=Paper=
{{Paper
|id=Vol-3934/paper2
|storemode=property
|title=On the Environmental Impact of the Algorithm LatentOut for Unsupervised Anomaly Detection (SHORT PAPER)
|pdfUrl=https://ceur-ws.org/Vol-3934/short2.pdf
|volume=Vol-3934
|authors=Fabrizio Angiulli,Fabio Fassetti,Luca Ferragina
|dblpUrl=https://dblp.org/rec/conf/greenai/AngiulliFF24
}}
==On the Environmental Impact of the Algorithm LatentOut for Unsupervised Anomaly Detection (SHORT PAPER)==
https://ceur-ws.org/Vol-3934/short2.pdf
On the Environmental Impact of the Algorithm LatentOut
for Unsupervised Anomaly Detection
Fabrizio Angiulli1,โ , Fabio Fassetti1,โ and Luca Ferragina1,โ,โ
1
DIMES Dept., University of Calabria, 87036 Rende (CS), Italy.
Abstract
Because of their astonishing performances, Deep Neural Network-based approaches have become pervasive in
many human activities. However, they often require a long, energy-intensive training phase, which has a huge
environmental impact.
In recent years, there has been a significant increase in the emphasis placed on environmental themes across
various sectors, driven by growing concerns over climate change and sustainability. This heightened focus has
led to many initiatives, policies and discussions aimed at addressing ecological challenges and promoting a more
sustainable future. For the reasons stated above, Deep Learning cannot be exempted from such initiatives and the
literature is starting to pay attention to these issues. This paper aims at contributing to this field, in particular,
concerning the Anomaly Detection Task whose environmental impact, due to its widespread employment,
deserves to be addressed.
Specifically, we focus on the Anomaly Detection field that, such as many other Data Mining tasks, is not
excluded from this analysis. In particular, we consider Latent๐๐ข๐ก, a recently introduced Deep Learning-based
framework for unsupervised Anomaly Detection that exploits both the latent space and the baseline anomaly
score (i. e. the reconstruction error) of a Variational Autoencoder (VAE) to provide a refined anomaly score
performing density estimation in the augmented latent-space/baseline-score feature space.
We analyze the environmental impact of Latent๐๐ข๐ก in terms of carbon footprint by measuring the (estimated)
๐ถ๐2 consumption through the Python library CodeCarbon. We observe that, with equal ๐ถ๐2 consumption,
Latent๐๐ข๐ก achieves much better performances than the standard VAE. Moreover, we compare Latent๐๐ข๐ก with
other Anomaly Detection Neural Network-based methods and we highlight that it is the one that obtains the best
results in terms of a balance between high accuracy performance and low carbon footprint.
Keywords
Anomaly Detection, Variational Autoencoder, Carbon Footprint
1. Introduction
Anomalies can be defined as examples that significantly deviate from the majority of the data to arise
the suspect of being generated by a different mechanism. Anomaly Detection represents a fundamental
task in many human activities, including Healthcare, Cyber-security, Industrial Monitoring, Fraud
Detection, and many others.
It is possible to identify three different types of settings of Anomaly Detection [1]. In the Supervised
setting a dataset whose items are labeled as normal and abnormal is available to build a classifier,
typically the dataset is highly unbalanced and the anomalies form a rare class. The Semi-supervised
setting, also called one-class, is characterized by the presence in input of only examples from the normal
class that are used to train the detector. In the Unsupervised setting the goal is to assign an anomaly
score to each object of the input dataset in order to find anomalies in it.
Classical data mining and machine learning algorithms performing the task of detecting outliers
include statistical-based [2], distance-based [3, 4, 5, 6], density-based [7, 8], reverse nearest neighbor-
based [9, 10, 11], SVM-based [12, 13], and many others [1].
1st Workshop on Green-Aware Artificial Intelligence, 23rd International Conference of the Italian Association for Artificial
Intelligence (AIxIA 2024), November 25โ28, 2024, Bolzano, Italy
โ
Corresponding author.
โ
These authors contributed equally.
