of anomaly leakage, PTAD applies mask modeling in both data and projection spaces. A soft masking strategy selectively conceals potentially abnormal regions in the data space. Simultaneously, in a disentangled projection space, PTAD creates learnable masks based on orthogonal basis vectors, emphasizing feature-wise discrepancies that aid in obscuring suspicious areas while maintaining nominal patterns for accurate reconstruction. PTAD’s prototype learning further strengthens its anomaly detection by capturing global feature dependencies in tabular data. These “association prototypes” represent typical correlations among nominal features and are learned as part of the model's decoding process. This is framed as an optimal transport (OT) problem, aligning the reconstructed data distribution with the prototype distribution to emphasize nominal patterns and assist in accurate anomaly scoring. Both the projection-space mask modeling and association prototype learning are formulated as OT problems, which calibrate the anomaly scoring based on the degree of deviation from normal patterns. The model’s multi-branch decoder allows for parallel reconstructions of masked representations, capturing complex feature relationships. This integration of data-adaptive masks, OT-aligned prototype learning, and a multi-branch decoding approach allows PTAD to capture nominal feature dependencies effectively, resulting in robust and interpretable anomaly detection across a range of tabular benchmarks.
- The criteria for the selection of the data sets selected for the evaluation are not set out (see questions).
- Although current baselines were used, baselines that perform strongly in other works were omitted (see questions).
- Due to the first two points and the combination of both, there is a lack of comparability to be able to make a definitive assessment of the method.
Yes
No ethics review needed.
The term "anomaly leakage" is new to me. What is anomaly leakage? In what situation will we observe the issue? Why can the masking strategy solve this issue?
* I am not sure if this is a strength point or not, but I do think the proposed framework is pretty complex. 

* The proposed approach can achieve good performance on multiple datasets and outperform various baselines.

* A relatively comprehensive ablation study is also conducted to demonstrate the effectiveness of each component.
This paper develops a complex framework for tabular data anomaly detection, consisting of multiple components, such as data-space mask, projection-space mask, and prototype learning.
* Although the proposed framework is complex, it seems each component is based on the existing work. It is not a weakness to do the combination. However, it would be better to highlight the unique challenges of the combination and why each component is essential for the whole framework.

* Because the whole framework consists of too many pieces, it makes the whole framework is not easy to follow, and some notations are not very consistent.

    - In Lines 135 -- 154, mixing using $N$ and $n$ is confusing but still guessable. However, based on Equation 1, I cannot get how to derive Z as defined in Line 224.

    - If I understand correctly, the framework should have the basis vectors $\mathcal{B}$ first via the projection space learning and then derive the projection-space mask. If so, it may be better to present the projection space learning first. 

    - In the projection space learning part, what does $\theta_E$ indicate? What does $\sigma_{\beta^k}$ in $Q(\mathcal{B})$ indicate?  What is the relationship between $\sigma_{\beta^k}$ and the basis vector $\beta^k$?

   - To be honest, I already felt lost when reading Sec 4.2. Similar questions as above, what does $P(\pi)$ indicate in Line 296? What is the purpose of the objective function defined in Eq 7? What is the expectation for this objective?
Yes
No ethics review needed.
## Typos:
- Line 150, authors stipulate that [2] introduce NPT while [3] are actually the ones that introduced it, while [2] use it for AD. Moreover, the authors should consider including [2] in the related work section regarding **Tabular Anomaly Detection** to avoid confusion.
- Paragraph **Projection-Space Mask Generation.** in section 4.1. is not easy to follow. In equation (4), the authors write $(z_{nh} - \beta^{k})^2$ and do not define $z_{nh}$. We hypothesize that it corresponds to the $h$-th element of the $H$ dimensional $z_n$ vector, in which case, we do not understand the operation between a scalar and the basis vector of dimension $H$.

## Questions and clarifications
There are a few elements that need clarification:
- **(i)** In Equation (3) in the paper the authors include weights used to construct the masks $\mathbf{W}_i$ for $i\in\{1,2,3\}$ as done in [4]. We suppose that those weights are conjointly learned with the rest of the hyperparameters. Given the overall learning objective, **(i-1) how do you ensure that the learned weights do not yield a trivial solutions, e.g. no features are masked or the masks are identical?** As there is no constraint on the $\hat{\mathbf{X}}$ representation or on the obtained masks, it could very much be that $\mathbf{X} = \hat{\mathbf{X}}$. For example, in [4] the authors include a **diversity loss** that ensures that masks are diverse and non-trivial. [4] mention that,
    "```it raises another vital problem: how to prevent the mask generator generating same and redundant masks. This determines whether MCM can extract different and diverse correlations. Our solution is to constrain the similarity between different masking matrices.```"
**(i-2) What motivated the authors to not include this loss?**

- **(ii)** In the original paper that propose NPTs [3] and in [2] that relies on NPT for AD, both approaches include a mask token that increases the feature representation by one dimension, $(x_i, mask)$, where $x_i$ is a scalar for numerical values and the one-hot representation for categorical features. This representation is then mapped to an $h$-dimensional representation using a linear layer. **(ii-1) How do you perform data-space masking for the categorical features using equation (3) in the paper?** Similarly, is a mask token involved in the pipeline? A detailed description of the pipeline as done in App. C.3. of [3] or App. B of [2] might clarify things. We suggest the authors include such description in the appendix.

