Why Does Counterintuitive Likelihood Behavior Rarely Emerge in Tabular Anomaly Detection?

Donghwan Kim; Junghun Phee; Hyunsoo Yoon

cs.LGFeb 10, 2026

Why Does Counterintuitive Likelihood Behavior Rarely Emerge in Tabular Anomaly Detection?

Authors: Donghwan Kim, Junghun Phee, Hyunsoo Yoon

Organizations: Department of Industrial Engineering, University of Yonsei, Republic of Korea, Seoul · H. Milton Stewart School of Industrial and Systems Engineering (ISyE), Georgia Institute of Technology, USA, GA

Abstract

Deep generative models with tractable likelihoods, exemplified by normalizing flows, offer an effective basis for anomaly detection through likelihood-based scoring. We demonstrate that, unlike in the image domain where deep generative models frequently assign higher likelihoods to anomalous data, such counterintuitive behavior occurs rarely in tabular settings. We first introduce a domain-agnostic formulation that enables consistent detection and evaluation of the counterintuitive phenomenon, addressing the lack of a precise definition in prior work. Through extensive experiments on 47 tabular datasets benchmarked against 13 baseline models and on 10 CV/NLP embedding datasets from ADBench, we show that the phenomenon is consistently rare in general tabular data and that normalizing flow likelihood achieves competitive anomaly detection performance. We further provide theoretical and empirical analyses attributing this disparity to differences in dimensionality and feature correlation between tabular and image data. Therefore, our results indicate that likelihood-based detection with normalizing flows is a practical approach for tabular anomaly detection.

Figures & tables

Method	AUROC $\uparrow$	AUPRC $\uparrow$	Avg. Rank $\downarrow$	Top2 Cum. Ratio $\uparrow$	Fail Ratio $\downarrow$
PCA	0.7715	0.5209	7.13	0.15	0.45
LOF	0.8169	0.5606	6.11	0.17	0.26
IF	0.8014	0.5060	6.23	0.19	0.21
OCSVM	0.6562	0.3833	10.34	0.06	0.77
COPOD	0.7471	0.4419	8.40	0.11	0.57
ECOD	0.7425	0.4530	8.74	0.06	0.68

Table 1: (Top): Evaluation performance on 47 tabular datasets. (Bottom): Evaluation performance on 10 CV/NLP embedding datasets. Top2 Cum. Ratio indicates the proportion of datasets where a method ranks within the top-2 in AUROC, and Fail Ratio indicates the proportion where it ranks 9th or lower.

In-dist ( $P$ ) / Out-dist ( $Q$ )	1024	512	256	30	In-dist ( $P$ ) / Out-dist ( $Q$ )	1024	512	256	30
CIFAR-10 / SVHN	0.2311	0.2924	0.2984	0.3143	SVHN / CIFAR-10	0.9917	0.9843	0.9486	0.8520
CIFAR-100 / SVHN	0.0843	0.1160	0.2036	0.3490	SVHN / CIFAR-100	0.9933	0.9536	0.9137	0.8622
CelebA / SVHN	0.1207	0.1782	0.2745	0.4711	SVHN / CelebA	0.9976	0.9811	0.9722	0.9481

Table 2: AUROC scores for likelihood tests as a function of the number of retained independent components using RealNVP with MLP (images preprocessed by ICA). The left block corresponds to

\mathbb{H}(P)>\mathbb{H}(Q)

, and the right block corresponds to

\mathbb{H}(P)<\mathbb{H}(Q)

Panel of Figure 1 — Figure 1: (Left, Center) : Estimation of ID according to changes in $\rho$ . The x-axis represents the value of $\rho$ and the y-axis represents dimension. The horizontal line represents the ambient dimension. (Right) : Log-scale scatter plot for ID estimate and ambient dimension using the TwoNN method of real dataset and synthetic dataset sampled by $\mathcal{N}(0,I_{d})$ . The estimated ID for the image dataset are from Table 1 in Pope et al. (2021) . The distance recorded in the legend represents the average value of the distance between each point and the green line indicating when the ID estimate and ambient dimension are the same. Each blue/red point corresponds to one ADBench/image dataset.

