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Diffusion Time Estimation

Official implementation of On Diffusion Modeling for Anomaly Detection from The Twelfth International Conference on Learning Representations (ICLR 2024). Includes the code for diffusion-based models for tabular data and image datasets with Diffusion Time Estimation (DTE) and multiple other baselines.

Citation

@inproceedings{
   livernoche2024on,
   title={On Diffusion Modeling for Anomaly Detection},
   author={Victor Livernoche and Vineet Jain and Yashar Hezaveh and Siamak Ravanbakhsh},
   booktitle={The Twelfth International Conference on Learning Representations},
   year={2024},
   url={https://openreview.net/forum?id=lR3rk7ysXz}
}

Setup Instructions

1. Install the required packages

You will need to install ADBench and torchvision for this project. Python needs to be version 3.8+. ADBench has already most of the dependencies needed for the project.

To install all packages, run the following command:

pip install -r requirements.txt

After this is done, as of right now there is a dependency issue with ADBench and PyOD, so you need to install manually PyoD with:

pip install --upgrade PyOD

Note: this is not necessary to run only the diffusion models. You would only needs:

  • numpy
  • torch
  • scikit-learn
  • scipy

2. Download the ADBench Datasets

You will have to download all the necessary datasets to reproduce the results. This is not necessary if you do not want to train on ADBench datasets. The diffusion methods and other implemented baselines do not rely on it. You can do this by running the following command:

from adbench.myutils import Utils
utils = Utils() # utility function
utils.download_datasets(repo='github')

Run the ADBench experiments

To reproduce the results from the paper uses run.py with the argument for the supervision setting to use.

For unsupervised, use: python run.py --setting unsup --seed 0

For semi-supervised, use: python run.py --setting semi --seed 0

We ran the seeds 0,1,2,3,4 for the experiments and report the average and standard deviations over thoses seeds.

Run the image embeddings experiments

For VisA, you first need to follow the data preprocessing from https://github.com/amazon-science/spot-diff/ with a split type of 1cls. Place the folder "/VisA_pytorch" in the main directory. To create the embeddings, you can select the model wanted to create the embedding with either resnet34 or vicreg and run:

python vision/data/visa_preprocess.py --model resnet34

For CIFAR10 and MNIST, to get the ResNet-34 pre-trained classification embeddings, run python vision/data/preprocess.py.

For CIFAR10 with vicreg pre-trained embeddings, you first need to download the weights available here, found at https://github.com/augustwester/vicreg, weights provided by August Wester (2023) (c). Then, run python vision/data/preprocess.py --model vicreg and python vision/data/preprocess.py --model resnet34 keep the file "checkpoint.pt" in the main directory.

You can now run the experiment using python run_embeddings.py

Run the image experiments

As in the previous section, place the folder "/VisA_pytorch" in the main directory after having followed the preprocessing at https://github.com/amazon-science/spot-diff/. Then simply run python run_images.py

Using the models on new datasets

To run using a new dataset, here is an example on thyroid of ADBench. Note the importance of Standard Scaling for the diffusion-based models; we found that it is crucial since the added noise assumes that each feature is centered at 0 and, as we use gaussian noise, having standard scaling helps the noise to cover the whole space for anomaly detection.

import numpy as np
import sklearn.metrics as skm
from sklearn.preprocessing import StandardScaler

from diffusion.DTE import DTECategorical
import os
import pkg_resources

DATA_PATH = pkg_resources.resource_filename('adbench', 'datasets/')

dataset = "38_thyroid"
data = np.load(os.path.join(DATA_PATH, 'Classical', dataset + '.npz'), allow_pickle=True)

X = data['X']
y = data['y']


test_size = 0.5 # number of normal samples to go in the test set

# split the data to have the normal data as training set (semi-supervised setting)
indices = np.arange(len(X))
normal_indices = indices[y == 0]
anomaly_indices = indices[y == 1]

train_size = round((1-test_size) * normal_indices.size)
train_indices, test_indices = normal_indices[:train_size], normal_indices[train_size:]
test_indices = np.append(test_indices, anomaly_indices)

X_train = X[train_indices]
y_train = y[train_indices]
X_test = X[test_indices]
y_test = y[test_indices]

# Standard scaling
scaler = StandardScaler().fit(X_train)
X_train = scaler.transform(X_train)
X_test = scaler.transform(X_test)

model = DTECategorical()

model.fit(X_train)

scores = model.predict_score(X_test)

auc_roc = skm.roc_auc_score(y_test, scores)
print(auc_roc)

Settings and Results

For the semi-supervised setting, we use 0.5 of the normal data in the training set, and the rest is in the test set with anomalies. For the unsupervised setting, we sample the whole dataset with replacement for the training data, while the test data is the whole dataset. This bootstrapping method allows us to test the variance over the training dataset for each method.

The total amount of compute required to reproduce our experiments with five seeds, including all of the baselines and the proposed DTE model amounts to 473 GPU-hours for the unsupervised setting and 225 GPU-hours for the semi-supervised setting on an RTX8000 GPU with 48 gigabytes of memory. There are a few models that are running on CPU only, which account for a few hours of runtime. Here are figures of the results on ADBench of all the methods. The first figure is for the semi-supervised setting, the second is for the unsupervised setting.

Semi-supervised AUCROC Figure 1: Mean AUC ROC with standard deviation over 5 seeds for the semi-supervised setting.

Unsupervised AUCROC Figure 2: Mean AUC ROC with standard deviation over 5 seeds for the unsupervised setting.

Table 1: AUC ROC with standard deviation over 5 seeds for the semi-supervised setting.