- **(iii)** During training, prototypes are obtained from the encoded **masked** representations of normal samples. While constructing the basis vector can be natural for unmasked samples, it appears very complicated to capture normal behaviors in normal samples that may have been masked very differently. Let us consider a very simplistic example where we have a batch of $3$ samples, and that the mask produced in equation (3) in the paper is
    $$
    M^{ds} = \begin{pmatrix} 1 & 0 & 0 \\\\
                             0 & 1 & 0 \\\\
                             0 & 0 & 1
    \end{pmatrix}
    $$ 
    how can the basis vectors be relevant in that case? More precisely, in the general case, if the mask produced in equation (3) is a diagonal matrix, which is possible since no constraint on the mask in included, **(iii-1) how can the obtained basis vector contain meaningful information?**
    In particular, in the more general case as the number of basis vectors is set to be $5$ in all tested datasets, what if the $M^{ds}$ matrix produces significantly more than $5$ mask types, it seems very unlikely that those basis vector will disentangle properly the representations.
- **(iv)** Prototype generation is also used to capture normal inter-features dependencies. We could be wrong, but it appears to us that aiming at learning inter-feature dependencies on representations that result from a double masking strategy (in the data space and in the encoded space) is particularly challenging and we are surprised that the model could perform such task. **(iv-1) How do you ensure that the inter-feature dependencies learned by the NPT itself does not suffice to discriminate between normal samples and anomalies?**
- **(v)** In inference, since $\mathbf{X}$ contains both normal samples and anomalies, how do you ensure that the basis vector computed in the pipeline still capture normal behavior (both for $s_n^{ap}$ and $s_n^{bv}$). **(v-1) If anomalies originate from a similar distribution (but distinct from the normal distribution), couldn't some obtained basis vectors also capture anomalous behavior thus polluting the anomaly score through anomaly leakage?**
- **(vi)** An average over three runs seems very low. While we acknowledge that [4] also reports an average over $3$ runs, other recent work [1],[2] report an average over $20$ runs which seems more reasonnable. Increasing the number of runs might be relevant, in particular since the training cost seems reasonnable as reported in table 5. Moreover, **(vi-1) could the authors report the standard deviations (as done in [1], [2])?** **(vi-2) Are bold results significantly higher than competing methods?** No mention of a statistical test can be found in the paper.
- **(vii)** Some previous papers [1],[2] have also relied on the F1-Score, it would be best if the authors could include this metrics used in previous benchmarks. In particular, the code provided shows that F1-Score is stored and can be included without too much effort.


Overall, we believe that the present work is promising as it combines existing ideas to provide a novel pipeline for tabular anomaly detection. However given the listed weakness and interrogations, we lean towards reject. However, we are very open to discussion and would be happy to increase our score if the authors are able to clarify our interrogations as well as provide the code to run all the experiments presented in the paper.

[1] Tom Shenkar and Lior Wolf. Anomaly detection for tabular data with internal contrastive learning. In International conference on learning representations, 2022.

[2] Hugo Thimonier, Fabrice Popineau, Arpad Rimmel, and Bich-Liên Doan. Beyond individual input for deep anomaly detection on tabular data. In Forty-first International Conference on Machine Learning, 2024.

[3] Jannik Kossen, Neil Band, Clare Lyle, Aidan N Gomez, Thomas Rainforth, and Yarin Gal. Self-attention between datapoints: Going beyond individual input-output pairs in deep learning. Advances in Neural Information Processing Systems, 2021.

[4] Jiaxin Yin, Yuanyuan Qiao, Zitang Zhou, Xiangchao Wang, and Jie Yang. Mcm: Masked cell modeling for anomaly detection in tabular data. In The Twelfth International Conference on Learning Representations, 2024.