Envelope-Open f.angiulli@dimes.unical.it (F. Angiulli); f.fassetti@dimes.unical.it (F. Fassetti); luca.ferragina@unical.it (L. Ferragina)
Orcid 0000-0002-9860-7569 (F. Angiulli); 0000-0002-8416-906X (F. Fassetti); 0000-0003-3184-4639 (L. Ferragina)
ยฉ 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
Recently, the approaches that have achieved the most success have been those based on deep learning
[14], which can be divided into three main families: reconstruction error-based methods employing
Autoencoders (AE), models based on Generative Adversarial Networks (GAN), and SVM-like neural
architectures.
At the basis of the application of Autoencoders (AE) and Variational Autoencoders (VAE) [15, 16, 14] to
Anomaly Detection relies the concept of reconstruction error. More in detail, (Variational) Autoencoders
are trained to map data into a low dimensional latent space and then map them back into the original
space generating in output a reconstruction of the input as similar as possible to it. Since the majority
of the data used for training models belongs to the normal class, it is assumed that these networks are
able to reconstruct the inliers better than the outliers and, thus, the reconstruction error can be adopted
as an anomaly score.
GAN-based models [17, 18, 19, 20] basically consist in the combined, adversarial training of two
sub-architectures, the generator and the discriminator. Specifically, the generator network produces
artificial anomalies as realistic as possible, and the discriminator assigns an anomaly score to each item.
SVM-like methods [21, 22, 23] leverage the idea of enclosing normal data into a hypersphere employing
a One-Class SVM-like loss function combined with a deep neural architecture. A slightly different
approach that can be included in this family, is introduced in [24] where the architecture presents an
additional final layer composed of just one neuron that produces an anomaly score that, for anomalies,
is as far as possible from a value obtained as the average of randomly sampled normal items anomaly
scores.
Moreover, in [25] has been introduced Deep Isolation Forest (DIF), a novel methodology that utilizes
casually initialized neural networks to map original data into random representation ensembles, where
random axis-parallel cuts are subsequently applied to perform data partition.
Nevertheless, the cost of high power and energy combines with the high accuracy and training speed
of the Deep Learning models. This is leading researchers to be aware of the environmental impact
of deep neural architectures by trading off accuracy against energy consumption and also to perform
characterization in terms of performance, power and energy for guiding the architecture design of DNN
models [26, 27, 28, 29].
This paper aims to provide a contribution in this direction, and, in particular, to the field of Anomaly
Detection by analyzing the behaviour of recent methods from the point of view of the detection
performance as well as from the point of view of their carbon footprint. Specifically, we focus on the
Latent๐๐ข๐ก algorithm [30, 31, 32, 33], an anomaly detection framework that applies to any deep neural
architecture as a baseline to obtain a refined score, and we compare it with the baseline architecture on
which it is applied and deep learning-based competitors from the other families.
2. The Latent๐๐ข๐ก algorithm for Unsupervised Anomaly Detection
Due to the quite good performances they obtained as well as their versatility, the ones based on
(Variational) Autoencoders have become the most widespread Anomaly Detection approaches relying
on Deep Neural Networks.
The main issue about them is that they often generalize so well to reconstruct also anomalies [30],
thus worsening the capability of detecting anomalies of the reconstruction error.
In [31] Latent๐๐ข๐ก is introduced. It is a methodology that enhances both the reconstruction error and
the latent space distribution of the Variational Autoencoder in order to obtain a refined anomaly score.
Specifically, the first variant of the Latent๐๐ข๐ก (Figure 1) algorithm considers the enlarged feature space
๐น = ๐ฟ ร ๐ธ, where ๐ฟ represents the latent space and ๐ธ is the reconstruction error space (usually ๐ธ โ โ),
and performs a ๐-NN density estimation in the space ๐น.
In Figure 1 the complete workflow of Latent๐๐ข๐ก is showed. Each point of the dataset ๐ฅ โ ๐ is mapped
into the latent space ๐ฟ of the VAE (blue points represent inliers, red ones represent anomalies) by means
of the encoder ๐๐ and then reconstructed back in the original space ๐ฅฬ โ ๐ by means of the decoder ๐๐ .
