<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.0 20120330//EN" "JATS-archivearticle1.dtd">
<article xmlns:xlink="http://www.w3.org/1999/xlink">
  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Networks Using a Graph-Autoregressive Approach⋆</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Valeriy Lakhno</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Dmytro Kasatkin</string-name>
          <email>d.kasatkin@nubip.edu.ua</email>
          <xref ref-type="aff" rid="aff0">0</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Mykola Tsiutsiura</string-name>
          <email>mitsiutsiura@gmail.com</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Valentyna Makoiedova</string-name>
          <email>makoiedova.valentyna@gmail.com</email>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>National University of Life and Environmental Sciences of Ukraine</institution>
          ,
          <addr-line>Heroiv Oborony 15, 03041, Kyiv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>State University of Trade and Economics</institution>
          ,
          <addr-line>Kyoto 19, 02156, Kyiv</addr-line>
          ,
          <country country="UA">Ukraine</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2026</year>
      </pub-date>
      <fpage>31</fpage>
      <lpage>43</lpage>
      <abstract>
        <p>A new mathematical model of risk-oriented security management in Internet of Things (IoT) networks is proposed. The model combines a graph-autoregressive approach to load forecasting with a decision-making mechanism based on the Conditional Value-at-Risk (CVaR) indicator. The study aims to improve the cyber resilience of IoT networks by integrating spatio-temporal traffic analysis, information security indicators, and economic risk assessment. It is proved that existing methods and models for predicting and detecting anomalies are focused mainly on time series. However, they do not take into account the topological structure of IoT networks and the relationships between nodes, which reduces their effectiveness. The developed graph-autoregressive model simultaneously takes into account the time dependence of traffic and the spatial correlation between network nodes through the Laplacian of the graph. Based on the forecast residuals, the level of anomaly and the probability of an attack are estimated, taking into account behavioral and network security indicators. A risk-oriented decision-making module is proposed that uses CVaR as a criterion for the optimal choice of protective actions. This allowed the defense system to focus on the worstcase scenarios of high-cost attacks, minimizing potential losses. Experimental testing on the data of a smart home-type IoT network confirmed the effectiveness of the proposed model. A comparative analysis with classical approaches (ARIMA, LSTM, Isolation Forest) showed an increase in load prediction accuracy by 15% and an improvement in attack detection quality (F1-score) by 7-10%. The scientific novelty of the work is the synthesis of a graph-autoregressive model with risk-oriented optimization, which takes into account both spatial and temporal changes in the network and economic aspects of security management. The practical significance lies in the possibility of using the model as an analytical module in IoT monitoring and cybersecurity systems for automated selection of countermeasures in real time.</p>
      </abstract>
      <kwd-group>
        <kwd>Internet of Things (IoT)</kwd>
        <kwd>information security</kwd>
        <kwd>graph autoregressive model</kwd>
        <kwd>load forecasting</kwd>
        <kwd>anomaly detection</kwd>
        <kwd>risk-oriented management</kwd>
        <kwd>Conditional Value-at-Risk (CVaR)</kwd>
        <kwd>graph methods 1</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Over the past decades, the Internet of Things (IoT) technology has become an integral part of many
business processes in various fields - from household smart home systems to industrial complexes
and critical infrastructure [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. However, an increase in the number of devices and the complexity of
the IoT network topology is accompanied by an increase in the risk of information security (IS)
incidents [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. According to analytical agencies [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ], the number of active IoT devices will exceed 25
billion by 2030. And the amount of data generated by IoT devices will grow to several zettabytes per
year. That is, the exponential growth in the number of IoT devices is accompanied by a significant
complication of the network topology and an increase in inter-node interactions. As a result, this
will lead to an increased risk of information incidents.
      </p>
      <p>Unlike classical IT systems, the IoT environment has a much higher degree of heterogeneity. This
makes existing information security methods focused on centralized architectures ineffective.
Moreover, the large number of connected IoT network sensors and actuators has created new attack
vectors. These include remote control over nodes, data spoofing, distributed denial-of-service (DDoS)
attacks, the use of IoT devices in botnets, and more. As a result, IoT networks have become one of
the most vulnerable components of modern cyber-physical systems.</p>
      <p>
        It should be noted that most existing anomaly detection and monitoring systems for IoT networks
operate in a reactive mode. They only detect deviations after an incident has actually occurred. Such
solutions are based mainly on statistical indicators or fixed thresholds. That is, a priori, such solutions
reduce their effectiveness in using statistical indicators in the case of targeted low-intensity attacks
or changes in device behavior over time. At the same time, the development of machine learning
(ML) and time series analysis methods has opened up opportunities for the synthesis of flexible
hybrid models capable of predicting the future state of an IoT network and identifying potential
threats at the stage of their formation. It should be noted that most of the research in the field of IoT
device security is currently focused on time dependencies. These studies do not take into account
the spatial structure of the IoT network. Meanwhile, the interconnections between nodes
topological, informational, and behavioral - have a significant impact on the parameters of attacks.
For example, compromising a central router or a node with a high degree of centrality will lead to
an avalanche of threats to neighboring devices. Therefore, an integrated approach that combines
time series analysis, network graph structure, and information security indicators is a relevant topic
[
        <xref ref-type="bibr" rid="ref3 ref4">3, 4</xref>
        ].