Dataset	MNIST	CIFAR-10	CIFAR-100	SVHN
MLE	13	26	23	19
TwoNN	15	11	9	7
$d$ -Ratio	0.019	0.004	0.003	0.002
Dataset	magicgamma	satellite	landsat	waveform
MLE	5	9	11	16
TwoNN	7	15	14	17

Table 3: (Top): ID estimates for real datasets. (Bottom): Among the 28 datasets on which NF-SLT ranks

\geq 3

, the fraction whose

d

-Ratio falls below each threshold. The

d

-Ratio is the ratio of the ID (TwoNN) to the ambient dimension. Image-dataset results follow Pope et al. (2021) .

Appendix figures & tables33 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 2 — Figure 2: Performance of NF-SLT implemented by NICE across different dimensions. The y-axis represents AUROC, and the x-axis indicates the dimensionality of the data. The titles of each subfigure specify distributions’ parameters. Subplots 1 and 2 have a larger In/Out of Distribution difference than Subplots 3 and 4, and the speed of performance decay as the dimension increases becomes faster as the distribution difference becomes smaller.

Panel of Figure 3 — Figure 3: Performance of NF-SLT implemented by RealNVP across different dimensions. The y-axis represents AUROC, and the x-axis indicates the dimensionality of the data. The titles of each subfigure specify distributions’ parameters.

Panel of Figure 4 — Figure 4: Histogram of log-likelihood values for the 1st subfigure in Figure 2

Panel of Figure 5 — Figure 5: Histogram of log-likelihood values for the 2nd subfigure in Figure 2

Panel of Figure 6 — Figure 6: Histogram of log-likelihood values for the 3rd subfigure in Figure 2

Panel of Figure 7 — Figure 7: Histogram of log-likelihood values for the 4th subfigure in Figure 2

Panel of Figure 8 — Figure 8: Histogram of latent norm values for the 1st subfigure in Figure 3

Panel of Figure 9 — Figure 9: Histogram of volume values for the 1st subfigure in Figure 3

Panel of Figure 10 — Figure 10: Histogram of latent norm values for the 3rd subfigure in Figure 3

Panel of Figure 11 — Figure 11: Histogram of volume values for the 3rd subfigure in Figure 3

In-dist ( $P$ ) / Out-dist ( $Q$ )	1024	512	256	30	In-dist ( $P$ ) / Out-dist ( $Q$ )	1024	512	256	30
CIFAR-10 / SVHN	0.1262	0.0950	0.1729	0.3547	SVHN / CIFAR-10	0.9932	0.9807	0.9460	0.8670
CIFAR-100 / SVHN	0.0668	0.0975	0.2015	0.3410	SVHN / CIFAR-100	0.9926	0.9783	0.9436	0.8723
CelebA / SVHN	0.1598	0.2179	0.2988	0.4728	SVHN / CelebA	0.9969	0.9857	0.9709	0.9389
CIFAR-100 / CIFAR-10	0.4804	0.5058	0.4982	0.5021	CIFAR-10 / CIFAR-100	0.5415	0.5287	0.5257	0.5630
CelebA / CIFAR-10	0.8424	0.8511	0.8344	0.6492	CIFAR-10 / CelebA	0.6350	0.5878	0.6747	0.7326

Appendix

Table 4: AUROC scores for likelihood tests as a function of dimensionality (number of retained principal components) using RealNVP with MLP (images preprocessed by PCA). The left block corresponds to

\mathbb{H}(P)>\mathbb{H}(Q)

and the right block corresponds to

\mathbb{H}(P)<\mathbb{H}(Q)