Then, the reconstruction error ๐ธ(๐ฅ) = โ๐ฅ โ ๐ฅโฬ 22 is computed, the feature space ๐น = ๐ฟ ร ๐ธ is created, and
Figure 1: Latent๐๐ข๐ก receives the dataset as input and maps it into ๐น. The transformed dataset is then processed
by unsupervised anomaly detection methods which provide an anomaly score for each point.
the ๐-NN density estimation is performed in it to compute the Latent๐๐ข๐ก anomaly score.
The motivation behind this procedure is based on the observation that anomalies tend to lie in the
sparsest regions of the augmented feature space ๐น. This happens because even when their reconstruction
error is not exceptionally large, is still significantly larger than that of their most similar normal items.
In [32] Latent๐๐ข๐ก has been expanded in order to be potentially applied to any neural architecture
that has three fundamental properties:
โข it outputs an anomaly score,
โข it has a latent space ๐ฟ,
โข it performs a mapping from the original data space ๐ to ๐ฟ through an encoder-shaped module.
In particular, the neural models on which Latent๐๐ข๐ก has actually been tested are AE, VAE, GANomaly,
FastโAnoGAN, SO โ GAAL, and MO โ GAAL.
Moreover, in [33] it has been showed that the separation properties of the enlarged space ๐น allow any
generic anomaly score (not only the ๐-NN) to perform better when applied on it than on the input data
space ๐.
3. Experimental results
3.1. Experimental setup
In our experiments we consider the tabular datasets cardio, letter, lympho, mammography, pendigits,
pima, satellite, satimage-2, speech, thyroid, from the ODDS repository [34] as well as the image datasets
MNIST [35], Fashion-MNIST [36], and CIFAR10 [37].
The last three datasets (differently from the ones from the ODDS repository) are multi-class, thus to
make them suitable for the anomaly detection task we adopt a one-vs-all strategy, meaning that we
consider one class as normal and we randomly sample ๐ items from each other class. If not otherwise
stated, we set ๐ = 10. Specifically, we select the class โ0โ as normal for the MNIST dataset, the class
โSandalโ for Fashion-MNIST, and the class โdeerโ for CIFAR-10.
As for the implementation details of the algorithm, we consider the original version of Latent๐๐ข๐ก
with the VAE as baseline architecture, and the ๐-NN with ๐ = 50 as estimator of the density of the
feature space ๐น. The latent space dimension โ of the VAE is set to โ = 2 for tabular ODDS datasets and
to โ = 32 for image datasets. As for the encoder structure (the decoder is symmetric to it) we adopt
the same strategy used in [33], i. e. we insert hidden layers of dimension โ๐ = โ 4๐๐ โ between the input
๐-dimensional space and the โ-dimensional latent space for each ๐ โ โ+ such that โ 4๐๐ โ > โ.
The ๐ถ๐2 emissions are estimated by means of the Python library CodeCarbon [38] which bases its
tracking on the power consumption and the geographic location where the code is executed.
3.2. Evolution of performance and emissions of Latent๐๐ข๐ก and VAE during training
The energy consumption of any Deep Learning model is related to the training phase, and, in particular,
to the number of training epochs.
Therefore, it is of crucial importance to understand the behavior of these algorithms as the training
proceeds to optimize the trade-off between the maximization of the performance and the minimization
of energy consumption.
The quantity of ๐ถ๐2 produced by Latent๐๐ข๐ก, which we represent as โฐLatent๐๐ข๐ก , is fundamentally
constituted by two terms:
โข the emissions โฐ๐ ๐ด๐ธ needed for the training of the architecture and the computation, which is
shared with the Variational Autoencoder,
โข the emissions โฐ๐-NN used for the building of the feature space โฑ and the computation of the
๐-NN algorithm in it.
Since the two operations are carried out in sequence and independently of each other, we have that
โฐLatent๐๐ข๐ก = โฐ๐ ๐ด๐ธ + โฐ๐-NN
which means that, with equal training epochs, the carbon footprint of Latent๐๐ข๐ก is always greater
than the one of the Variational Autoencoder. Thus, for a fair comparison, we train the Variational
Autoencoder for 100 epochs and we stop the training earlier for evaluating the Latent๐๐ข๐ก score.