      </p>
      <p>The issue of decision-making in cyber defense systems also requires special attention. In most
cases, the choice of countermeasures is made without taking into account the expected risks or
possible consequences for the quality of service (QoS). This can potentially lead to excessive resource
consumption, downtime, or even loss of communication between nodes. In this vein, it is advisable
to apply risk-oriented methods. These methods are able to take into account both the probability of
an attack and the potential damage in case of its realization. One of these criteria is Conditional
Value-at-Risk (CVaR). This indicator will allow to focus the protection strategy on the worst-case
scenarios with high losses, increasing the cyber resilience of the system. That is why it is relevant to
develop adaptive risk-oriented models that combine predicting the behavior of the IoT system with
threat detection and selecting optimal preventive actions to ensure network security.</p>
    </sec>
    <sec id="sec-2">
      <title>2. Problem statement</title>
      <p>Modern methods of load forecasting in IoT networks are mostly based on time series analysis, which
allows to model traffic dynamics and identify periodic patterns in the functioning of individual
devices. However, such approaches, despite their technical maturity, have a number of limitations
that significantly reduce their effectiveness in cybersecurity tasks for distributed infrastructures. The
main drawback is that most models focus exclusively on time dependencies and do not take into
account the spatial structure of the IoT network - its topology, the nature of connections between
nodes, the intensity of interaction, and the correlation of the behavior of individual devices. As a
result, the models ignore the interaction of nodes, which can be crucial when failures or attacks
spread across the network.</p>
      <p>Another significant limitation of classical approaches is the lack of mechanisms to take into
account information security policies and device behavior. In most existing traffic forecasting
systems, security factors are not integrated into the analytical core, but are treated as external
conditions. This leads to the fact that the breach detection system cannot timely differentiate
technical deviations from potentially malicious activity. In particular, even modern machine learning
algorithms used in the field of IoT monitoring do not always take into account events detected by
Intrusion Detection Systems (IDS) or Security Information and Event Management (SIEM) platforms.
As a result, the analytical system is unable to synthesize a holistic picture of network security and
correctly assess the likelihood of cyberattacks.</p>
      <p>Another critical aspect is the limitations of existing anomaly detection methods, which mostly
rely only on statistical analysis of deviations in traffic or device behavior from the average. While
such approaches can identify individual atypical events, they do not provide sufficient contextual
depth to detect complex, multi-stage attacks that propagate through interconnected network nodes.
As a result, the system responds to incidents mostly after the fact, when the damage has already been
done and the ability to prevent or localize threats is limited.</p>
      <p>The lack of integrated risk-oriented decision-making mechanisms is another significant problem
with modern IoT cybersecurity systems. The vast majority of existing solutions focus on recording
attacks or breaches, but do not include components capable of quantitatively assessing the risk of
their occurrence or predicting potential losses. In such conditions, security administrators are unable
to strategically plan actions to minimize losses or prioritize responses. In particular, the lack of
formalized models based on criteria such as CVaR makes it impossible to assess worst-case scenarios,
which is especially dangerous for systems with critical resources and limited computing power.</p>
      <p>Together, these factors form a scientific and practical problem, which is the lack of a
comprehensive model capable of simultaneously predicting load, detecting anomalies, and assessing
the risk of attacks, taking into account the topological and behavioral characteristics of IoT networks.
Solving this problem requires the integration of machine learning, graph analysis, and risk theory
methods into a single analytical system focused on adaptive cyber defense management in dynamic,
distributed Internet of Things environments.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Literature review</title>
      <p>
        Analyzing cyberattacks on IoT networks and developing effective methods for detecting them is one
of the most relevant issues in the field of cybersecurity. Existing research is mostly focused on the
use of machine learning (ML) methods to detect anomalies and cyber threats. In particular, the
authors of [
        <xref ref-type="bibr" rid="ref5 ref6 ref7">5, 6, 7</xref>
        ] conducted a comparative analysis of various ML methods for detecting anomalies
in cyberattacks on IoT networks. A broader overview of modern approaches based on ML, including
their analysis and prospects, is presented in [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ].
      </p>
      <p>
        A number of studies focus on the development of specific models and approaches. For example,
in [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ], the authors proposed a hybrid deep neural network for detecting attacks in industrial IoT. In
[
        <xref ref-type="bibr" rid="ref10">10</xref>
        ], the authors discussed the use of ML to identify attacks in smart IoT networks. At the same time,
an important step in this process is feature engineering, which is studied in [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ]. Ensemble
learningbased methods, such as the voting approach, have also been used to detect cyberattacks in industrial
IoT [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ].
      </p>
      <p>
        As the analysis of previous publications has shown, most applied research focuses on the use of
machine learning algorithms for classification and anomaly detection, including the following works:
Inuwa M. M. and Das R. [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]; Alanazi M., Aljuhani A. [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]; Inayat U. and Zia M. et al. [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]; These authors
investigated the advantages of individual methods, such as SVM, Isolation Forest, LSTM,
autoencoders for detection tasks. However, these works did not investigate the spatial relationships
between nodes. And the "node-by-node" approach does not take into account how the compromise
of one element of the IoT network will affect the adjacent ones.
      </p>
      <p>
        On the other hand, publications in recent years have demonstrated a clear shift to graph-based
methods. In several papers, such as [
        <xref ref-type="bibr" rid="ref5 ref6">5, 6</xref>
        ], the authors used Graph Neural Networks (GNNs) or graph
regularizers in the task of attack detection and network traffic forecasting. Although this has
improved the quality of modeling inter-node impacts, it is not possible to detect atypical behavior in
an IoT network using GNNs alone.
      </p>
      <p>
        A separate area of research is publications containing models based on autoregression and their
extension for graphs. Classical AR/ARIMA models work well for one-dimensional time series, but do
not take into account topology. Instead, recent methods and models to "graph-autoregressive" or AR
for sequences of graphs allow to formalize both temporal and spatial dependencies [
        <xref ref-type="bibr" rid="ref13 ref14 ref15 ref16">13-16</xref>
        ].
      </p>
      <p>
        Another important component is risk-oriented decision-making. VaR and CVaR metrics have long
been used in financial and operational risk management [
        <xref ref-type="bibr" rid="ref14 ref15 ref16">14-16</xref>
        ]. Such models have been actively
used in cybersecurity to optimize security resources and focus on worst-case scenarios. Studies [
        <xref ref-type="bibr" rid="ref15 ref16 ref17">15,
16, 17</xref>
        ] on the use of CVaR in cyber risks have shown that this approach allows formalizing the choice
of countermeasures, taking into account the probability of large losses and uncertainty of the
attacker's behavior. Integration of CVaR into decision-making modules makes the system more
conservative with respect to catastrophic events and minimizes expected losses.