Dataset CBLOF COPOD ECOD FeatureBagging HBOS IForest KNN LODA LOF MCD OCSVM PCA DAGMM DeepSVDD DROCC GOAD ICL PlanarFlow VAE GANomaly SLAD DIF DDPM DTE-NP DTE-IG DTE-C
aloi 53.69(0.15) 49.51(0.0) 51.73(0.0) 49.07(0.53) 52.23(0.0) 50.74(0.68) 51.04(0.0) 49.24(2.75) 48.76(0.0) 48.54(0.35) 54.29(0.0) 54.04(0.0) 50.84(2.97) 50.89(2.05) 50.0(0.0) 48.01(0.92) 47.5(0.98) 48.52(2.34) 54.04(0.0) 53.94(1.65) 50.76(0.29) 51.1(0.0) 49.91(0.35) 51.19(0.46) 50.87(1.17) 50.44(0.19)
amazon 58.17(0.12) 56.78(0.0) 53.79(0.0) 57.94(0.04) 56.32(0.0) 56.4(0.95) 60.58(0.0) 52.23(2.84) 57.88(0.0) 60.36(0.09) 56.48(0.0) 54.9(0.0) 50.47(2.01) 51.2(4.42) 50.0(0.0) 56.07(0.9) 54.21(0.22) 49.94(2.12) 54.9(0.0) 53.42(0.94) 52.01(0.06) 51.43(0.34) 55.09(0.1) 60.82(0.0) 51.93(3.5) 56.71(2.15)
annthyroid 90.14(1.08) 76.77(0.0) 78.45(0.0) 88.95(1.61) 66.02(0.0) 90.28(1.52) 92.81(0.0) 77.35(7.51) 88.63(0.0) 90.19(0.02) 88.45(0.0) 85.19(0.0) 72.23(15.13) 55.01(3.62) 88.9(2.31) 81.01(5.16) 81.11(1.07) 93.19(2.14) 85.44(0.0) 67.52(5.54) 93.34(0.36) 88.36(0.0) 88.82(1.34) 92.9(0.25) 87.6(4.46) 97.52(0.15)
backdoor 69.65(5.23) 50.0(0.0) 50.0(0.0) 94.83(0.62) 70.81(0.89) 74.89(2.67) 93.75(0.53) 47.62(22.63) 95.33(0.25) 85.13(8.87) 62.52(0.64) 64.57(0.65) 54.36(19.91) 91.14(2.62) 94.25(0.73) 52.9(14.48) 93.62(0.69) 76.03(11.56) 64.67(0.74) 87.17(1.43) 50.0(0.0) 83.73(0.76) 80.93(0.56) 93.31(1.7) 94.02(1.46) 91.65(1.73)
breastw 99.11(0.23) 99.46(0.09) 99.14(0.22) 59.07(15.44) 99.23(0.17) 99.5(0.08) 99.05(0.26) 98.13(0.35) 88.91(6.8) 98.66(0.65) 99.39(0.16) 99.21(0.17) 89.53(10.2) 96.96(0.92) 47.32(31.95) 98.86(0.33) 98.28(0.45) 97.93(0.82) 99.22(0.18) 94.75(2.73) 99.53(0.13) 56.34(11.9) 98.7(0.43) 99.28(0.12) 78.65(11.1) 92.78(1.75)
campaign 77.05(0.31) 78.15(0.0) 76.86(0.0) 69.1(3.85) 77.06(0.0) 73.64(1.48) 78.48(0.0) 58.88(4.48) 70.55(0.0) 78.51(0.81) 77.67(0.0) 77.07(0.0) 61.47(2.73) 62.21(12.88) 50.0(0.0) 47.89(12.32) 80.92(0.79) 69.75(3.75) 77.07(0.0) 69.21(3.28) 76.75(0.16) 57.87(0.0) 74.51(0.42) 78.79(0.25) 74.81(1.69) 77.95(1.11)
cardio 93.49(1.47) 93.16(0.0) 94.95(0.0) 92.12(0.56) 80.7(0.0) 93.32(1.43) 92.0(0.0) 91.34(2.93) 92.21(0.0) 82.82(0.85) 95.61(0.0) 96.54(0.01) 77.92(8.85) 65.43(4.37) 62.14(23.76) 96.01(0.27) 80.01(2.12) 88.9(0.93) 96.55(0.0) 86.06(4.31) 83.05(1.1) 68.25(0.0) 86.94(1.96) 91.8(0.59) 73.79(14.09) 87.26(1.0)
cardiotocography 67.61(2.21) 66.35(0.0) 79.3(0.0) 63.64(2.4) 61.24(0.0) 74.24(2.88) 62.11(0.0) 72.79(7.6) 64.49(0.0) 57.11(1.41) 75.22(0.0) 78.89(0.0) 67.11(9.03) 47.75(8.59) 45.98(16.75) 76.06(1.4) 54.2(1.8) 69.88(5.65) 78.9(0.0) 62.77(8.62) 47.32(0.31) 41.79(0.0) 54.54(2.96) 63.76(1.88) 52.44(3.67) 60.13(2.59)
celeba 79.28(1.3) 75.72(0.59) 76.33(0.63) 46.89(1.8) 76.68(0.66) 71.23(2.27) 73.14(0.72) 62.46(13.17) 43.73(0.75) 84.37(2.34) 79.79(0.77) 80.53(0.7) 63.81(4.28) 56.17(22.46) 68.89(1.11) 43.8(10.49) 72.21(0.82) 71.64(7.91) 80.32(0.48) 52.25(11.79) 67.43(1.64) 66.69(3.55) 78.56(1.99) 70.4(0.37) 74.51(2.39) 82.18(2.38)
census 70.84(0.28) 50.0(0.0) 50.0(0.0) 55.92(1.0) 62.5(0.47) 62.55(2.38) 72.26(0.29) 51.12(11.19) 58.46(1.06) 74.14(1.94) 70.02(0.21) 70.51(0.21) 52.24(1.19) 54.16(4.33) 55.36(3.62) 35.24(4.19) 70.56(0.35) 59.33(2.89) 70.52(0.22) 68.07(3.66) 57.91(10.84) 61.45(2.04) 70.15(0.23) 72.1(0.4) 61.79(4.94) 69.62(0.91)
cover 94.04(0.28) 88.2(0.27) 91.86(0.21) 99.16(0.63) 71.11(0.82) 86.31(2.07) 97.54(0.15) 94.93(3.07) 99.18(0.1) 70.02(0.66) 96.17(0.11) 94.41(0.14) 75.94(14.06) 49.12(14.74) 95.79(0.69) 13.83(13.34) 89.34(4.02) 47.52(8.02) 94.35(0.15) 76.35(19.11) 73.97(13.8) 57.69(5.24) 98.35(0.66) 97.73(0.55) 95.83(1.55) 97.76(1.28)
donors 93.47(0.23) 81.5(0.21) 88.74(0.38) 95.21(1.72) 81.19(0.61) 89.44(2.22) 99.49(0.06) 63.52(27.27) 96.97(0.24) 81.93(10.78) 92.09(0.22) 88.12(0.57) 62.15(16.19) 72.95(17.81) 74.18(22.09) 33.57(16.0) 99.9(0.05) 91.64(3.52) 88.6(0.25) 75.34(11.69) 88.51(5.51) 90.04(1.79) 82.5(1.83) 99.26(0.29) 99.25(0.6) 98.15(0.37)
fault 59.0(1.29) 49.14(0.0) 50.37(0.0) 48.32(0.95) 53.06(0.0) 55.86(2.03) 58.73(0.0) 50.27(1.88) 47.42(0.0) 59.44(3.79) 57.21(0.0) 55.87(0.0) 52.85(7.19) 54.31(1.62) 55.73(5.33) 58.89(0.61) 60.63(0.5) 57.51(5.15) 55.87(0.0) 59.5(5.14) 63.93(0.19) 62.31(0.0) 61.09(1.16) 58.64(0.65) 59.42(1.46) 59.46(1.45)
fraud 94.91(1.08) 94.3(1.41) 94.89(1.27) 94.83(1.56) 95.02(0.67) 94.73(1.23) 95.43(1.04) 89.05(8.12) 94.35(1.41) 91.1(1.79) 95.61(0.69) 95.38(0.68) 85.33(6.76) 83.13(6.6) 50.0(0.0) 69.75(21.3) 92.78(1.46) 90.72(2.26) 95.47(0.75) 93.25(2.85) 94.58(1.01) 82.58(2.27) 93.65(0.92) 95.64(1.05) 90.79(3.24) 93.52(1.53)
glass 89.35(1.48) 76.0(1.94) 71.14(3.54) 88.49(1.71) 82.59(3.23) 81.09(2.56) 92.04(1.12) 67.34(5.39) 88.82(1.98) 79.71(1.37) 69.73(5.89) 73.44(2.22) 65.33(15.53) 83.67(16.2) 64.89(23.64) 59.03(12.64) 99.44(0.58) 85.33(6.2) 72.55(1.66) 79.77(8.72) 86.04(5.69) 96.45(1.39) 66.67(13.63) 89.64(3.54) 98.53(0.86) 92.42(2.3)
hepatitis 86.26(2.35) 80.9(1.22) 73.84(1.99) 67.76(6.5) 84.84(0.78) 82.69(2.75) 96.46(1.46) 68.98(3.97) 66.92(7.01) 80.64(4.23) 90.58(1.79) 84.48(2.29) 70.22(6.66) 99.57(0.24) 51.8(17.93) 84.5(3.25) 99.94(0.13) 95.8(1.67) 84.84(2.27) 87.39(7.55) 99.93(0.15) 96.07(2.32) 97.74(1.18) 93.22(3.9) 99.93(0.15) 98.78(0.88)
http 99.93(0.01) 99.19(0.09) 97.95(0.12) 92.1(0.57) 98.58(1.04) 99.35(0.29) 100.0(0.0) 47.72(45.49) 99.98(0.03) 99.95(0.01) 100.0(0.0) 99.95(0.01) 91.78(17.91) 61.31(51.49) 50.0(0.0) 99.68(0.13) 98.24(3.45) 99.38(0.08) 99.94(0.01) 50.14(34.85) 99.91(0.08) 99.36(0.07) 100.0(0.0) 99.98(0.03) 80.72(43.08) 99.45(0.1)
imdb 49.94(0.01) 51.05(0.0) 46.88(0.0) 49.53(0.1) 49.94(0.0) 49.53(0.78) 50.08(0.0) 47.23(2.24) 49.57(0.0) 51.24(0.18) 48.72(0.0) 47.97(0.0) 48.6(0.38) 49.97(5.71) 51.35(2.05) 48.46(0.65) 52.34(0.49) 49.23(2.75) 47.97(0.0) 51.58(0.71) 51.26(0.1) 51.4(0.49) 47.91(0.1) 50.43(0.0) 50.97(3.41) 48.05(2.22)
internetads 65.16(0.08) 65.94(0.0) 66.01(0.0) 71.38(2.32) 49.18(0.0) 47.87(2.11) 68.08(0.0) 58.73(3.84) 71.72(0.0) 47.73(0.01) 65.63(0.0) 65.12(0.0) 49.47(5.05) 72.96(3.24) 53.4(7.55) 65.65(0.21) 72.2(0.55) 70.87(0.84) 65.12(0.0) 69.86(0.23) 75.94(0.11) 49.33(0.34) 65.76(0.06) 69.96(2.22) 71.52(3.89) 77.57(1.54)