In-dist ( $P$ ) / Out-dist ( $Q$ )	1024	512	256	30	In-dist ( $P$ ) / Out-dist ( $Q$ )	1024	512	256	30
CIFAR-10 / SVHN	0.2311	0.2924	0.2984	0.3143	SVHN / CIFAR-10	0.9917	0.9843	0.9486	0.8520
CIFAR-100 / SVHN	0.0843	0.1160	0.2036	0.3490	SVHN / CIFAR-100	0.9933	0.9536	0.9137	0.8622
CelebA / SVHN	0.1207	0.1782	0.2745	0.4711	SVHN / CelebA	0.9976	0.9811	0.9722	0.9481
CIFAR-100 / CIFAR-10	0.5133	0.5169	0.5046	0.5037	CIFAR-10 / CIFAR-100	0.4970	0.5081	0.5146	0.5588
CelebA / CIFAR-10	0.8511	0.8501	0.8364	0.6515	CIFAR-10 / CelebA	0.3988	0.4041	0.4692	0.6725

Appendix

Table 5: AUROC scores for likelihood tests as a function of dimensionality (number of retained independent components) using RealNVP with MLP (images preprocessed by ICA). The left block corresponds to

\mathbb{H}(P)>\mathbb{H}(Q)

and the right block corresponds to

\mathbb{H}(P)<\mathbb{H}(Q)

In-dist ( $P$ ) / Out-dist ( $Q$ )	$32{\times}32$	$16{\times}16$	$8{\times}8$	In-dist ( $P$ ) / Out-dist ( $Q$ )	$32{\times}32$	$16{\times}16$	$8{\times}8$
CIFAR-10 / SVHN	0.0716	0.3586	0.4512	SVHN / CIFAR-10	0.9902	0.9777	0.9195
CIFAR-100 / SVHN	0.0846	0.4448	0.3918	SVHN / CIFAR-100	0.9900	0.9798	0.9481
CelebA / SVHN	0.1541	0.3056	0.7037	SVHN / CelebA	0.9850	0.9968	0.9982
CIFAR-100 / CIFAR-10	0.4857	0.4933	0.5016	CIFAR-10 / CIFAR-100	0.5259	0.5446	0.5567
CelebA / CIFAR-10	0.7481	0.7137	0.7557	CIFAR-10 / CelebA	0.5087	0.6181	0.6751

Appendix

Table 6: AUROC scores for likelihood tests as a function of image size using Glow (images resized by bilinear interpolation). The left block corresponds to

\mathbb{H}(P)>\mathbb{H}(Q)

, and the right block corresponds to

\mathbb{H}(P)<\mathbb{H}(Q)

Ratio	1.00	0.95	0.90	0.85	0.80	0.75
NF-SLT	0.8180	0.8561	0.8579	0.8377	0.8246	0.8240
MCM	0.7242	0.7217	0.7189	0.7161	0.7158	0.6978

Appendix

Table 7: AUROC on the InternetAds dataset for NF-SLT and MCM as a function of the retained dimensionality. The ratio denotes the fraction of principal components retained out of 500 PCs (after PCA reduction to 500 dimensions).

Type	Metric	GOAD	DeepSVDD	NeuTraLAD	ICL	MCM	DRL	NF-SLT
Local	AUROC	0.7297	0.9605	0.9664	0.9646	0.9948	0.9545	0.9919
Local	AUPRC	0.7922	0.9678	0.9702	0.9697	0.9953	0.9635	0.9926
Clustered	AUROC	1	1	0.9174	1	1	1	1
Clustered	AUPRC	1	1	0.8620	1	1	1	1
Global	AUROC	1	1	1	1	1	1	1
Global	AUPRC	1	1	1	1	1	1	1

Appendix

Table 8: Anomaly detection performance across various anomaly types for deep models.