[5] Hangting Ye, Wei Fan, Xiaozhuang Song, Shun Zheng, He Zhao, Dandan Guo, and Yi Chang. Ptarl: Prototype-based tabular representation learning via space calibration. In International Conference on Learning Representations, 2024
- The paper is well-structured, and the context of the study is well introduced. Authors detail extensively the existing work found in the relevant literature, identify some weaknesses and propose to address them.
- The present work **augments** the existing mask reconstruction scheme for AD with (i) proper mask selection in inference and during training as done in [4], (ii) prototype-based anomaly scores inspire from prototype generation as done in [5] and shows through their experiments that their methods performs well in comparison with existing methods.
- Their approach is **novel** and combines the work showcased in PTaRL [5] in the SSL for tabular data literature and MCM [4] as well as NPT-AD [2], that all have proven to work well for tabular data.
- The ablation study are extensive and well detailed, demonstrating the relevance of each addition to the existing frameworks.
The authors propose a novel reconstruction-based anomaly detection (AD) method for tabular data that combines previous approaches [4], [2] from the AD literature and the SSL literature [5]. Their approach relies on mask reconstruction as done in [4], [2] in the original data space but is also augmented by three components:
- (i) mask selection in the original data space as done in [4],
- (ii) inter-sample prototype generation in the hidden space to measure distance to the generated prototypes for (1) mask generation in the hidden space during training and (2) anomaly scoring in inference,
- (iii) inter-feature prototypes generation to measure distance to those prototypes for both training and inference.

The main novelty and contribution of the present paper is the use of previously proposed concepts to improve tabular anomaly detection by:
- (1) guiding the learning process towards more desirable equilibria by including new loss functions and generating better suited masks, 
- (2) augmenting the vanilla reconstruction-error anomaly score to include more precise measures of inter-feature and inter-sample discrepancies between normal samples and anomalies.

They experiment their method on a benchmark of 20 tabular datasets and show strong performance in comparison to existing methods. Authors conduct extensive ablation studies to provide evidence of the relevance of their approach, and provide explanation on how some key hyperparameters were selected.
- While well-structured the paper can be complicated to follow as style can sometimes be wordy and contain several typos that hinder the overall understandability of the paper. For example, line 235 "*$M_{nh}^k$ denotes the mask value of the $h$-th feature dimension of n-th sample concerning about the k-th basis vector $\beta^{k}$ (...) Furthermore, multiple masks encourage the model to reconstruct samples with various masks, anomalies are prone to be detected by a comprehensive measurement*". Moreover, the term ```nominal``` is sometimes used to refer to ```normal``` samples and this might be confusing, we encourage the authors to stick to the term ```normal```. 

- Experiments performed by the authors include only $3$ iterations for $3$ different seeds, which can be considered low in comparison with previous papers that performed experiments 10 or 20 times [1], [2] (while we also acknowledge that [4] also only conducted $3$ runs for each dataset). No statistical tests are mentionned, are any perfomed? Some values are highlighted in the tables while they are unlikely to be significantly different from the second highest value (e.g. Wine dataset, PTAD gets an AUPRC of $0.9323$ vs MCM [4] that gets $0.9269$).

- Presented results are **not reproductible**. We acknowledge that the authors provide the overall code for the main experiments. However, the authors mention a grid search strategy for the learning rate, and do not explicitely mention (i) what objective was used to select the learning rate for this grid search, we assume the loss achieved after 200 epochs?, (ii) the obtained learning rate for each dataset so the experiments can be run again. Only the hyperparameters for the cardio dataset is provided. Moreover, none of the ablation studies can be reproduced without excessive effort while they constitute critical evidence of the relevance of the proposed approach. Overall none of the experiments conducted in section 5 can be reproduced either. **We strongly encourage the authors to provide the full easy-to-run code to support their statements.**
@inproceedings{
anonymous2024ptad,
title={{PTAD}: Prototype-Oriented Tabular Anomaly Detection via Mask Modeling},
author={Anonymous},
booktitle={Submitted to The Thirteenth International Conference on Learning Representations},
year={2024},
url={https://openreview.net/forum?id=Vi6p2TeujL},
note={under review}
}
Tabular anomaly detection, which aims at identifying deviant samples, has been crucial in a variety of real-world applications, such as medical disease identification, financial fraud detection, intrusion monitoring, etc. Although recent deep learning-based methods have achieved competitive performances, these methods suffer from representation entanglement and the lack of global correlation modeling, which leads to the 'abnormal leakage' issue and hinders anomaly detection performance. To tackle the problem, we incorporate mask modeling and prototype learning into tabular anomaly detection. The core idea is to design learnable masks by disentangled representation learning within a projection space and extracting nominal dependencies as explicit global prototypes. Specifically, the overall model involves two parts: (i) During encoding, we perform mask modeling in both the data space and projection space with orthogonal basis vectors for masking out the suspicious abnormal locations; (ii) During decoding, we decode multiple masked representations in parallel for reconstruction and learn association prototypes to extract nominal characteristic correlations. Our proposal derives from a distribution-matching perspective, where both projection space learning and association prototype learning are formulated as optimal transport problems, and the calibration distances are utilized to refine the anomaly scores. By conducting both quantitative and qualitative experiments on 20 tabular benchmarks, our model surpasses other competitors and possesses good interpretability.
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PTAD: Prototype-Oriented Tabular Anomaly Detection via Mask Modeling
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