ionosphere 96.78(1.5) 78.32(2.13) 71.77(1.43) 94.47(2.1) 70.68(2.85) 91.21(1.37) 97.44(0.98) 85.56(3.59) 94.29(2.2) 95.4(0.64) 96.32(0.93) 89.11(1.31) 73.95(5.98) 97.2(1.26) 61.14(28.54) 91.54(3.05) 98.98(0.32) 96.86(1.21) 89.76(1.2) 93.89(2.03) 98.21(0.6) 93.59(2.06) 94.6(0.85) 97.77(1.39) 95.15(3.6) 95.42(0.58)
landsat 57.21(0.26) 49.29(0.0) 42.01(0.0) 66.38(0.17) 73.21(0.0) 58.8(2.21) 68.25(0.0) 44.65(3.3) 66.58(0.0) 56.78(6.08) 47.98(0.0) 43.9(0.0) 56.27(3.46) 59.44(1.41) 53.86(2.57) 40.52(2.32) 65.13(0.44) 50.85(2.13) 54.22(9.45) 55.34(10.03) 65.03(0.18) 56.56(0.0) 51.37(1.0) 68.2(1.75) 44.72(5.52) 52.79(1.63)
letter 33.24(0.66) 36.53(0.0) 45.37(0.0) 44.84(1.0) 35.91(0.0) 32.04(1.64) 35.43(0.0) 30.2(0.94) 44.83(0.0) 31.47(4.16) 32.17(0.0) 30.3(0.0) 38.97(8.38) 36.4(3.05) 55.26(11.04) 31.08(0.55) 42.68(1.17) 38.73(3.53) 30.23(0.0) 34.02(0.74) 36.8(0.41) 74.07(0.0) 38.05(1.12) 34.38(0.98) 39.86(2.29) 36.72(0.95)
lymphography 99.83(0.02) 99.53(0.2) 99.52(0.15) 96.61(2.84) 99.69(0.17) 99.45(0.32) 99.93(0.08) 67.04(13.87) 98.21(0.75) 98.88(0.55) 100.0(0.0) 99.86(0.05) 94.94(3.85) 99.73(0.3) 32.42(37.75) 99.89(0.08) 100.0(0.0) 99.58(0.51) 99.88(0.09) 99.09(0.86) 100.0(0.01) 99.84(0.22) 99.94(0.09) 99.93(0.09) 99.98(0.05) 98.99(0.4)
magic.gamma 75.81(0.0) 68.0(0.0) 63.58(0.0) 84.19(0.72) 74.53(0.0) 77.09(1.29) 83.27(0.0) 70.53(1.36) 83.4(0.0) 73.67(0.12) 74.25(0.0) 70.64(0.0) 59.23(4.32) 62.97(1.07) 78.83(0.66) 69.46(2.39) 75.56(0.42) 74.12(2.75) 70.64(0.0) 59.18(1.6) 72.0(0.01) 63.86(0.0) 85.97(1.08) 83.57(0.76) 86.46(1.12) 87.5(0.9)
mammography 84.74(0.02) 90.59(0.0) 90.67(0.0) 86.31(0.35) 85.01(0.0) 88.02(0.3) 87.58(0.0) 89.62(0.87) 85.52(0.0) 72.87(0.64) 88.63(0.0) 89.93(0.0) 76.03(14.65) 71.5(7.4) 81.82(1.94) 69.94(8.59) 71.87(9.11) 78.93(5.71) 89.58(0.17) 85.54(7.43) 74.51(0.67) 73.87(0.2) 81.01(2.04) 87.62(0.09) 84.64(3.47) 86.42(1.72)
mnist 91.1(0.23) 50.0(0.0) 50.0(0.0) 92.55(0.4) 62.34(0.0) 86.6(1.99) 93.85(0.0) 64.74(7.74) 92.93(0.0) 88.3(1.03) 90.56(0.0) 90.21(0.0) 72.19(7.16) 66.37(11.03) 83.13(1.64) 90.07(0.35) 90.11(1.13) 81.9(2.67) 90.21(0.0) 77.9(6.44) 89.73(0.44) 50.21(0.0) 87.27(3.22) 94.02(0.42) 80.78(5.91) 87.43(2.48)
musk 100.0(0.0) 99.71(0.0) 99.87(0.0) 100.0(0.0) 100.0(0.0) 90.58(6.2) 100.0(0.0) 99.67(0.35) 100.0(0.0) 93.91(2.55) 100.0(0.0) 100.0(0.0) 95.01(4.27) 99.99(0.01) 32.99(33.18) 100.0(0.0) 99.37(0.63) 76.65(18.72) 100.0(0.0) 100.0(0.0) 100.0(0.0) 97.76(0.0) 100.0(0.0) 100.0(0.0) 94.22(12.93) 100.0(0.0)
optdigits 83.52(1.69) 50.0(0.0) 50.0(0.0) 96.27(0.49) 89.92(0.0) 81.07(3.28) 93.72(0.0) 32.77(8.62) 96.65(0.0) 64.86(0.92) 63.38(0.0) 58.17(0.0) 40.04(20.45) 39.45(18.65) 85.25(2.9) 67.46(4.94) 97.18(0.8) 34.12(8.29) 58.17(0.0) 74.3(12.58) 95.28(0.17) 48.64(0.0) 90.76(2.12) 94.28(1.67) 79.81(9.35) 82.38(2.68)
pageblocks 91.23(0.11) 80.85(0.0) 87.95(0.0) 91.11(0.3) 65.62(0.0) 82.64(0.89) 89.65(0.0) 83.62(2.6) 91.3(0.0) 87.07(0.02) 88.58(0.0) 86.12(0.0) 82.8(10.44) 78.39(1.53) 92.33(1.18) 88.05(1.19) 88.39(0.77) 84.85(1.19) 86.16(0.0) 72.83(9.94) 87.86(0.01) 87.39(0.0) 86.93(0.42) 89.32(0.26) 85.66(1.77) 89.89(0.55)
pendigits 96.67(0.07) 90.74(0.0) 92.95(0.0) 99.5(0.11) 93.55(0.0) 97.22(0.48) 99.87(0.0) 92.13(1.02) 99.05(0.0) 83.69(0.09) 96.36(0.0) 94.37(0.0) 56.49(21.83) 46.29(11.35) 75.91(13.38) 89.97(2.03) 96.71(0.83) 83.45(6.13) 94.5(0.0) 67.93(21.6) 94.61(0.41) 89.71(0.0) 98.11(0.23) 99.61(0.17) 96.96(1.63) 97.79(0.68)
pima 72.94(1.07) 66.59(1.32) 60.56(1.57) 71.93(2.22) 74.76(1.6) 74.26(1.63) 76.94(1.87) 62.68(7.55) 70.53(2.19) 73.64(1.37) 71.53(1.79) 72.28(1.99) 54.54(6.0) 57.99(2.85) 47.53(16.52) 62.31(13.7) 79.68(3.06) 72.17(2.71) 73.18(1.93) 60.45(3.01) 60.62(4.21) 55.19(6.92) 70.27(2.28) 81.5(2.57) 68.59(3.93) 69.88(1.95)
satellite 73.2(0.92) 68.34(0.0) 62.22(0.0) 80.11(0.11) 85.5(0.0) 77.46(1.48) 82.24(0.0) 69.73(1.15) 80.3(0.0) 72.76(3.68) 73.91(0.0) 66.63(0.0) 72.79(2.01) 76.19(2.66) 73.38(4.44) 68.76(0.92) 85.15(0.48) 72.3(1.73) 74.14(0.25) 79.87(0.56) 87.49(0.1) 66.91(0.0) 77.7(0.53) 82.11(0.67) 76.52(2.68) 78.61(0.7)
satimage-2 99.42(0.01) 97.92(0.0) 97.09(0.0) 99.47(0.03) 97.95(0.0) 99.12(0.21) 99.71(0.0) 98.67(0.52) 99.38(0.0) 99.92(0.0) 99.61(0.0) 98.17(0.0) 91.82(4.43) 92.94(2.84) 99.22(0.42) 98.99(0.06) 99.48(0.22) 96.67(0.57) 98.98(0.04) 97.57(1.19) 99.77(0.0) 86.9(0.0) 99.62(0.16) 99.67(0.0) 95.34(1.84) 99.34(0.07)
shuttle 99.72(0.02) 99.47(0.0) 99.33(0.0) 86.89(8.22) 98.64(0.0) 99.65(0.07) 99.91(0.0) 71.68(33.88) 99.98(0.0) 98.98(0.0) 99.62(0.0) 99.36(0.0) 84.58(18.68) 99.79(0.07) 50.0(0.0) 70.44(16.28) 99.92(0.04) 86.5(5.68) 99.35(0.0) 97.53(0.74) 99.9(0.01) 99.76(0.0) 99.91(0.01) 99.93(0.02) 99.86(0.12) 99.75(0.0)
skin 91.82(0.21) 47.21(0.18) 49.14(0.18) 78.39(0.91) 76.92(0.35) 89.42(0.58) 99.49(0.08) 75.51(5.43) 86.34(1.77) 88.37(0.26) 90.25(0.24) 59.73(0.31) 67.91(30.02) 59.95(4.47) 89.48(1.07) 64.95(2.25) 6.58(0.63) 91.27(7.09) 66.05(0.19) 48.48(2.87) 91.05(2.61) 87.55(0.76) 88.74(4.4) 98.86(0.46) 98.71(1.13) 91.77(0.22)
smtp 87.28(5.65) 91.15(1.58) 88.26(2.46) 84.81(3.66) 82.75(5.31) 90.36(2.13) 92.43(2.7) 73.03(6.65) 93.42(2.48) 94.87(0.84) 84.65(4.49) 81.81(7.32) 87.08(5.31) 85.24(6.6) 57.13(15.93) 78.78(13.12) 74.36(7.07) 84.22(6.88) 81.93(5.67) 54.55(5.98) 92.15(1.87) 95.51(1.36) 95.43(1.26) 92.98(2.91) 81.64(9.87) 95.27(1.28)
spambase 81.52(0.55) 72.09(0.0) 68.83(0.0) 69.64(2.09) 77.88(0.0) 85.18(1.69) 83.36(0.0) 72.39(6.9) 73.23(0.0) 80.69(3.02) 81.7(0.0) 81.4(0.0) 69.41(4.42) 70.24(5.02) 75.37(4.45) 81.78(0.36) 83.53(0.45) 82.26(3.35) 81.4(0.0) 82.57(1.34) 84.86(0.2) 41.31(0.0) 64.54(0.8) 83.74(0.69) 77.5(3.37) 83.01(0.41)
speech 35.88(0.15) 37.03(0.0) 35.96(0.0) 37.48(0.37) 36.66(0.0) 37.7(1.72) 36.36(0.0) 38.02(2.67) 37.53(0.0) 38.81(0.36) 36.57(0.0) 36.38(0.0) 50.66(3.9) 48.88(2.88) 48.96(2.21) 36.63(1.14) 48.86(2.72) 48.56(4.54) 36.38(0.0) 38.7(3.43) 41.37(0.94) 52.29(3.42) 36.96(0.86) 41.37(0.0) 39.57(1.54) 38.17(0.57)