Dataset	DeepSVDD	GOAD	NeuTraLAD	ICL	MCM	DRL	NF-SLT
InternetAds	0.6013 / 7	0.7356 / 5	0.7112 / 6	0.8815 / 1	0.7973 / 3	0.7603 / 4	0.8746 / 2
campaign	0.7929 / 3	0.2837 / 7	0.7814 / 4	0.6933 / 6	0.7987 / 2	0.7525 / 5	0.8059 / 1
census	0.6421 / 3	0.4140 / 6	0.4991 / 5	0.3917 / 7	0.7478 / 1	0.5646 / 4	0.7186 / 2
nsl-kdd	0.8951 / 5	0.9026 / 4	0.9374 / 3	0.8798 / 6	0.8757 / 7	0.9459 / 2	0.9598 / 1

Appendix

Table 9: AUROC on datasets with mostly categorical features. The number after the slash indicates the relative rank among the seven deep models.

Contamination Ratio	annthyroid	cardio	letter
1%	0.9048	0.9032	0.9195
3%	0.8806	0.8797	0.9126
5%	0.8752	0.8621	0.9005

Appendix

Table 10: Contamination sensitivity analysis of NF-SLT.

Method	magicgamma	satellite	landsat	waveform	Wilt	annthyroid	breastw	cover	fault	fraud
TwoNN	7	15	14	17	5	3	4	3	5	4
MLE	5	9	11	16	4	3	4	4	5	8
IPCA	3	2	2	2	1	1	3	1	5	4

Appendix

Table 11: ID estimates from an alternative estimator IPCA alongside TwoNN and MLE on representative tabular datasets.

Ratio	magicgamma	satellite	landsat	waveform	Wilt	annthyroid	breastw	fault
100%	7	15	14	17	5	3	4	5
90%	7	15	14	17	5	3	4	5
80%	7	14	14	17	5	3	4	5
50%	7	14	13	16	5	4	4	4

Appendix

Table 12: Stability of TwoNN ID estimates under different sub-sampling ratios on representative tabular datasets.

Scaler	magicgamma	satellite	landsat	waveform	Wilt	annthyroid	breastw	fault
No Scaler	7	15	14	17	5	3	4	5
Standard Scaler	7	15	14	16	4	5	4	5
Minmax Scaler	7	15	14	17	4	4	5	4

Appendix

Table 13: Sensitivity of TwoNN ID estimates to common feature-scaling choices on representative tabular datasets.

Model	Hyperparameter search space
PCA	$n_{\text{component\_ratio}}\in\{0.75,0.8,0.85,0.9,0.95\}$
LOF	$N\in\{1,3,5,10,20\}$
IF	$N\in\{30,50,100,200,400\}$
OCSVM	kernel $\in\{\texttt{linear},\texttt{rbf}\}$
COPOD	None
ECOD	None

Appendix

Table 14: Hyperparameter search space for each model.

\eta

denotes the learning rate.

Model	Optimal hyperparameter
PCA	$n_{\text{component\_ratio}}=0.8$
LOF	$N=20$
IF	$N=400$
OCSVM	kernel $=\texttt{linear}$
COPOD	None
ECOD	None

Appendix

Table 15: Optimal hyperparameter combination for each model.

Method	AUROC Diff	Avg Rank Diff	Fail Ratio Diff
DeepSVDD	0.0366	-1.02	-0.21
GOAD	0.1124	-0.68	-0.04
NeuTraLAD	0.0310	-0.53	-0.06
ICL	0.0284	-0.40	-0.15
MCM	0.0302	-0.96	-0.04
DRL	0.0233	-0.32	-0.02

Appendix

Table 16: Hyperparameter sensitivity of deep models. The columns that represent differences represent the differences between the indicators in Table 20 and Table 1 . If it is sensitive to changes in hyperparameters, there will be a large difference in performance when experiments are performed with the optimal hyperparameter combination in the hyperparameter searching space for each dataset, compared to when experiments are performed with the same hyperparameter combination for all datasets.