Figure 2: Comparison between the performances of the Variational Autoencoder and Latent๐๐ข๐ก in terms of
AUC during the training epochs. ODDS datasets, group 1.
In figures 2, 3, 4, we show the performances of both Latent๐๐ข๐ก (in orange) and the standard Variational
Autoencoder (in blue) in terms of Area Under the ROC Curve (AUC) as the training proceeds. Observe
that on the horizontal axis is reported the ๐ถ๐2 emissions (in ๐พ ๐), which means that, for the reasons
stated above, each value of the AUC of Latent๐๐ข๐ก is obtained with fewer epochs than the relative value
of the VAE.
As we can see, in almost every plot the curve of Latent๐๐ข๐ก is placed above the curve of the VAE.
Moreover, the trend of Latent๐๐ข๐ก is much more regular than the one of the VAE (see in particular the
plots of the datasets cardio, mammography, satellite, satimage-2, mnist, cifar). This implies that if we
fix a threshold on the amount of ๐ถ๐2 we want to emit, the score of Latent๐๐ข๐ก always outperforms the
standard score of the VAE. In other words, Latent๐๐ข๐ก is able to better exploit the emissions produced
than the standard architecture on which it is applied.
Figure 3: Comparison between the performances of the Variational Autoencoder and Latent๐๐ข๐ก in terms of
AUC during the training epochs. ODDS datasets, group 2.
Figure 4: Comparison between the performances of the Variational Autoencoder and Latent๐๐ข๐ก in terms of
AUC during the training epochs. MNIST, Fashion-MNIST and CIFAR10 datasets.
This happens because as the training proceeds the reconstruction capabilities of the VAE improve so
much that at some point it becomes able to reconstruct also outliers, thus lowering the anomaly detection
performances of the model. On the other side Latent๐๐ข๐ก benefits of the latent space organization that
produces a progressively better separation between normal examples and anomalies in the feature
space ๐น.
3.3. Comparison with competitors
We consider as competitors some of the neural networks algorithm implemented in the Python library
PyOD [39], namely Deep-SVDD [21], from the SVM-like family, AnoGAN [17] and ALAD [20], from
the GAN family, and DIF [25]. For the implementation details (number of layers and neurons, training
epochs, learning rate, potential hyperparameters), we refer to the default values fixed in PyOD. As for
Latent๐๐ข๐ก, we consider again the setup described in section 3.1 and we perform a few-epochs training,
due to the good convergence properties observed in the last section. Specifically, the VAE is trained for
15 epochs.
๐ถ๐
As evaluation metrics we adopt the standard Area Under the ROC Curve (AUC) and the ratio ๐ด๐ 2๐ถ
between the emissions of ๐ถ๐2 (in ๐พ ๐) produced for the training and the inference of a model, and the
AUC. This last value is a measure combining both performance and energy consumption, indeed it
indicates how much ๐ถ๐2 is needed (on average) to obtain a single percentage point of AUC.
Table 1 shows the results in terms of AUC. As we can see, Latent๐๐ข๐ก is the best method for half the
datasets, achieving performances close to the best also in the other half. In particular, confirming the
Dataset (๐) Latent๐๐ข๐ก Deep-SVDD AnoGAN ALAD DIF
cardio (21) 0.9300 0.9509 0.4460 0.4885 0.9129
letter (32) 0.6206 0.5189 0.5118 0.5094 0.6557
lympho (18) 0.9495 0.9460 0.9847 0.6549 0.8650
mammography (6) 0.8326 0.8767 0.1366 0.5450 0.7415
pendigits (16) 0.9880 0.9748 0.9729 0.4785 0.9363
pima (8) 0.6598 0.6289 0.7571 0.5472 0.6071
satellite (36) 0.7911 0.6460 0.5432 0.4037 0.7574
satimage-2 (36) 0.9984 0.9682 0.0165 0.4292 0.9935
speech (400) 0.5504 0.4968 0.4658 0.4906 0.4633
thyroid (6) 0.9055 0.8743 0.8967 0.4837 0.9613
MNIST (28 ร 28) 0.9863 0.9321 0.2176 0.3350 0.9572
Fashion-MNIST (28 ร 28) 0.9444 0.9392 0.6634 0.6623 0.6269
CIFAR-10 (32 ร 32 ร 3) 0.7474 0.6624 0.5756 0.5363 0.6383
Table 1
Comparison with competitors in terms of AUC.