stamps 93.41(1.66) 93.14(0.4) 87.62(0.91) 94.21(2.26) 91.8(1.0) 93.47(1.42) 95.89(1.44) 91.93(3.55) 93.74(2.36) 84.93(2.01) 93.72(1.74) 92.7(1.68) 80.11(11.56) 71.09(3.68) 50.15(22.93) 81.46(15.36) 96.68(1.09) 87.3(10.69) 93.28(1.28) 66.2(7.84) 81.97(8.29) 84.92(4.03) 91.84(4.15) 97.87(0.37) 93.38(3.31) 91.6(2.04)
thyroid 98.54(0.06) 93.81(0.0) 97.55(0.0) 93.15(1.52) 98.65(0.0) 98.96(0.2) 98.68(0.0) 96.06(1.65) 92.72(0.0) 98.49(0.01) 98.56(0.0) 98.55(0.0) 91.08(6.68) 88.77(3.69) 94.96(1.55) 95.15(0.85) 95.4(0.98) 98.42(0.51) 98.55(0.0) 94.78(3.22) 95.27(0.24) 96.29(0.0) 97.95(0.22) 98.63(0.04) 89.43(11.73) 98.74(0.14)
vertebral 54.43(1.97) 26.34(2.49) 41.95(4.78) 64.13(2.15) 40.09(3.97) 45.64(3.83) 57.67(3.58) 31.66(5.28) 64.3(1.31) 47.1(1.82) 50.47(2.23) 42.08(3.49) 50.6(11.93) 44.79(1.71) 43.84(24.28) 46.73(8.74) 79.19(5.06) 49.78(7.82) 42.63(2.75) 50.67(10.71) 44.96(9.25) 57.21(3.04) 70.67(6.28) 54.3(15.47) 74.63(7.58) 66.41(1.9)
vowels 78.72(4.01) 52.82(0.0) 61.47(0.0) 85.32(1.16) 53.31(0.0) 61.83(0.62) 82.21(0.0) 55.52(8.1) 86.3(0.0) 27.66(0.28) 75.91(0.0) 52.29(0.0) 42.55(11.56) 55.73(4.43) 54.74(21.32) 68.49(3.71) 85.1(2.13) 54.59(10.55) 52.12(0.02) 63.11(9.82) 85.02(0.02) 88.48(0.0) 86.38(1.94) 81.42(1.44) 85.68(3.16) 86.93(2.25)
waveform 72.93(0.9) 72.36(0.0) 59.44(0.0) 76.95(1.07) 69.28(0.0) 72.29(1.52) 75.21(0.0) 60.96(5.08) 76.0(0.0) 58.39(0.03) 70.44(0.0) 64.68(0.0) 51.89(7.39) 59.94(2.58) 67.7(5.0) 64.99(3.1) 68.68(3.66) 64.8(2.42) 64.84(0.0) 75.95(7.58) 48.92(0.08) 50.63(0.0) 62.17(2.64) 74.48(0.0) 73.68(2.68) 65.21(1.05)
wbc 98.31(1.31) 99.4(0.25) 99.39(0.25) 58.05(18.08) 99.0(0.41) 99.41(0.37) 99.12(0.19) 97.86(1.59) 80.52(4.47) 98.88(1.02) 99.63(0.19) 99.35(0.13) 86.76(15.33) 91.44(3.64) 44.24(28.21) 99.14(0.2) 99.66(0.36) 95.97(0.81) 99.25(0.27) 95.91(3.0) 99.78(0.18) 97.46(1.82) 99.2(0.39) 99.54(0.28) 90.98(11.64) 80.53(7.15)
wdbc 98.73(0.43) 99.18(0.21) 96.72(0.71) 99.63(0.18) 98.55(0.28) 98.73(0.64) 99.05(0.27) 96.98(2.04) 99.62(0.21) 97.03(0.47) 99.34(0.23) 99.14(0.22) 73.78(25.27) 99.31(0.4) 40.08(33.97) 98.96(0.25) 99.78(0.27) 98.86(0.76) 99.14(0.36) 96.22(3.1) 99.49(0.25) 68.03(7.24) 99.3(0.17) 99.52(0.38) 99.6(0.31) 98.48(0.77)
wilt 42.9(1.14) 32.09(0.0) 37.48(0.0) 73.35(10.5) 39.1(0.0) 47.97(3.12) 63.66(0.0) 41.1(7.0) 68.81(0.0) 81.72(0.01) 34.81(0.0) 26.07(0.0) 41.81(7.29) 34.41(1.7) 49.49(12.62) 51.38(5.33) 76.42(3.46) 74.62(4.18) 35.41(0.0) 44.01(5.48) 61.76(0.11) 55.02(0.0) 71.66(0.81) 62.91(5.59) 93.75(3.23) 85.1(1.13)
wine 97.75(0.59) 86.37(4.37) 73.86(5.42) 97.93(0.87) 95.63(2.63) 93.92(1.79) 99.19(0.22) 90.94(4.75) 98.36(0.38) 97.28(1.8) 97.82(0.45) 93.79(1.58) 66.17(39.61) 92.16(4.34) 43.8(32.33) 94.11(1.86) 99.87(0.29) 95.38(2.4) 94.25(1.47) 74.32(28.64) 100.0(0.0) 91.09(2.25) 99.61(0.09) 99.44(0.97) 99.95(0.11) 99.97(0.04)
wpbc 59.57(1.98) 52.33(2.93) 49.5(2.47) 56.79(1.86) 60.91(2.67) 56.33(2.72) 63.67(2.34) 51.32(3.74) 57.36(2.01) 63.36(0.93) 53.37(2.44) 52.54(2.3) 46.99(2.56) 82.67(5.47) 43.78(4.34) 51.39(5.74) 96.61(1.17) 57.46(2.93) 54.42(2.76) 60.11(5.48) 95.53(2.21) 82.51(3.26) 66.49(3.17) 83.16(13.46) 70.71(9.06) 68.88(2.7)
yeast 50.4(0.08) 38.88(0.0) 44.64(0.0) 46.4(1.33) 42.88(0.0) 41.8(0.75) 44.74(0.0) 46.51(5.8) 45.79(0.0) 43.05(0.1) 44.84(0.0) 43.24(0.0) 51.03(3.92) 47.62(5.96) 48.42(5.46) 52.53(3.88) 48.98(2.39) 45.07(3.33) 42.39(0.01) 47.64(6.7) 48.69(0.11) 38.44(0.0) 49.13(2.85) 44.58(0.33) 48.58(2.89) 47.08(1.1)
yelp 63.8(0.07) 60.21(0.0) 57.39(0.0) 67.06(0.12) 59.95(0.0) 61.07(0.53) 68.07(0.0) 56.26(3.78) 67.2(0.0) 66.15(0.04) 62.08(0.0) 59.16(0.0) 49.87(1.25) 49.9(3.3) 50.67(1.15) 61.07(0.98) 55.79(0.5) 53.6(2.03) 59.14(0.04) 56.11(1.6) 54.88(0.19) 48.36(0.23) 59.3(0.09) 68.66(0.0) 57.32(4.3) 59.94(5.32)
MNIST-C 81.11(0.09) 50.0(0.0) 50.0(0.0) 87.33(0.15) 70.43(0.0) 76.75(1.45) 84.11(0.0) 69.39(5.31) 87.21(0.0) 75.26(1.24) 79.55(0.0) 78.35(0.0) 63.71(6.37) 64.7(4.6) 57.2(11.1) 79.34(0.41) 85.62(0.52) 71.21(1.5) 78.35(0.01) 80.08(1.16) 83.51(0.11) 54.05(2.27) 80.12(0.14) 84.74(0.0) 79.92(3.93) 86.1(0.84)
FashionMNIST 89.1(0.15) 50.0(0.0) 50.0(0.0) 91.67(0.11) 75.42(0.0) 84.15(1.07) 89.87(0.0) 79.28(4.1) 91.6(0.0) 84.37(1.11) 88.16(0.0) 87.6(0.0) 70.8(4.89) 75.45(2.22) 51.58(14.44) 88.03(0.24) 90.56(0.27) 82.19(0.96) 87.6(0.0) 89.43(0.52) 89.94(0.04) 65.53(1.77) 88.52(0.07) 90.14(0.0) 84.32(2.44) 90.21(0.55)
CIFAR10 67.87(0.21) 54.98(0.0) 56.88(0.0) 70.31(0.21) 57.89(0.0) 64.04(0.93) 67.53(0.0) 61.62(4.35) 70.3(0.0) 65.15(0.58) 67.79(0.0) 67.42(0.0) 53.97(2.96) 56.12(2.2) 49.63(3.46) 67.53(0.72) 63.6(0.83) 62.75(1.09) 67.42(0.0) 67.19(0.84) 66.6(0.1) 52.06(1.59) 67.91(0.13) 67.82(0.0) 62.4(3.33) 68.53(1.59)
SVHN 60.97(0.17) 50.0(0.0) 50.0(0.0) 63.93(0.14) 54.65(0.0) 58.99(0.88) 61.69(0.0) 54.5(4.02) 63.82(0.0) 58.87(0.65) 61.25(0.0) 60.79(0.0) 53.36(2.12) 53.92(3.05) 49.99(2.47) 60.75(0.49) 61.7(0.5) 58.87(0.87) 60.79(0.0) 61.25(0.77) 60.87(0.07) 52.98(0.67) 61.37(0.08) 62.13(0.0) 59.19(2.5) 62.91(1.1)
MVTec-AD 79.96(2.02) 50.0(0.0) 50.0(0.0) 80.45(2.2) 75.97(1.84) 77.38(1.95) 81.51(1.82) 72.31(3.37) 80.36(2.14) 86.75(2.12) 77.44(2.03) 76.37(1.91) 64.69(5.63) 89.55(2.19) 60.52(11.42) 77.06(2.1) 94.75(0.84) 72.8(2.39) 76.21(1.81) 81.1(1.8) 93.24(1.09) 81.99(2.78) 78.0(1.99) 89.66(1.51) 85.88(3.63) 89.39(2.0)
20news 57.1(1.23) 52.92(0.43) 54.11(0.24) 60.25(0.7) 53.57(0.35) 54.91(1.17) 57.36(0.66) 53.45(4.0) 60.19(0.62) 62.85(1.63) 56.25(0.62) 54.39(0.41) 51.48(4.08) 55.64(4.17) 52.77(4.09) 54.92(1.04) 61.3(1.05) 51.59(3.0) 54.59(0.74) 59.68(1.87) 59.47(0.8) 53.18(2.56) 54.88(0.52) 59.97(0.74) 58.28(6.15) 64.3(3.17)
agnews 62.82(0.08) 55.05(0.0) 55.11(0.0) 74.64(0.09) 55.69(0.0) 58.43(1.09) 67.05(0.0) 56.95(3.54) 74.58(0.0) 67.98(0.25) 60.64(0.0) 56.9(0.0) 51.03(3.6) 49.83(5.63) 49.65(0.76) 59.87(0.86) 62.55(0.47) 50.15(1.19) 56.9(0.0) 58.63(1.14) 58.43(0.07) 52.02(0.89) 57.82(0.12) 67.98(0.0) 56.55(4.15) 68.16(3.22)