      </p>
      <p>
        Finally, it is important to consider data dynamics. It is the behavior of IoT devices and traffic profiles
that change over time. In recent years, online algorithms and ensemble approaches have emerged
that have adapted to drift and allowed to maintain the quality of detecting atypical behavior in
streaming data. This is typical of recent work on online attack detection for IoT [
        <xref ref-type="bibr" rid="ref17 ref18 ref19 ref20 ref21 ref22">17-22</xref>
        ]. These studies
apply weighted update mechanisms. The combination of graph representation, online learning, and
a risk-oriented optimizer is an unexplored but, in our opinion, promising area. That is why the
proposed work is focused on it. Thus, despite significant advances, most existing approaches do not
fully take into account the spatial and temporal dependencies between network nodes and IoT, as
well as rare but costly threats. That is why new research in this area is relevant.
      </p>
    </sec>
    <sec id="sec-4">
      <title>4. The purpose of the study</title>
      <p>The purpose of this study is to create and substantiate a mathematical model for load forecasting and
incident detection in IoT networks with the subsequent formation of a system of optimal
management actions based on a risk-oriented approach. The use of the CVaR criterion as a basis for
decision-making allows not only to estimate expected losses but also to model the impact of extreme,
rare, but potentially catastrophic events, which significantly increases the level of cyber resilience of
IoT infrastructures.</p>
      <p>Thus, the study is aimed at developing a comprehensive analytical tool capable of integrating
temporal, spatial, and behavioral aspects of IoT networks in order to timely predict traffic anomalies
and prevent critical disruptions in their operation. To achieve this goal, it is necessary to solve a
number of interrelated scientific and applied tasks:
• improvement of the graph-autoregressive load forecasting model, which would take into
account both the temporal patterns of traffic changes and the spatial relationships between
individual IoT network nodes. This combination makes it possible to describe not only local
dependencies, but also global correlations between devices operating within a single digital
environment.
• integration of behavioral and network indicators of information security into the model,
which are necessary to quantify the probability of attacks on IoT network nodes. This
involves building a weighted loss function that takes into account the criticality of nodes,
their role in the overall system topology, and the statistical rarity of attacks. This approach
is designed to strike a balance between the accuracy of load forecasting and the effectiveness
of information security incident detection, which will simultaneously optimize both network
resources and the process of responding to potential threats.
• development of a decision-making module that will use Conditional Value-at-Risk as an
optimization criterion in the process of assessing and minimizing loss risks. The use of CVaR
in this context enables the system to respond adaptively to changing threat levels, paying
particular attention to scenarios with high potential for harm but low probability of
occurrence. Thus, the module will contribute to the implementation of the principles of
adaptive security management and the formation of strategies aimed at minimizing both
direct and indirect consequences of cyberattacks.</p>
      <p>Together, these tasks form a comprehensive research concept that combines elements of
mathematical modeling, risk theory, and cybernetic control within a single analytical architecture.
Implementation of the proposed methodology makes it possible to increase the efficiency of IoT
where V = 1,..., Nis the set of nodes in the IoT network;  t is the set of edges at time t; W  RNN
t +
is the matrix of link weights (for an IoT network, these are bandwidth, delay, reliability, etc.).</p>
      <p>For the node v V at time t, we enter the following parameters:
load vector y1(v) = ( yt(,v1) ,..., yt(,vd)y )  Rdy , where dy is the number of IoT network load metrics;
vector of exogenous security indicators of the IoT network x1(v) = ( xt(,v1) ,..., xt(,vd)y )  Rdx , where d x
is the number of IS indicators (atypical IPs, port entropy, authentication errors, etc.);
attack label at(v) 0,1, a1(v) = 1  IoT network node compromised.</p>
      <p>coefficient matrices; p
where yt is IoT network load; xt</p>
      <p>Then we use a graph-autoregressive model to predict the load:</p>
      <p>p q
yˆt+1 =  Al  yt−1 + Bl  xt−1 −t  Lt  yt ,
l=1 l=0</p>
      <p>IS indicators; Lt = Dt −Wt is Laplacian of the graph (1); Al , Bl
memory depth of load time series (AR part); q
memory depth of
exogenous features; t</p>
      <p>regularization matrix.</p>
      <sec id="sec-4-1">
        <title>Then the level of anomalies in the node v is given as follows:</title>
        <p>
          st(+v1) = (rt(+v1) ) t(v)−1rt(v) , rt+1 = rt+1 − yˆt+1, ,
where rt(v) is the threshold obtained from the theory of extreme values [
          <xref ref-type="bibr" rid="ref5">5</xref>
          ]; t(v) is the covariance
matrix of residuals estimated on a sliding window of time until the moment t for node v .
        </p>
        <p>We assume that the feature vector t(+v1) includes anomalies, IoT network security indicators, and
aggregated neighborhood metrics. Then we estimate the probability of an attack by logistic
regression (4):
network monitoring systems, reduce the likelihood of failures, and ensure the stable functioning of
critical components in the dynamic and unpredictable conditions of the information environment.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Model for predicting and detecting incidents in an IoT network</title>
      <sec id="sec-5-1">
        <title>Let the topology of the IoT network at time t be described by a graph</title>
        <p>
          Gt = (V , t ,Wt ) ,
 t(+v1) =  ( wt(+v1) ) ,  ( z ) =
where  t(+v1) 0,1 is the probability of an attack on node v at time t+1; t(+v1) is the feature vector of
node v at time t+1;  ( z ) is a sigmoid activation function that converts a linear combination of
features wt(+v1) into a probability in the range [
          <xref ref-type="bibr" rid="ref1">0,1</xref>
          ].
        </p>
        <p>Thus, equation (4) reflects a fundamentally important approach to assessing the risk of an attack
on an IoT network node. The probability of compromising a particular node is determined not only
by the level of anomalies in its own behavior, i.e., deviations from typical activity patterns, but also
by the broader context of network interaction. This means that the modeling process includes
additional information security (IS) indicators, such as query frequency, data exchange intensity,
delay indicators, communication channel stability, and information about the behavior of the nearest
neighbors in the network topological graph. This approach provides a more complete reflection of
the interdependencies between nodes, which allows for the effects of "chain reactions" or "cascading
failures" that are typical in many IoT environments.