Model	AUROC $\uparrow$	AUPRC $\uparrow$	Avg. Rank $\downarrow$	Top2 Cum. Ratio $\uparrow$	Fail Ratio $\downarrow$
NICE	0.8575	0.6398	3.74	0.40	0.06
RealNVP	0.8480	0.6385	4.45	0.30	0.09

Appendix

Table 17: Performance comparison between NICE and RealNVP

Model	Ionosphere	Lymphography	WPBC	thyroid	yeast	glass	pendigits
NICE	0.9581	0.9746	0.5051	0.9840	0.4652	0.8867	0.9930
MAF	0.8406	0.9908	0.5070	0.9752	0.4359	0.7677	0.9926

Appendix

Table 18: Performance comparison between NICE and MAF

Model	AUROC $\uparrow$	AUPRC $\uparrow$	Avg. Rank $\downarrow$	Top2 Cum. Ratio $\uparrow$	Fail Ratio $\downarrow$
SLT	0.8575	0.6398	3.74	0.40	0.06
Typicality Test	0.8184	0.6270	5.83	0.26	0.30

Appendix

Table 19: Performance comparison between SLT and the typicality test

Method	AUROC $\uparrow$	AUPRC $\uparrow$	Avg. Rank $\downarrow$	Top2 Cum. Ratio $\uparrow$	Fail Ratio $\downarrow$
PCA	0.7752	0.5240	7.60	0.09	0.51
LOF	0.8447	0.5979	6.15	0.23	0.36
IF	0.8036	0.5099	6.85	0.17	0.36
OCSVM	0.6651	0.3895	10.51	0.04	0.77
COPOD	0.7471	0.4419	9.06	0.06	0.66
ECOD	0.7425	0.4530	9.45	0.04	0.70

Appendix

Table 20: AUROC and AUPRC performance under per-dataset optimal hyperparameter selection.

Dataset	PCA	LOF	IF	OCSVM	COPOD	ECOD
ALOI	0.5492	0.6971	0.5418	0.5038	0.5153	0.5304
Cardiotocography	0.8248	0.7207	0.8150	0.7349	0.6625	0.7856
Hepatitis	0.8145	0.8249	0.7753	0.5905	0.7986	0.7473
InternetAds	0.7012	0.8276	0.4242	0.3755	0.6764	0.6770
Ionosphere	0.9037	0.9550	0.9141	0.5439	0.7975	0.7328
Lymphography	0.9923	0.9843	0.9972	0.8761	0.9986	0.9974

Appendix

Table 21: AUROC performance of shallow models.

Dataset	DAGMM	DeepSVDD	GOAD	NeuTraLAD	ICL	MCM	DRL	NF-SLT
ALOI	0.5024	0.5653	0.5319	0.5700	0.5892	0.4831	0.5858	0.5479
Cardiotocography	0.6067	0.6759	0.3689	0.7626	0.6221	0.5713	0.6862	0.7558
Hepatitis	0.6167	0.6844	0.6054	0.6516	0.6070	0.7985	0.7735	0.7475
InternetAds	0.5590	0.6013	0.7356	0.7112	0.8815	0.7973	0.7603	0.8746
Ionosphere	0.6580	0.9597	0.9459	0.9708	0.9556	0.9574	0.9660	0.9581
Lymphography	0.8643	0.9756	0.9847	0.9779	0.9624	0.9934	0.9847	0.9746

Appendix

Table 22: AUROC performance of deep models.

Dataset	PCA	LOF	IF	OCSVM	COPOD	ECOD
ALOI	0.0711	0.1334	0.0649	0.0592	0.0607	0.0637
Cardiotocography	0.7324	0.6321	0.7085	0.5931	0.5516	0.6598
Hepatitis	0.6398	0.6612	0.5448	0.4062	0.5783	0.4707
InternetAds	0.5689	0.7937	0.2782	0.2448	0.6206	0.6216
Ionosphere	0.9223	0.9609	0.9252	0.7024	0.7988	0.7743
Lymphography	0.8923	0.8121	0.9741	0.6735	0.9830	0.9717

Appendix

Table 23: AUPRC performance of shallow models.