Table 2: AUC ROC with standard deviation over 5 seeds for the unsupervised setting.

Dataset CBLOF COPOD ECOD FeatureBagging HBOS IForest KNN LODA LOF MCD OCSVM PCA DAGMM DeepSVDD DROCC GOAD ICL PlanarFlow VAE GANomaly SLAD DIF DDPM DTE-NP DTE-IG DTE-C
aloi 55.58(0.2) 51.53(0.01) 53.06(0.01) 79.15(0.56) 53.11(0.21) 54.22(0.39) 61.32(0.04) 49.52(1.02) 76.66(0.35) 52.04(0.17) 54.86(0.01) 54.9(0.08) 51.69(2.13) 51.42(2.92) 50.0(0.0) 49.69(0.64) 54.84(0.62) 52.01(1.37) 54.85(0.0) 54.75(1.09) 54.24(0.68) 49.77(1.14) 53.22(0.25) 64.5(0.09) 54.1(0.99) 52.48(0.31)
amazon 57.92(0.24) 57.05(0.06) 54.1(0.05) 57.18(0.49) 56.3(0.08) 55.76(0.65) 60.27(0.04) 52.63(3.04) 57.09(0.56) 59.73(0.42) 56.47(0.1) 54.95(0.1) 50.12(1.97) 46.38(2.16) 50.0(0.0) 55.97(2.07) 52.84(0.7) 49.49(0.97) 54.98(0.0) 55.12(1.1) 51.8(0.34) 50.91(1.39) 55.13(0.09) 60.3(0.4) 53.45(1.61) 55.64(2.54)
annthyroid 67.57(0.98) 77.67(0.17) 78.91(0.11) 78.77(2.68) 60.84(2.38) 81.63(1.18) 76.05(0.14) 45.33(12.81) 70.95(1.05) 91.8(0.35) 68.17(0.21) 67.56(0.39) 54.81(7.26) 73.9(1.57) 63.07(2.69) 45.25(10.03) 59.94(3.53) 96.58(1.49) 67.44(0.01) 61.91(1.12) 57.26(6.06) 49.5(0.85) 81.37(1.37) 78.11(0.22) 92.32(2.08) 96.36(0.52)
backdoor 89.71(0.72) 50.0(0.0) 50.0(0.0) 79.03(3.04) 74.04(0.77) 72.46(3.35) 82.64(0.5) 51.5(16.4) 76.42(2.72) 84.78(9.77) 88.86(0.77) 88.75(0.73) 75.24(8.88) 73.49(2.66) 50.0(0.0) 58.68(10.74) 93.62(0.75) 78.66(7.09) 88.79(0.76) 90.75(3.52) 50.0(0.0) 50.21(0.9) 89.18(0.62) 80.56(0.48) 75.34(11.82) 87.52(1.0)
breastw 96.08(0.93) 99.44(0.16) 99.04(0.25) 40.83(2.6) 98.44(0.3) 98.32(0.46) 98.02(0.53) 96.97(3.27) 44.61(3.25) 98.52(0.45) 93.49(2.12) 94.63(1.2) 81.1(6.33) 62.54(12.59) 84.73(6.24) 84.54(9.29) 80.73(3.93) 96.48(1.43) 92.8(4.07) 94.27(3.9) 81.74(1.91) 51.14(2.06) 76.64(4.22) 97.62(0.47) 90.45(2.0) 89.07(2.24)
campaign 73.78(0.3) 78.28(0.04) 76.94(0.05) 59.37(4.19) 76.81(0.27) 70.37(1.81) 74.95(0.14) 49.27(8.77) 61.44(0.34) 77.47(0.94) 73.65(0.07) 73.4(0.12) 58.07(2.76) 50.79(8.34) 50.0(0.0) 44.28(5.98) 76.61(0.5) 56.61(2.97) 73.42(0.0) 65.19(5.23) 70.41(0.71) 49.87(0.72) 72.38(0.77) 74.59(0.16) 65.99(6.09) 78.91(0.61)
cardio 83.16(1.77) 92.08(0.3) 93.49(0.12) 57.89(2.77) 83.94(1.23) 92.21(1.22) 83.02(1.85) 85.59(7.1) 55.12(2.42) 81.48(1.65) 93.42(0.35) 94.9(0.18) 62.47(10.89) 49.78(16.06) 65.54(4.78) 90.77(3.72) 46.07(4.06) 79.59(4.61) 95.0(0.04) 77.01(18.8) 49.5(4.13) 49.52(2.41) 72.33(5.93) 77.67(2.16) 63.11(10.52) 72.13(3.16)
cardiotocography 56.09(2.47) 66.42(3.42) 78.4(0.22) 53.79(1.73) 59.5(1.09) 68.09(2.61) 50.3(0.49) 70.8(13.23) 52.67(2.09) 49.99(0.49) 69.13(0.43) 74.66(0.68) 54.6(6.58) 48.8(5.25) 44.9(4.67) 62.42(12.71) 37.2(2.07) 64.25(6.21) 75.25(0.08) 66.57(10.45) 38.27(3.61) 50.42(0.97) 57.86(4.27) 49.28(0.7) 50.62(6.64) 51.03(2.7)
celeba 75.34(1.76) 75.7(0.62) 76.31(0.65) 51.39(2.7) 75.41(0.65) 70.72(1.27) 73.58(0.38) 59.97(11.91) 43.21(1.22) 80.25(3.67) 78.11(0.7) 79.23(0.61) 62.66(3.98) 49.12(17.53) 72.57(0.97) 43.2(12.41) 68.35(2.27) 70.32(11.86) 78.97(0.39) 43.67(19.16) 60.49(1.66) 49.93(0.99) 79.58(1.88) 69.87(0.51) 69.96(4.42) 81.22(1.54)
census 66.4(0.18) 50.0(0.0) 50.0(0.0) 53.75(0.31) 61.09(0.34) 60.73(2.15) 67.08(0.26) 45.44(13.11) 56.2(0.61) 73.12(2.05) 65.46(0.18) 66.15(0.16) 49.07(0.64) 52.7(5.12) 44.31(2.74) 48.8(5.06) 66.76(0.69) 60.36(1.36) 66.07(0.13) 64.99(5.58) 62.5(6.99) 50.13(1.0) 65.87(0.14) 67.2(0.27) 62.87(3.68) 64.64(1.14)
cover 92.24(0.17) 88.2(0.32) 91.85(0.2) 57.14(2.15) 70.68(1.16) 87.32(2.69) 86.57(2.41) 92.18(3.85) 56.75(1.89) 69.58(0.9) 95.2(0.16) 93.39(0.25) 74.15(14.15) 58.04(22.39) 74.69(22.59) 12.37(7.08) 68.07(5.04) 41.68(7.76) 93.25(0.23) 70.13(19.1) 72.34(1.89) 50.41(1.34) 80.76(1.65) 83.81(2.71) 63.52(7.37) 69.68(4.69)
donors 80.77(0.71) 81.53(0.27) 88.83(0.32) 69.06(1.74) 74.31(0.63) 77.08(1.5) 82.9(0.42) 56.62(38.02) 62.89(1.35) 76.48(7.46) 77.02(0.67) 82.5(0.94) 55.76(15.63) 51.11(24.73) 74.66(13.89) 22.45(11.53) 73.92(4.79) 89.89(1.85) 82.01(0.45) 63.87(15.51) 62.72(1.88) 49.76(0.41) 80.63(1.88) 83.23(0.45) 79.55(10.75) 78.49(7.9)
fault 66.5(2.51) 45.49(0.16) 46.81(0.19) 59.1(1.16) 50.62(6.66) 54.39(1.01) 71.52(0.62) 47.78(2.34) 57.88(1.35) 50.5(1.2) 53.69(0.3) 47.97(0.55) 49.54(5.92) 52.22(2.87) 66.84(2.7) 54.63(4.8) 66.05(1.1) 46.87(3.43) 48.46(0.08) 48.92(6.42) 70.48(0.88) 50.69(0.61) 56.22(0.95) 72.55(0.3) 57.74(5.42) 58.95(3.36)
fraud 95.39(0.81) 94.29(1.42) 94.89(1.27) 61.59(7.15) 94.51(1.22) 94.95(1.15) 95.5(1.13) 85.55(5.41) 54.77(7.3) 91.13(1.91) 95.37(0.72) 95.23(0.72) 85.71(5.32) 76.91(6.34) 50.0(0.0) 72.4(22.06) 93.09(1.05) 89.48(2.1) 95.24(0.76) 84.93(5.45) 93.79(1.88) 50.22(3.43) 92.37(1.37) 95.6(1.18) 94.18(1.16) 93.78(1.29)