(1)
(2)
(3)
(4)</p>
        <p>Using logistic regression as a basic method to estimate the probability of an attack has the added
benefit of making the results interpretable. The model coefficients can be viewed as weights that
characterize the contribution of each indicator to the overall risk. This makes it possible not only to
predict the probability of an incident, but also to explain analytically which parameters (for example,
increased latency, increased traffic, or decreased regularity of interaction) are critical to the current
state of security. In this way, the model becomes not just an assessment tool, but a means of
intelligent decision support in IoT cybersecurity systems.</p>
        <p>It should be emphasized that the above submodels - load forecasting (2), anomaly detection (3),
and attack probability assessment (4) - are not isolated components but rather an interconnected
three-tiered system in which each level enhances the accuracy and reliability of the other. However,
for their effective integration, it is necessary to agree on optimization criteria that will ensure the
unity of functioning of the entire model architecture. This problem is solved by formalizing a single
loss function.</p>
        <p>The loss function (5) is a generalized optimization criterion that simultaneously takes into account
three key security aspects: load forecasting accuracy, attack classification quality, and coherence
(consistency) of forecasts between adjacent nodes in the graph. This approach minimizes not only
local errors in the behavior of individual nodes, but also global inconsistencies in the structure of
network interaction, which is especially important for distributed IoT systems with a large number
of loosely connected components.</p>
        <p>Additionally, a regularization term was introduced into the loss function to control the model
complexity. This solution ensures resistance to overfitting, avoids overfitting to the specifics of
individual nodes, and guarantees the generalizability of the model on new data samples.
Regularization also serves as a stabilizer of the learning process, which is especially important when
working with large, heterogeneous IoT data sets with high noise and lack of complete labeling.</p>
        <p>Thus, the integration of the three submodels within a joint optimization approach forms a
coherent analytical framework in which forecasting, detection, and risk assessment function as a
single system. As a result, the general problem statement takes on a form that allows describing the
entire process of managing the security of an IoT network in terms of a single risk function optimized
in accordance with the CVaR principles. This opens up opportunities for further automation of
monitoring processes, adaptive learning, and strategic decision-making in the field of cybersecurity
of distributed infrastructures.</p>
        <p>min () Lpred +det  Ldet +graph graph +reg  2 ,
 2
(5)
where Lpred is the Huber loss; Ldet is the cross-entropy; graph is graph regularisation;  2 is the
2
L2- norm of the model parameter vector  ; det  0 is the balance between the task of predicting
and detecting attacks;</p>
        <p>graph  0 is the influence coefficient of graph regularisation; reg  0 is the regularisation
parameter for checking the model complexity.</p>
        <p>Note that even accurate load forecasting and correct assessment of the probability of an attack on
an IoT network is not the ultimate goal of the model. Therefore, let's move on to the procedure of
forming management decisions that minimise expected losses. Such decisions depend not only on
the estimated probability of an attack. They also depend on the potential losses in the event of an IS
incident, the costs of preventive actions, and penalties for degradation of quality of service (QoS). In
other words, it allows us to choose a protection strategy. We consider this an optimization task,
taking into account economic and service factors. The corresponding cost function for the node is
as follows. For the selected action ut(+v1) :</p>
        <p>Cos tt(v) (u ) =  t(+v1)ci(nvc) + ca(vct) (u ) + QoS  SLA(pve)nalty (u ) ,
where ci(nvc) is the potential damage of an IS incident at node v ;  t(+v1) is the predicted probability of
(6)
the penalty for QoS; SLA(pve)nalty is the QoS penalty for node v .</p>
        <p>The value function formulated in (6) allowed us to estimate the expected costs for different
options for the IoT network protection system. However, it should be no ted that rare but
catastrophic incidents should also be taken into account. In this case, the average costs do not reflect
the real risk. To this end, we use Conditional Value-at-Risk (CVaR) as a criterion for the optimal
solution. This allows us to focus the model on the worst-case scenarios with high IoT network
restoration costs. Thus, the choice of action for the node at time is formalised as follows:
ut(+v1) = arg min CVaR (Cos tt(v) (u)) ,</p>
        <p>uU
where  (0,1) is the level of trust; CVaR
scenarios.</p>
        <p>Network behavior and the nature of attacks change over time. Therefore, the model requires
regular updating of parameters  based on new data, with the gradual "forgetting" of outdated
information. To do this, we use a stochastic gradient descent with a forgetting factor. This allows us
to strike a balance between stability and speed of adjustment:</p>
        <p>t+1 = t −Lotnline + forget (t − t−1 ),
where t is the vector of model parameters (autoregression coefficients, logistic regression weights,
regularisation parameters, etc.) at time t ;   0 is the learning rate; Lonline is the loss function
t
calculated on the last mini-batch of data at time t;  Lonline is the gradient of the loss function
 t
relative to the parameters t ;  forget  (0,1) is the coefficient of reducing the influence of old
observations.</p>
        <p>That is, expression (8) describes the real-time update of the model. New data affect the parameters
through the gradient  Lonline . And the coefficient  forget gradually reduces the weight of old
 t
observations so that the model remains relevant when the IoT network changes.</p>
        <p>Figure 1 shows a conceptual diagram of the model for detecting and predicting attacks in IoT
networks.</p>
        <p>Below is also a pseudo-code structure to illustrate the model. This pseudo-code details the main
stages and logic of the proposed model. According to the model, it contains several interconnected
stages. These are load forecasting, attack probability assessment, and decision making.
// Input:
// G = (V, E, W): IoT network graph, where V are nodes, E are edges, W is adjacency matrix.
// Y_hist: Historical load vectors for each node.
// X_hist: Historical exogenous security indicator vectors for each node.
// U: Set of possible protective actions.
// alpha: Confidence level for CVaR.