Dataset (๐) Latent๐๐ข๐ก Deep-SVDD AnoGAN ALAD DIF
cardio (21) 4.7158e-6 9.6679e-6 1.2619e-3 2.0648e-5 4.0021e-5
letter (32) 5.7428e-6 1.8790e-5 1.3014e-3 1.9605e-5 5.6887e-5
lympho (18) 2.6640e-6 2.9348e-6 5.2290e-5 1.3394e-5 9.8577e-6
mammography (6) 1.5830e-5 4.8771e-5 2.4759e-2 2.9251e-5 1.7729e-4
pendigits (16) 9.2478e-6 3.7444e-5 2.1541e-3 2.7159e-5 1.0738e-4
pima (8) 4.1708e-6 9.1278e-6 1.9493e-6 1.6284e-5 3.3011e-5
satellite (36) 1.1943e-5 4.0915e-5 4.7031e-3 3.1390e-5 1.2655e-4
satimage-2 (36) 9.1152e-6 2.4921e-5 1.4122e-1 2.9071e-5 8.5686e-5
speech (400) 1.9139e-5 5.9722e-5 4.3628e-3 5.4631e-5 1.7098e-4
thyroid (6) 7.5721e-6 1.9487e-5 1.2720e-3 2.2425e-5 5.6633e-5
MNIST (28 ร 28) 2.1834e-5 3.7648e-5 1.7076e-2 8.5111e-5 1.3168e-4
Fashion-MNIST (28 ร 28) 2.3119e-5 4.6431e-5 5.5211e-3 3.7217e-5 1.9408e-4
CIFAR-10 (32 ร 32 ร 3) 4.9952e-5 6.9862e-5 7.7896e-3 5.8859e-5 2.1652e-4
Table 2
๐ถ๐
Comparison with competitors in terms of ๐ด๐ ๐ถ2 .
observation made in [31], Latent๐๐ข๐ก is especially effective on higher dimensional, structured data (for
example speech and the image datasets). In Table 2 are shown the results of the experiment in terms of
๐ถ๐
the ratio ๐ด๐ 2๐ถ . Here, Latent๐๐ข๐ก outperforms its competitors in all but one dataset, exhibiting the best
trade-off between performances obtained and the emissions of ๐ถ๐2 produced.
4. Conclusion
In this paper, we have focused on the algorithm Latent๐๐ข๐ก for unsupervised anomaly detection in
order to evaluate its performances and measure the environmental impact of its executions. When
compared to the standard architecture on which it is applied, i. e. the Variational Autoencoder, Latent๐๐ข๐ก
shows that low energy-consumptive training can lead it to conspicuously better results. Moreover, in
comparison with other neural network-based anomaly detection approaches it has shown superior
performances both in terms of absolute AUC and, most importantly, in terms of the ratio between the
emitted ๐ถ๐2 and the AUC obtained.
As future development, we intend to expand the discussion about the environmental impact of
Latent๐๐ข๐ก by including a more profound analysis of all its several variants and an investigation special-
ized on the hardware type (e.g., CPU vs. GPU), as well as propose novel measures to better capture the
trade-off between emissions and performances. Finally, as a more ambitious goal, we aim at introducing
a mechanism enabling Latent๐๐ข๐ก to consider the green-aware aspect at training time.
Acknowledgments
We acknowledge the support of the PNRR project FAIR - Future AI Research (PE00000013), Spoke 9 -
Green-aware AI, under the NRRP MUR program funded by the NextGenerationEU.
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