glass 85.5(4.18) 75.95(1.51) 71.04(3.41) 65.86(12.47) 82.02(1.77) 78.95(3.72) 87.03(1.1) 62.43(12.75) 61.76(12.42) 79.47(1.22) 66.07(6.69) 71.51(2.1) 62.99(16.27) 51.69(18.75) 74.29(16.19) 54.46(20.97) 72.85(5.65) 76.62(8.46) 69.95(1.81) 80.81(13.83) 74.87(2.69) 50.05(5.2) 56.04(9.11) 88.13(1.24) 68.05(23.1) 86.39(4.15)
hepatitis 63.47(14.61) 80.74(0.93) 73.7(1.73) 46.94(11.14) 76.77(1.57) 68.29(1.42) 66.94(7.9) 55.74(15.73) 46.77(8.48) 72.05(2.95) 70.38(1.52) 74.78(2.64) 60.0(9.71) 36.08(22.07) 58.18(4.23) 63.65(22.94) 61.64(3.75) 65.42(7.96) 74.84(1.89) 65.51(6.12) 43.06(10.04) 49.28(3.43) 46.12(8.03) 63.1(2.79) 45.14(13.88) 57.69(9.3)
http 99.61(0.03) 99.07(0.26) 97.96(0.1) 28.82(1.45) 99.11(0.16) 99.95(0.08) 5.05(1.98) 5.95(9.35) 33.75(1.07) 99.95(0.01) 99.36(0.05) 99.66(0.03) 83.81(35.3) 24.89(42.35) 50.0(0.0) 99.56(0.04) 92.11(7.15) 99.38(0.05) 99.62(0.02) 77.91(18.04) 99.43(0.1) 49.66(2.23) 99.76(0.16) 5.06(1.99) 97.33(4.05) 99.51(0.21)
imdb 49.56(0.21) 51.2(0.04) 47.05(0.03) 49.89(0.54) 49.86(0.08) 48.93(0.66) 49.44(0.14) 46.6(2.52) 50.02(0.55) 50.36(0.21) 48.39(0.13) 47.82(0.06) 48.68(0.29) 52.56(4.11) 49.95(0.12) 48.58(1.58) 52.07(0.36) 49.29(0.76) 47.83(0.0) 48.96(1.32) 50.54(0.4) 49.88(0.83) 47.79(0.11) 49.49(0.3) 48.61(4.27) 48.44(2.75)
internetads 61.55(0.12) 67.61(0.07) 67.66(0.06) 49.42(4.74) 69.56(0.04) 68.61(1.81) 61.62(0.08) 54.06(5.45) 58.73(1.53) 65.96(4.33) 61.52(0.07) 60.91(0.22) 51.48(2.63) 58.3(4.5) 50.0(1.4) 61.41(0.35) 59.21(1.26) 60.78(0.48) 61.47(0.0) 68.75(1.0) 60.08(2.14) 49.38(1.28) 61.37(0.03) 63.42(0.33) 63.53(3.89) 65.58(2.8)
ionosphere 89.19(1.14) 78.27(1.27) 71.65(1.21) 87.64(1.63) 54.44(3.14) 83.3(1.31) 92.18(1.24) 78.84(4.28) 86.38(2.12) 95.14(0.75) 83.79(1.44) 77.68(1.24) 64.1(4.77) 51.37(9.79) 76.6(7.87) 82.92(2.69) 62.9(2.96) 88.37(1.49) 78.55(1.59) 88.07(2.14) 88.4(1.06) 49.46(2.76) 75.75(2.41) 92.4(1.63) 69.72(11.39) 91.14(1.82)
landsat 54.77(4.28) 42.17(0.12) 36.83(0.13) 54.03(1.15) 57.5(0.58) 47.4(2.32) 61.44(0.32) 38.23(3.78) 54.86(1.33) 60.7(0.07) 42.33(0.26) 36.55(0.29) 53.25(1.1) 63.13(2.62) 62.56(0.47) 50.59(9.05) 64.86(1.86) 46.44(0.89) 54.85(1.48) 54.4(4.8) 67.27(0.61) 50.23(0.98) 49.62(0.59) 60.2(0.39) 47.31(8.29) 54.42(1.2)
letter 76.32(1.8) 56.02(0.07) 57.26(0.13) 88.58(0.51) 58.85(0.59) 61.56(1.17) 81.21(0.3) 53.71(4.29) 87.81(0.48) 80.43(0.42) 59.81(0.28) 52.35(0.29) 50.31(5.01) 51.74(2.09) 78.03(2.72) 59.77(1.85) 73.65(1.25) 68.92(3.77) 52.45(0.12) 68.15(9.18) 86.52(0.55) 50.45(1.04) 84.73(1.44) 85.0(0.5) 67.63(4.86) 78.13(1.49)
lymphography 99.35(0.74) 99.6(0.09) 99.49(0.14) 52.34(18.31) 99.49(0.18) 99.85(0.1) 99.51(0.28) 90.04(11.06) 63.63(18.01) 98.9(0.24) 99.56(0.27) 99.67(0.25) 84.0(4.77) 68.07(30.75) 87.75(8.04) 99.53(0.28) 88.43(4.62) 94.03(5.01) 99.72(0.21) 86.43(20.22) 96.11(1.79) 51.15(6.83) 95.77(4.02) 98.89(0.72) 85.23(7.81) 83.41(11.37)
magic.gamma 72.53(0.1) 68.1(0.04) 63.8(0.05) 69.96(0.64) 70.93(0.55) 72.1(0.79) 79.5(0.15) 65.5(1.41) 67.84(0.38) 69.87(0.1) 67.26(0.18) 66.73(0.11) 58.44(3.35) 60.37(1.2) 72.79(0.59) 44.24(4.6) 67.55(1.02) 74.23(4.69) 66.86(0.0) 57.73(3.14) 63.78(0.4) 50.2(0.48) 76.26(1.48) 80.07(0.15) 78.21(2.19) 76.45(1.39)
mammography 79.5(1.84) 90.54(0.03) 90.62(0.03) 72.61(0.51) 83.77(0.9) 85.96(1.73) 85.17(0.24) 86.69(2.45) 70.15(1.87) 69.02(1.35) 87.11(0.13) 88.84(0.29) 71.91(17.95) 45.13(6.77) 77.92(1.81) 41.41(13.31) 65.76(9.12) 78.22(2.96) 88.67(0.07) 87.12(4.62) 73.23(2.4) 50.17(2.0) 74.94(2.14) 84.86(0.22) 79.94(5.76) 81.02(2.74)
mnist 84.26(1.11) 50.0(0.0) 50.0(0.0) 66.44(1.42) 57.36(0.38) 81.06(2.17) 86.66(0.59) 56.4(11.07) 65.77(1.94) 85.62(1.32) 84.91(0.22) 84.76(0.43) 63.14(6.24) 60.48(14.11) 61.51(1.13) 69.76(8.76) 69.06(1.61) 64.49(15.63) 85.0(0.04) 72.05(3.57) 50.0(0.0) 49.51(1.34) 81.6(1.2) 85.27(0.77) 75.56(4.12) 81.89(1.32)
musk 100.0(0.0) 94.81(0.48) 95.28(0.29) 57.54(10.67) 100.0(0.0) 99.77(0.38) 96.42(3.15) 99.3(0.77) 58.07(8.89) 99.96(0.05) 100.0(0.0) 100.0(0.0) 91.22(7.47) 53.84(15.38) 57.49(5.9) 100.0(0.0) 79.0(2.58) 74.83(25.71) 100.0(0.0) 100.0(0.0) 83.66(4.44) 50.03(3.54) 99.95(0.03) 88.17(5.61) 78.48(12.07) 96.47(1.74)
optdigits 78.48(0.95) 50.0(0.0) 50.0(0.0) 53.93(5.59) 86.81(0.25) 69.63(4.81) 39.52(2.17) 49.29(9.35) 53.82(5.25) 41.27(5.26) 50.66(1.46) 51.78(0.53) 40.78(19.75) 51.94(25.08) 56.52(3.54) 65.66(7.61) 53.29(6.15) 49.15(13.23) 51.47(0.2) 44.79(14.06) 56.08(3.06) 50.18(1.59) 40.15(3.71) 38.61(2.33) 51.34(4.5) 50.77(6.25)