// Hyperparameters for loss function and forgetting.
// Output:
// u_t+1: Optimal protective action for each node at time t+1.
// Stage 1: Load Forecasting and Anomaly Detection
function ForecastAndDetect(G_t, Y_t, X_t):
// 1.1 Calculate Graph Laplacian
L_t = D_t - W_t // D_t is the degree matrix
// 1.2 Forecast next-step load using the graph-autoregressive model
// Equation (2)
y_hat_t+1 = sum(A_l * y_t-l) for l=1 to p + sum(B_l * x_t-l) for l=0 to q - Gamma_t * L_t * y_t
⋅100% attack
(7)
(8)
// 1.3 Calculate the anomaly score
// Equation (3)
for each node v in V:
r_t+1_v = y_t+1_v - y_hat_t+1_v</p>
        <p>S_t+1_v = (r_t+1_v)^T * (Sigma_t_v)^-1 * r_t+1_v
return y_hat_t+1, S_t+1
// Stage 2: Attack Probability Assessment
function AssessAttackProbability(y_hat_t+1, S_t+1, X_t, neighbors_data):
// 2.1 Construct feature vector phi_t+1
// Feature vector includes anomaly scores, security indicators, and aggregated neighbor
metrics.</p>
        <p>for each node v in V:</p>
        <p>phi_t+1_v = concat(S_t+1_v, X_t_v, aggregate(neighbors_data))
// 2.2 Estimate attack probability using logistic regression
// Equation (4)
for each node v in V:</p>
        <p>pi_t+1_v = sigma(w^T * phi_t+1_v)
return pi_t+1
// Stage 3: Model Optimization
function OptimizeModel(Y_hist, X_hist, pi_t+1):
// 3.1 Define the weighted loss function
// Combines prediction accuracy, classification quality, and graph consistency
// Equation (5)
L_pred = HuberLoss(y_t+1, y_hat_t+1)
L_det = CrossEntropy(a_t+1, pi_t+1)
R_graph = GraphRegularization(...)
Regularizer = ||Theta||_2^2
L_total = L_pred + lambda_det * L_det + lambda_graph * R_graph + lambda_reg * Regularizer
// 3.2 Update model parameters using online learning with a forgetting factor
// Equation (8)</p>
        <p>Theta_t+1 = Theta_t - Theta * gradient(L_online_t, Theta_t) + lambda_forget * (Theta_t -
Theta_t1)
infrastructure - a router, a video surveillance camera, a door lock, a garage door.</p>
        <p>For each node, a dataset was taken containing load time series with a duration of 50 steps. These
cycles reflected the periodic operation of the devices, as well as occasional anomalies. The anomalies
were garage door opening, smoke detector triggering, etc. Key network nodes, such as the router
and the video surveillance camera, are described in the initial dataset as having a stable background
load with a few random fluctuations. The experimental setup included three stages: 1. Prediction of
the load using a graphical autoregressive model that takes into account spatial and temporal
dependencies. 2. Detection of anomalies based on the forecast residuals, followed by estimation of
the Mahalanobis distance and application of adaptive thresholds. 3. Assessment of the probability of
an attack and decision-making using the integration of IS indicators and a management module based
on the Conditional Value-at-Risk (CVaR) criteria, see expression (7).
of anomalies, deep LSTM method for time series.</p>
        <p>MAE (mean absolute error of the forecast) and F1-score (quality of attack detection) were used as
metrics for comparison. The comparison results are presented in Table 1.</p>
        <p>According to the comparative analysis, the proposed method showed an improvement in the
quality of load forecasting by about 15%. The accuracy of attack detection increased by 7-10%
compared to existing methods. Thus, the comparison of the model with others confirmed the
feasibility of simultaneously taking into account spatial and temporal dependencies and risk-oriented
optimization based on CVaR.</p>
      </sec>
    </sec>
    <sec id="sec-6">
      <title>6. Discussion of research results</title>
      <p>The results of the computational experiment (Fig. 2) convincingly prove the effectiveness and
functional viability of the proposed model. During the analysis of time series, it was found that the
model correctly describes both stable background processes characteristic of constantly active
devices (in particular, a network router or video surveillance system) and periodic, cyclical patterns
of behavior of household devices, such as a thermostat or refrigerator. The high accuracy of modeling
these patterns confirmed that the developed approach is capable of reproducing the real dynamic
processes inherent in heterogeneous IoT networks.</p>
      <p>The use of a risk-oriented concept based on the Conditional Value-at-Risk (CVaR) indicator has
made it possible to expand the classical risk assessment paradigm. This approach takes into account
not only the average expected losses, but also the probability of the most critical attack scenarios on
the network infrastructure. This provides a more realistic modeling of the potential consequences
of cyberattacks and forms the basis for making informed decisions in security systems aimed at
minimizing losses in the worst possible conditions.</p>
      <p>Despite the overall effectiveness of the model, the experiment revealed a number of
methodological limitations. First, the use of a linear graph autoregressive structure limits the model's
ability to represent complex nonlinear relationships between network nodes. This reduces the
accuracy of predictions in situations where traffic is chaotic or stochastic in nature. Second, the
current stage of the study did not take into account the real attributes of network traffic, such as
packet types, protocol features, and delay metrics. Including such characteristics in future work
could significantly increase the model's informativeness. Third, to increase the model's applied
reliability, it needs to be tested on large open or corporate datasets containing real attack labels,
including DDoS, port scanning, or malware injection scenarios.</p>
      <p>The scientific novelty of the study lies in several key aspects. First, the graph autoregressive
model for forecasting load in IoT networks has been improved, allowing simultaneous consideration
of traffic time dependencies and spatial correlations between nodes through the graph Laplacian.