Dataset	DAGMM	DeepSVDD	GOAD	NeuTraLAD	ICL	MCM	DRL	NF-SLT
ALOI	0.0589	0.1186	0.0749	0.0937	0.1058	0.0578	0.1163	0.0831
Cardiotocography	0.4520	0.6307	0.3829	0.6679	0.5864	0.5245	0.6272	0.6742
Hepatitis	0.4622	0.5382	0.4831	0.3848	0.3773	0.5708	0.5664	0.5310
InternetAds	0.3792	0.4077	0.5967	0.4142	0.8345	0.7551	0.6564	0.8399
Ionosphere	0.7007	0.9702	0.9615	0.9761	0.9673	0.9705	0.9731	0.9676
Lymphography	0.5683	0.7607	0.8225	0.7839	0.7166	0.9187	0.8244	0.7691

Appendix

Table 24: AUPRC performance of deep models.

Dataset	PCA	LOF	IF	OCSVM	COPOD	ECOD
ALOI	0.0012	0.0031	0.0025	0.0007	0.0009	0.0008
Cardiotocography	0.0055	0.0208	0.0114	0.0106	0.0046	0.0051
Hepatitis	0.0137	0.0284	0.0341	0.0431	0.0275	0.0373
InternetAds	0.0334	0.0070	0.0526	0.0094	0.0045	0.0044
Ionosphere	0.0153	0.0106	0.0162	0.0667	0.0217	0.0161
Lymphography	0.0061	0.0072	0.0036	0.1011	0.0028	0.0031

Appendix

Table 25: Standard deviation of the AUROC for shallow models.

Dataset	DAGMM	DeepSVDD	GOAD	NeuTraLAD	ICL	MCM	DRL	NF-SLT
ALOI	0.0182	0.0085	0.0030	0.0096	0.0158	0.0063	0.0131	0.0017
Cardiotocography	0.0939	0.0109	0.0144	0.0157	0.0314	0.0141	0.0336	0.0169
Hepatitis	0.0835	0.0753	0.0582	0.0815	0.0963	0.0200	0.0664	0.0787
InternetAds	0.0430	0.0213	0.0442	0.0179	0.0150	0.0013	0.0181	0.0114
Ionosphere	0.0788	0.0075	0.0164	0.0054	0.0082	0.0011	0.0072	0.0085
Lymphography	0.1437	0.0111	0.0087	0.0210	0.0150	0.0020	0.0099	0.0120

Appendix

Table 26: Standard deviation of the AUROC for deep Models

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LLM as Detector: An In-context Learning Approach for Tabular Anomaly Detection

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Applied Artificial Intelligence Initiative (A2I2), Deakin University, Australia · Adelaide University, Australia · Monash University, Australia

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Anomaly detection in tabular data is challenging because abnormal samples often arise as violations of cross-feature dependencies rather than simple marginal deviations. Existing detectors rely on geometric or reconstruction signals, while prior LLM-based approaches mainly fine-tune LLMs with normal samples or generate synthetic anomalies. We propose LLM-Detector, a framework that utilizes the in-context learning capacity of LLMs for structured, prompt-conditioned scoring synthesis, enabling LLMs to derive anomaly detection logic from structured normal-state knowledge. Specifically, normal training data are converted into statistical summaries, causal dependencies, and distilled prototypes that are organized into a prompt for code generation. The resulting scoring engine evaluates statistical deviation, structural inconsistency, and density-based abnormality then computes an anomaly score for each test sample. We evaluate LLM-Detector on 24 tabular datasets, comparing against 15 SOTA baselines. Results show consistent improvements across both mixed-type and continuous-only settings. Moreover, this design eliminates the need for LLM fine-tuning or neural network training, reducing computational cost and enabling practical anomaly detection in real-world tabular systems.

Abstract

Anomaly Detection

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