pageblocks 89.3(2.14) 87.48(0.21) 91.37(0.1) 75.83(1.79) 77.89(2.07) 89.72(0.35) 91.94(0.32) 71.24(10.47) 70.33(1.55) 92.3(0.22) 91.42(0.21) 90.67(0.47) 75.29(4.49) 59.24(11.13) 91.38(1.48) 60.93(7.81) 76.75(1.0) 90.8(2.02) 90.57(0.0) 80.13(2.79) 74.57(4.01) 50.26(1.09) 82.0(0.91) 90.64(0.63) 85.02(8.84) 92.39(0.84)
pendigits 86.38(7.22) 90.6(0.43) 92.69(0.15) 51.82(5.22) 92.47(0.38) 94.69(0.78) 82.81(3.01) 89.51(0.85) 53.42(4.61) 83.41(0.94) 92.86(0.48) 93.58(0.12) 54.8(21.37) 38.26(12.39) 52.01(4.93) 59.23(15.6) 65.02(4.5) 77.99(9.67) 93.66(0.03) 83.75(10.03) 68.63(2.86) 49.65(2.66) 70.03(5.43) 78.64(3.13) 62.39(10.39) 71.33(6.62)
pima 65.49(1.65) 66.2(1.21) 60.38(1.54) 57.31(3.88) 70.38(1.21) 67.37(1.88) 72.33(1.74) 59.52(7.09) 56.34(3.89) 68.64(2.09) 63.11(1.82) 65.11(2.53) 52.16(3.2) 51.01(3.01) 54.18(11.49) 60.57(18.25) 52.4(2.56) 61.51(5.6) 67.03(1.72) 55.05(6.29) 47.11(3.76) 51.24(2.19) 53.74(5.29) 70.71(2.47) 59.92(3.39) 62.37(3.09)
satellite 74.19(3.23) 63.34(0.04) 58.3(0.05) 54.54(1.26) 76.18(0.55) 69.5(1.07) 72.09(0.14) 61.39(2.92) 54.98(1.29) 80.39(0.07) 66.24(0.21) 60.14(0.07) 67.46(2.21) 56.21(5.85) 60.8(1.23) 70.21(3.55) 62.65(1.77) 67.05(1.01) 75.55(0.75) 68.13(6.86) 74.56(1.53) 49.84(0.7) 71.53(0.52) 70.15(0.19) 58.17(6.67) 71.05(1.82)
satimage-2 99.88(0.01) 97.46(0.04) 96.52(0.05) 52.55(7.36) 97.6(0.12) 99.28(0.16) 99.24(0.61) 98.14(0.49) 53.91(7.29) 99.53(0.06) 99.67(0.01) 97.72(0.03) 91.13(4.48) 55.12(12.77) 57.86(11.12) 99.56(0.06) 89.76(2.38) 97.03(0.86) 98.51(0.12) 98.36(1.01) 96.65(1.42) 50.77(2.25) 99.55(0.05) 97.95(1.48) 85.81(5.97) 94.56(1.27)
shuttle 62.06(3.96) 99.5(0.1) 99.3(0.01) 49.29(3.4) 98.63(0.23) 99.71(0.03) 73.16(0.66) 38.87(13.16) 52.55(1.09) 99.01(0.01) 99.18(0.0) 98.99(0.03) 89.77(5.59) 57.58(13.24) 50.0(0.0) 20.78(28.35) 64.17(14.05) 85.16(6.0) 98.98(0.0) 98.11(0.69) 90.72(18.12) 50.08(0.35) 97.5(2.28) 69.83(0.34) 66.86(26.52) 97.62(1.2)
skin 67.51(3.8) 47.12(0.19) 48.97(0.1) 53.38(0.29) 58.84(0.37) 66.97(0.65) 71.97(0.13) 44.16(1.92) 54.97(0.17) 89.15(0.15) 54.73(0.45) 44.69(0.58) 55.44(17.81) 54.82(7.49) 70.84(1.68) 57.86(4.33) 26.45(9.05) 77.33(3.97) 52.27(0.25) 46.54(3.91) 75.01(0.51) 50.15(0.38) 46.09(2.11) 71.81(0.13) 74.05(3.66) 74.05(2.35)
smtp 86.29(4.76) 91.17(1.63) 88.22(2.47) 79.36(5.06) 80.91(4.76) 90.5(2.2) 93.26(1.74) 81.88(3.56) 89.92(5.31) 94.84(0.93) 84.49(4.46) 85.62(4.92) 86.77(5.56) 89.53(5.1) 50.0(0.0) 91.53(1.82) 65.61(12.08) 78.37(11.9) 81.98(5.52) 59.01(16.05) 92.13(1.68) 54.1(6.53) 95.56(1.3) 92.97(1.89) 76.92(14.33) 95.07(1.36)
spambase 54.13(0.68) 68.79(0.08) 65.57(0.12) 42.41(0.84) 66.41(1.18) 63.72(2.0) 56.56(0.27) 47.98(10.23) 45.29(0.42) 44.55(3.6) 53.43(0.18) 54.77(0.69) 48.84(4.87) 58.44(7.73) 49.04(1.5) 49.57(9.44) 45.88(1.79) 52.83(6.32) 54.99(0.03) 55.18(2.65) 49.26(0.44) 49.51(0.82) 51.01(1.51) 54.47(0.38) 50.93(4.84) 51.52(1.9)
speech 47.11(0.24) 48.89(0.29) 46.95(0.04) 50.85(0.71) 47.32(0.19) 47.62(0.7) 48.0(0.09) 46.57(1.85) 51.15(0.65) 49.37(1.87) 46.59(0.1) 46.89(0.04) 52.22(4.41) 51.24(3.1) 48.27(1.74) 45.81(1.99) 51.16(2.23) 49.56(3.55) 46.94(0.05) 50.66(2.29) 50.85(2.15) 48.09(2.89) 46.57(1.17) 48.73(1.02) 48.84(4.05) 49.46(1.46)
stamps 66.04(2.92) 92.92(0.83) 87.72(1.03) 50.16(7.61) 90.4(1.0) 90.72(1.09) 86.97(2.04) 83.1(9.15) 51.18(9.24) 83.83(3.64) 88.24(1.44) 90.94(1.59) 71.89(9.56) 46.51(7.98) 76.0(7.44) 77.44(13.78) 50.51(4.05) 83.81(4.86) 90.63(1.26) 77.4(12.76) 51.2(3.79) 50.7(4.35) 55.55(12.83) 82.02(4.05) 69.17(18.33) 75.25(5.15)
thyroid 90.93(1.07) 93.91(0.26) 97.71(0.11) 70.68(1.69) 94.84(1.01) 97.91(0.55) 96.52(0.21) 81.89(12.49) 65.69(3.08) 98.57(0.04) 95.83(0.12) 95.48(0.31) 71.85(12.11) 50.45(2.0) 88.89(4.95) 57.42(27.16) 69.25(5.72) 99.18(0.26) 95.56(0.0) 81.9(17.35) 80.02(3.3) 50.85(2.85) 87.06(1.5) 96.43(0.3) 82.75(12.16) 99.02(0.12)
vertebral 46.34(1.41) 26.28(3.94) 41.67(3.03) 47.32(5.6) 31.73(3.46) 36.18(3.44) 37.9(2.03) 29.44(5.11) 48.68(3.4) 38.9(2.16) 42.61(0.9) 37.82(2.71) 46.96(9.72) 39.42(2.69) 42.45(15.87) 46.81(12.68) 44.9(1.08) 40.86(14.66) 38.4(2.54) 37.66(8.85) 39.75(3.09) 49.28(2.03) 56.34(7.41) 40.04(2.58) 45.07(14.43) 45.76(8.79)
vowels 88.38(0.5) 49.6(0.44) 59.3(0.38) 93.29(1.73) 67.91(0.98) 76.26(3.14) 95.09(0.23) 70.52(4.82) 93.18(1.07) 73.21(8.48) 77.87(0.98) 60.35(0.6) 46.44(13.27) 51.37(2.96) 73.81(15.9) 79.08(5.62) 78.42(2.32) 88.82(3.83) 62.08(0.09) 55.43(18.53) 93.19(0.78) 49.29(2.87) 90.34(2.76) 96.42(0.42) 70.49(8.5) 91.42(5.8)
waveform 70.14(0.99) 73.89(0.4) 60.31(0.21) 71.52(2.12) 69.38(0.64) 70.69(5.94) 74.97(0.82) 59.4(6.16) 69.26(1.81) 57.16(0.49) 66.88(0.3) 63.53(0.26) 52.3(7.42) 60.86(7.12) 67.4(1.94) 59.15(5.89) 66.05(2.92) 63.97(5.61) 63.85(0.05) 62.01(16.16) 43.65(0.95) 48.7(3.49) 61.72(3.41) 72.91(1.34) 52.29(6.3) 60.2(3.55)