This integration has made it possible to adequately describe the interdependent behavior of network
elements, identify cross-correlation effects, and improve the accuracy of short-term forecasts.</p>
      <p>Second, a method has been developed for integrating behavioral and network indicators of
information security into the process of assessing the probability of an attack. Unlike classical
models, a weighted loss function is proposed that takes into account the criticality of nodes and the
frequency of abnormal events. This approach provides a flexible balance between load prediction
accuracy and cyber incident detection quality, which is especially important for
resourceconstrained IoT systems.</p>
      <p>Third, a decision-making module based on the Conditional Value-at-Risk risk criterion has been
implemented. This component allows for the consideration of not only average scenarios, but also
extreme scenarios. The use of CVaR makes it possible to adapt the threat response process to real
conditions of high uncertainty, providing an additional level of resilience for IoT networks against
rare but potentially catastrophic attacks.</p>
      <p>The practical value of this research lies in the creation of a prototype analytical tool that can be
integrated into IoT network monitoring systems for early detection of information security incidents
and prediction of peak loads during attacks. The proposed implementation allows automating the
threat detection process, increasing the efficiency of computing resources, and reducing the system's
response time to potential incidents.</p>
      <p>The CVaR-based decision-making software module deserves special attention. It can be
integrated into IoT cyber defense systems for automated selection of the optimal threat response
strategy. This minimizes financial losses, reduces service downtime, and increases network
continuity even in the event of complex attacks.</p>
      <p>In the future, the model is expected to be integrated into automated IoT cybersecurity
management systems. The research results can be used to enhance the functionality of modern
Security Information and Event Management (SIEM) systems that process telemetry data streams in
real time. Integrating the proposed solutions into such platforms will improve the accuracy of event
classification, reduce the number of false alerts, and improve the overall analytical transparency of
monitoring processes.</p>
    </sec>
    <sec id="sec-7">
      <title>7. Conclusions</title>
      <p>In the course of the study, a model for load forecasting and incident detection in IoT networks based
on the integration of temporal and spatial traffic characteristics was developed and tested. The
proposed approach provides a new level of analytical depth, as it allows simultaneously taking into
account the behavioral patterns of nodes, their interconnections in the graph structure of the
network, and the temporal dynamics of events. The results of the experimental modeling showed
the system's ability to correctly reproduce both background stable processes and cyclic patterns of
household IoT devices, as well as to effectively record deviations that may indicate potential
cyberattacks.</p>
      <p>The use of the Conditional Value-at-Risk (CVaR) criterion in the decision-making module made
it possible to shift the focus from average risk assessments to the analysis of unlikely but critically
dangerous scenarios. This approach enhances the system's ability to respond in advance to events
that could lead to significant financial or operational losses, thereby strengthening the resilience of
the network infrastructure to extreme impacts.</p>
      <p>It has been confirmed that the integration of graph and autoregressive model components
improves the accuracy of forecasting in environments with a high level of traffic heterogeneity,
which is inherent in most IoT systems. This combination allows modeling not only direct but also
indirect connections between nodes, reflecting complex topological and behavioral patterns of the
network.</p>
      <p>An additional scientific result is the development of a weighted loss function that takes into
account the importance of each node and the frequency of certain types of attacks. This strikes a
balance between the priority of threat detection and the need to maintain network efficiency in
normal operation. Thus, the model can be adapted to various use cases, from home smart networks
to industrial IoT segments. The practical significance of the results is manifested in the possibility
of implementing the prototype analytical module in existing IoT network monitoring systems. This
will not only increase the level of situational awareness but also ensure automated decision-making
in real time. The introduction of the CVaR module into cybersecurity systems opens up prospects
for building adaptive response strategies that can minimize the consequences of attacks even in the
event of unpredictability.</p>
      <p>Prospects for further research are to extend the model by taking into account the full attributes
of traffic, including protocol characteristics, packet size, and time delays. In addition, an important
area of future work is the use of deep learning methods to model nonlinear dependencies between
node behavior and incident development. Significant attention will be paid to scalability issues, i.e.,
testing the model's performance on large industrial datasets and in real environments where data
volumes are growing exponentially.</p>
      <p>Equally relevant is the issue of integrating the developed model into SIEM ecosystems. This
approach will combine the model's analytical capabilities with existing mechanisms for collecting
and correlating security events. This will create the basis for the formation of new generations of
intelligent risk management systems that will provide not only reactive but also proactive
management of cyber threats in IoT environments. Thus, the results obtained form a scientific and
practical basis for the further development of adaptive decision support systems in the field of cyber
defense. The proposed model can become the basis for creating a universal analytical core that will
provide high accuracy of anomaly detection, the ability to predict their development and make
effective decisions in complex dynamic IoT environments.</p>
    </sec>
    <sec id="sec-8">
      <title>Declaration on Generative AI</title>
      <p>The authors have not employed any Generative AI tools.</p>
    </sec>
  </body>
  <back>
    <ref-list>
      <ref id="ref1">
        <mixed-citation>
          [1]
          <string-name>
            <surname>Rath</surname>
            ,
            <given-names>K. C.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Khang</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Roy</surname>
            ,
            <given-names>D.</given-names>
          </string-name>
          (
          <year>2024</year>
          ).
          <article-title>The role of Internet of Things (IoT) technology in Industry 4.0 economy. In Advanced IoT technologies and applications in the industry 4.0 digital economy</article-title>
          (pp.
          <fpage>1</fpage>
          -
          <lpage>28</lpage>
          ). CRC Press.
        </mixed-citation>
      </ref>
      <ref id="ref2">
        <mixed-citation>
          [2]
          <string-name>
            <surname>Raimundo</surname>
            ,
            <given-names>R. J.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Rosário</surname>
            ,
            <given-names>A. T.</given-names>
          </string-name>
          (
          <year>2022</year>
          ).
          <article-title>Cybersecurity in the internet of things in industrial management</article-title>
          .
          <source>Applied Sciences</source>
          ,
          <volume>12</volume>
          (
          <issue>3</issue>
          ),
          <fpage>1598</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref3">
        <mixed-citation>
          [3]
          <string-name>
            <surname>Lone</surname>
            ,
            <given-names>A. N.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Mustajab</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Alam</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          (
          <year>2023</year>
          ).
          <article-title>A comprehensive study on cybersecurity challenges and opportunities in the IoT world</article-title>
          .
          <source>Security and Privacy</source>
          ,
          <volume>6</volume>
          (
          <issue>6</issue>
          ),
          <year>e318</year>
          .
        </mixed-citation>
      </ref>
      <ref id="ref4">
        <mixed-citation>
          [4]
          <string-name>
            <surname>Prince</surname>
            ,
            <given-names>N. U.</given-names>
          </string-name>
          , Al Mamun,
          <string-name>
            <given-names>M. A.</given-names>
            ,
            <surname>Olajide</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A. O.</given-names>
            ,
            <surname>Khan</surname>
          </string-name>
          ,
          <string-name>
            <given-names>O. U.</given-names>
            ,
            <surname>Akeem</surname>
          </string-name>
          ,
          <string-name>
            <given-names>A. B.</given-names>
            , &amp;
            <surname>Sani</surname>
          </string-name>
          ,
          <string-name>
            <surname>A. I.</surname>
          </string-name>
          (
          <year>2024</year>
          ).
          <article-title>IEEE Standards and Deep Learning Techniques for Securing Internet of Things (IoT) Devices Against Cyber Attacks</article-title>
          .
          <source>Journal of Computational Analysis &amp; Applications</source>
          ,
          <volume>33</volume>
          (
          <issue>7</issue>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref5">
        <mixed-citation>
          [5]
          <string-name>
            <surname>Inuwa</surname>
            ,
            <given-names>M. M.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Das</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          (
          <year>2024</year>
          ).
          <article-title>A comparative analysis of various machine learning methods for anomaly detection in cyber attacks on IoT networks</article-title>
          .
          <source>Internet of Things</source>
          ,
          <volume>26</volume>
          ,
          <fpage>101162</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref6">
        <mixed-citation>
          [6]
          <string-name>
            <surname>Alanazi</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Aljuhani</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          (
          <year>2022</year>
          ).
          <article-title>Anomaly Detection for Internet of Things Cyberattacks</article-title>
          . Computers, Materials &amp; Continua,
          <volume>72</volume>
          (
          <issue>1</issue>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref7">
        <mixed-citation>
          [7]
          <string-name>
            <surname>Singh</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Sharma</surname>
            ,
            <given-names>P. K.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Park</surname>
            ,
            <given-names>J. H.</given-names>
          </string-name>
          (
          <year>2023</year>
          ).
          <article-title>Blockchain-based lightweight security framework for IoT-enabled industrial networks</article-title>
          .
          <source>IEEE Internet of Things Journal</source>
          ,
          <volume>10</volume>
          (
          <issue>4</issue>
          ), 3021
          <fpage>3034</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref8">
        <mixed-citation>
          [8]
          <string-name>
            <surname>Inayat</surname>
            ,
            <given-names>U.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Zia</surname>
            ,
            <given-names>M. F.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Mahmood</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Khalid</surname>
            ,
            <given-names>H. M.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Benbouzid</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          (
          <year>2022</year>
          ).
          <article-title>Learning-based methods for cyber attacks detection in IoT systems: A survey on methods, analysis, and future prospects</article-title>
          .
          <source>Electronics</source>
          ,
          <volume>11</volume>
          (
          <issue>9</issue>
          ),
          <fpage>1502</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref9">
        <mixed-citation>
          [9]
          <string-name>
            <surname>Huma</surname>
            ,
            <given-names>Z. E.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Latif</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Ahmad</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Idrees</surname>
            ,
            <given-names>Z.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Ibrar</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Zou</surname>
            ,
            <given-names>Z.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Baothman</surname>
            ,
            <given-names>F.</given-names>
          </string-name>
          (
          <year>2021</year>
          ).
          <article-title>A hybrid deep random neural network for cyberattack detection in the industrial internet of things</article-title>
          .
          <source>IEEE access</source>
          ,
          <volume>9</volume>
          ,
          <fpage>55595</fpage>
          -
          <lpage>55605</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref10">
        <mixed-citation>
          [10]
          <string-name>
            <surname>Malathi</surname>
            ,
            <given-names>C.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Padmaja</surname>
            ,
            <given-names>I. N.</given-names>
          </string-name>
          (
          <year>2023</year>
          ).
          <article-title>Identification of cyber attacks using machine learning in smart IoT networks</article-title>
          .
          <source>Materials Today: Proceedings</source>
          ,
          <volume>80</volume>
          ,
          <fpage>2518</fpage>
          -
          <lpage>2523</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref11">
        <mixed-citation>
          [11]
          <string-name>
            <surname>Dissanayake</surname>
            ,
            <given-names>M. B.</given-names>
          </string-name>
          (
          <year>2021</year>
          ).
          <article-title>Feature Engineering for Cyber-attack detection in Internet of Things</article-title>
          .
          <source>International Journal of wireless and microwave technologies</source>
          ,
          <volume>11</volume>
          (
          <issue>6</issue>
          ),
          <fpage>46</fpage>
          -
          <lpage>54</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref12">
        <mixed-citation>
          [12]
          <string-name>
            <surname>Golchha</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Joshi</surname>
            ,
            <given-names>A.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Gupta</surname>
            ,
            <given-names>G. P.</given-names>
          </string-name>
          (
          <year>2023</year>
          ).
          <article-title>Voting-based ensemble learning approach for cyber attacks detection in industrial internet of things</article-title>
          .
          <source>Procedia Computer Science</source>
          ,
          <volume>218</volume>
          ,
          <fpage>1752</fpage>
          -
          <lpage>1759</lpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref13">
        <mixed-citation>
          [13]
          <string-name>
            <surname>Jiang</surname>
            ,
            <given-names>W.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Luo</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>He</surname>
            ,
            <given-names>M.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Gu</surname>
            ,
            <given-names>W.</given-names>
          </string-name>
          (
          <year>2023</year>
          ).
          <article-title>Graph neural network for traffic forecasting: The research progress</article-title>
          .