wbc 97.71(1.1) 99.4(0.1) 99.38(0.12) 38.83(10.4) 98.7(0.16) 99.58(0.15) 98.21(0.47) 99.17(0.13) 60.66(8.68) 98.77(1.03) 98.72(0.54) 99.28(0.25) 82.09(14.37) 50.34(17.76) 82.08(10.35) 94.86(4.74) 85.34(4.73) 93.36(3.36) 99.15(0.18) 95.76(3.23) 96.08(4.57) 48.01(3.85) 94.8(1.16) 97.94(0.76) 89.38(7.64) 87.06(3.83)
wdbc 98.98(0.42) 99.29(0.14) 97.05(0.65) 86.65(8.37) 98.94(0.24) 98.83(0.39) 98.04(0.64) 98.04(0.77) 84.87(9.38) 96.9(1.12) 98.42(0.37) 98.8(0.31) 71.51(25.04) 60.2(20.82) 34.73(16.78) 98.28(1.25) 73.78(7.19) 98.54(0.81) 97.79(0.97) 96.23(2.96) 78.99(12.13) 48.52(3.7) 96.54(0.93) 97.49(1.11) 56.64(26.56) 83.51(6.61)
wilt 39.59(1.76) 34.49(0.27) 39.4(0.12) 66.59(7.27) 34.81(2.83) 45.13(3.34) 51.05(0.65) 31.31(9.9) 67.81(1.65) 85.88(0.06) 31.66(0.3) 23.94(0.42) 43.18(5.91) 46.5(1.58) 39.99(3.03) 55.46(8.59) 64.85(3.41) 79.36(2.41) 33.08(0.0) 41.32(1.11) 68.06(1.02) 50.91(1.72) 65.9(3.92) 55.15(0.61) 83.38(7.17) 85.12(1.73)
wine 45.27(33.4) 86.46(4.66) 73.77(4.79) 32.34(5.54) 90.72(3.31) 78.61(6.71) 47.04(3.12) 82.17(3.91) 32.97(14.63) 97.54(1.59) 67.14(3.79) 81.91(2.83) 51.27(29.94) 50.72(23.41) 62.05(21.99) 73.37(23.81) 45.47(4.33) 38.99(21.89) 81.22(3.63) 68.17(16.01) 37.42(8.26) 48.45(3.14) 37.39(8.37) 42.45(6.29) 31.01(10.98) 55.71(11.39)
wpbc 48.68(3.14) 51.87(3.09) 48.91(2.35) 43.61(3.13) 54.81(2.85) 51.55(1.88) 51.22(2.52) 50.07(3.44) 44.66(3.87) 53.41(4.03) 48.51(2.34) 48.62(2.27) 44.94(2.82) 49.34(2.52) 48.26(3.3) 46.64(5.66) 48.76(5.04) 48.34(3.69) 46.77(1.77) 48.87(4.0) 48.33(1.22) 48.82(2.44) 49.31(3.97) 50.22(3.27) 48.91(3.81) 46.79(6.57)
yeast 46.06(1.23) 38.03(0.15) 44.31(0.16) 46.45(1.53) 40.17(0.97) 39.42(1.16) 39.62(0.95) 46.13(4.68) 45.3(2.12) 40.64(1.1) 41.95(0.43) 41.75(0.4) 50.33(4.55) 52.04(3.8) 39.57(4.74) 50.31(3.51) 46.59(2.15) 44.2(5.92) 40.07(0.01) 47.64(5.98) 49.55(1.21) 50.01(2.19) 46.31(0.72) 39.98(1.1) 44.61(4.27) 42.03(2.62)
yelp 63.53(0.34) 60.52(0.15) 57.78(0.04) 66.1(0.42) 59.97(0.11) 60.15(0.34) 67.01(0.17) 58.1(2.89) 66.11(0.48) 65.49(0.64) 62.08(0.04) 59.19(0.1) 49.83(1.27) 52.43(8.88) 50.35(0.54) 59.02(3.78) 54.52(0.49) 52.67(1.98) 59.29(0.08) 60.51(0.91) 54.37(0.27) 49.1(1.34) 59.38(0.12) 67.08(0.37) 51.37(3.24) 60.16(3.22)
MNIST-C 75.71(1.0) 50.0(0.0) 50.0(0.0) 70.19(1.05) 68.92(0.22) 73.34(1.89) 78.64(0.13) 59.06(9.66) 69.94(0.95) 73.9(1.62) 75.11(0.09) 74.05(0.18) 58.13(6.73) 55.24(9.15) 59.37(2.13) 75.16(1.73) 66.95(1.05) 70.48(1.97) 74.05(0.01) 72.56(3.12) 74.59(0.67) 49.73(1.14) 75.1(0.14) 78.83(0.24) 70.3(3.97) 74.56(2.21)
FashionMNIST 87.06(0.33) 50.0(0.0) 50.0(0.0) 74.78(0.94) 74.82(0.2) 83.08(0.94) 87.51(0.14) 67.23(7.64) 73.81(0.86) 83.95(1.2) 86.03(0.05) 85.32(0.17) 66.37(5.59) 64.66(7.04) 56.39(3.06) 85.99(0.52) 75.8(1.2) 81.88(1.33) 85.32(0.01) 86.65(0.97) 85.83(2.38) 50.31(1.74) 86.1(0.08) 87.31(0.25) 76.67(6.18) 84.05(1.28)
CIFAR10 66.31(0.3) 54.78(0.07) 56.66(0.06) 68.71(0.63) 57.23(0.17) 62.9(1.09) 65.85(0.09) 59.09(5.51) 68.62(0.59) 63.9(0.75) 66.25(0.08) 65.93(0.18) 53.0(2.94) 55.45(4.1) 50.32(2.39) 65.85(1.04) 55.68(1.4) 62.13(1.33) 65.92(0.01) 66.19(1.19) 64.81(0.56) 50.32(1.77) 66.34(0.14) 66.0(0.22) 59.52(2.81) 62.87(1.57)
SVHN 60.13(0.25) 50.0(0.0) 50.0(0.0) 62.9(0.4) 54.22(0.12) 58.03(0.7) 60.36(0.08) 53.4(4.29) 62.8(0.41) 58.31(0.84) 60.38(0.08) 59.92(0.17) 52.75(2.11) 52.05(3.23) 52.12(2.09) 59.7(1.44) 57.06(1.05) 58.04(1.09) 59.91(0.01) 60.17(1.06) 59.57(0.4) 49.66(1.16) 60.45(0.13) 60.69(0.2) 56.73(2.89) 59.96(1.24)
MVTec-AD 75.41(2.26) 50.0(0.0) 50.0(0.0) 74.54(2.66) 73.18(1.9) 74.67(1.85) 76.28(1.56) 64.42(5.16) 74.17(2.73) 61.79(4.89) 73.52(1.86) 72.44(1.94) 59.57(4.79) 60.28(6.07) 54.38(4.52) 72.96(2.61) 68.3(3.37) 63.73(6.77) 72.46(1.61) 73.85(2.83) 69.88(3.91) 49.94(2.48) 73.21(1.92) 76.11(2.26) 65.48(5.76) 72.95(3.11)
20news 56.38(1.44) 53.26(0.59) 54.42(0.42) 60.97(1.63) 53.69(0.62) 55.0(1.81) 56.65(1.23) 53.85(4.56) 60.98(1.65) 58.29(2.78) 55.92(0.97) 54.48(0.69) 51.78(3.92) 51.49(5.34) 49.58(2.77) 55.28(1.84) 54.73(2.58) 51.27(2.61) 54.59(0.69) 55.74(1.98) 55.31(1.21) 50.99(3.11) 54.74(0.56) 56.98(1.59) 52.72(5.59) 57.87(3.45)
agnews 61.91(0.31) 55.1(0.04) 55.24(0.04) 71.5(0.62) 55.4(0.08) 58.43(1.32) 64.65(0.1) 56.81(3.57) 71.36(0.64) 66.5(0.5) 60.09(0.11) 56.61(0.08) 50.8(3.45) 49.36(4.46) 50.01(0.55) 59.16(3.06) 59.08(0.61) 49.65(1.27) 56.6(0.0) 64.53(1.65) 57.44(0.25) 50.17(1.17) 57.06(0.1) 65.22(0.31) 54.45(5.22) 62.66(3.75)

Note: DTE-NP is for the non-parametric DTE DTENonParametric, DTE-IG is for the inverse gamma DTE DTEInverseGamma, and DTE-C is for the categorical DTE DTECategorical.

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