          <source>ISPRS International Journal of Geo-Information</source>
          ,
          <volume>12</volume>
          (
          <issue>3</issue>
          ),
          <fpage>100</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref14">
        <mixed-citation>
          [14]
          <string-name>
            <surname>Sun</surname>
            ,
            <given-names>Z.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Teixeira</surname>
            ,
            <given-names>A. M.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Toor</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          (
          <year>2024</year>
          ,
          <article-title>July)</article-title>
          .
          <article-title>GNN-IDS: Graph neural network based intrusion detection system</article-title>
          .
          <source>In Proceedings of the 19th international conference on availability, reliability and security</source>
          (pp.
          <fpage>1</fpage>
          -
          <lpage>12</lpage>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref15">
        <mixed-citation>
          [15]
          <string-name>
            <surname>Lin</surname>
            ,
            <given-names>L.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Zhong</surname>
            ,
            <given-names>Q.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Qiu</surname>
            ,
            <given-names>J.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Liang</surname>
            ,
            <given-names>Z.</given-names>
          </string-name>
          (
          <year>2025</year>
          ).
          <article-title>E-GRACL: an IoT intrusion detection system based on graph neural networks</article-title>
          .
          <source>The Journal of Supercomputing</source>
          ,
          <volume>81</volume>
          (
          <issue>1</issue>
          ),
          <fpage>42</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref16">
        <mixed-citation>
          [16]
          <string-name>
            <surname>Zambon</surname>
            ,
            <given-names>D.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Grattarola</surname>
            ,
            <given-names>D.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Livi</surname>
            ,
            <given-names>L.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Alippi</surname>
            ,
            <given-names>C.</given-names>
          </string-name>
          (
          <year>2019</year>
          ,
          <article-title>July)</article-title>
          .
          <article-title>Autoregressive models for sequences of graphs</article-title>
          .
          <source>In 2019 International Joint Conference on Neural Networks (IJCNN)</source>
          (pp.
          <fpage>1</fpage>
          -
          <lpage>8</lpage>
          ). IEEE.
        </mixed-citation>
      </ref>
      <ref id="ref17">
        <mixed-citation>
          [17]
          <string-name>
            <surname>Franco</surname>
            ,
            <given-names>M. F.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Künzler</surname>
            ,
            <given-names>F.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Von der Assen</surname>
          </string-name>
          , J.,
          <string-name>
            <surname>Feng</surname>
            ,
            <given-names>C.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Stiller</surname>
            ,
            <given-names>B.</given-names>
          </string-name>
          (
          <year>2024</year>
          ).
          <article-title>RCVaR: An economic approach to estimate cyberattacks costs using data from industry reports</article-title>
          .
          <source>Computers &amp; Security</source>
          ,
          <volume>139</volume>
          ,
          <fpage>103737</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref18">
        <mixed-citation>
          [18]
          <string-name>
            <surname>Yoon</surname>
            ,
            <given-names>S.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Lee</surname>
            ,
            <given-names>Y.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Lee</surname>
            ,
            <given-names>J. G.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Lee</surname>
            ,
            <given-names>B. S.</given-names>
          </string-name>
          (
          <year>2022</year>
          ,
          <article-title>August)</article-title>
          .
          <article-title>Adaptive model pooling for online deep anomaly detection from a complex evolving data stream</article-title>
          .
          <source>In Proceedings of the 28th ACM SIGKDD conference on knowledge discovery and data mining</source>
          (pp.
          <fpage>2347</fpage>
          -
          <lpage>2357</lpage>
          ).
        </mixed-citation>
      </ref>
      <ref id="ref19">
        <mixed-citation>
          [19]
          <string-name>
            <surname>Hu</surname>
            ,
            <given-names>Z.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Yu</surname>
            ,
            <given-names>X.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Liu</surname>
            ,
            <given-names>L.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Zhang</surname>
            ,
            <given-names>Y.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Yu</surname>
            ,
            <given-names>H.</given-names>
          </string-name>
          (
          <year>2024</year>
          ).
          <article-title>ASOD: an adaptive stream outlier detection method using online strategy</article-title>
          .
          <source>Journal of Cloud Computing</source>
          ,
          <volume>13</volume>
          (
          <issue>1</issue>
          ),
          <fpage>120</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref20">
        <mixed-citation>
          [20]
          <string-name>
            <surname>Wang</surname>
            ,
            <given-names>R.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Qiu</surname>
            , H., Cheng,
            <given-names>X.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Liu</surname>
            ,
            <given-names>X.</given-names>
          </string-name>
          (
          <year>2023</year>
          ).
          <article-title>Anomaly detection with a container-based stream processing framework for industrial internet of things</article-title>
          .
          <source>Journal of Industrial Information Integration</source>
          ,
          <volume>35</volume>
          ,
          <fpage>100507</fpage>
          .
        </mixed-citation>
      </ref>
      <ref id="ref21">
        <mixed-citation>
          [21]
          <string-name>
            <surname>Ngo</surname>
            ,
            <given-names>M. V.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Chaouchi</surname>
            ,
            <given-names>H.</given-names>
          </string-name>
          ,
          <string-name>
            <surname>Luo</surname>
            ,
            <given-names>T.</given-names>
          </string-name>
          , &amp;
          <string-name>
            <surname>Quek</surname>
            ,
            <given-names>T. Q.</given-names>
          </string-name>
          (
          <year>2020</year>
          ).
          <article-title>Adaptive anomaly detection for IoT data in hierarchical edge computing</article-title>
          . arXiv preprint arXiv:
          <year>2001</year>
          .03314.
        </mixed-citation>
      </ref>
      <ref id="ref22">
        <mixed-citation>
          [22]
          <string-name>
            <surname>Szydlo</surname>
            ,
            <given-names>T.</given-names>
          </string-name>
          (
          <year>2022</year>
          ).
          <article-title>Online anomaly detection based on reservoir sampling and LOF for IoT devices</article-title>
          .
          <source>arXiv preprint arXiv:2206</source>
          .
          <fpage>14265</fpage>
          .
        </mixed-citation>
      </ref>
    </ref-list>
  </back>
</article>