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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>A Framework Quantifying Trustworthiness of Supervised Machine and Deep Learning Models</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Alberto Huertas Celdran</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Jan Kreischer</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Melike Demirci</string-name>
          <email>melike.de!mi!rc!i@u</email>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Joel Leupp</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Pedro M. Sanchez Sanchez</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Muriel Figueredo Franco</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Gérôme Bovet</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Gregorio Martinez Perez</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Burkhard Stiller</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff3">3</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Communication Systems Group CSG, Department of Informatics IfI, University of Zurich UZH</institution>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Cyber-Defence Campus, armasuisse Science &amp; Technology</institution>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Department of Information and Communications Engineering, University of Murcia</institution>
        </aff>
        <aff id="aff3">
          <label>3</label>
          <institution>MGMlEoEbTaTlRRIICCSS</institution>
        </aff>
      </contrib-group>
      <abstract>
        <p>Trusting Artificial Intelligence (AI) is controversial since models and predictions might not be fair, understandable by humans, robust against adversaries, or trained appropriately. Existing toolkits help data scientists to create fair, explainable, robust, and transparent Machine and Deep Learning (ML/DL) models. However, tools to quantify AI trustworthiness according to pillars and metrics relevant for heterogeneous scenarios are still missing. This work proposes a novel algorithm that quantifies the trustworthiness level of supervised ML/DL models according to their fairness, explainability, robustness, and accountability. The algorithm is deployed on a Web application to allow the general public to calculate the trustworthiness of their models. Finally, a validation scenario with models classifying cyberattacks demonstrates the applicability of the Web application and algorithm.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Trust</kwd>
        <kwd>Supervised Machine Learning</kwd>
        <kwd>Trust Framework</kwd>
        <kwd>Deep Learning Trust</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        accountability as pillars for trusted AI [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ]. Concerning
fairness, bias is one of the main issues against trusting AI
Artificial Intelligence (AI) made great strides over the last systems [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. Bias can be introduced by human prejudice
decade [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. Some relevant examples are the victory of in the training dataset or assumptions made during the
IBM Watson in the open-domain Q&amp;A game of Jeopardy process of training Machine and Deep Learning (ML/DL)
(2011), the first version of Tesla Autopilot, with lane con- models. Furthermore, too small, incomplete, or not
ditrol, breaking, and speed limit adjustment (2014), or when verse enough training datasets might introduce bias as
AlphaGo defeated world champion Lee Sedol in the Go well. The literature has proposed diferent solutions to
degame (2016). In parallel to these achievements, AI has also tect and avoid bias. For instance, IBM AI Fairness 360 [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]
gained relevance as support to human decision-making, contains a set of metrics to detect bias in ML/DL models
spanning from trivial to highly complex applications. and datasets. Algorithms to mitigate bias during the
preThe diagnosis and treatment of diseases, assessment of processing, in-processing, and post-processing stages are
legal issues, or admission to credits are good examples of also available in the IBM toolkit. Another de-biasing
apcurrent tasks supported by AI systems. In these scenar- proach is called Fairness GAN [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ], which creates new and
ios and many others, delegating partially or entirely the unbiased datasets from original biased ones. However,
decision-making process to automated and intelligent aspects dealing with the explainability, robustness, or
systems generates a trust dependency. Thus, it is critical accountability of models are not taken into account by
to have mechanisms to quantify the trustworthiness level these tools.
of AI systems and their predictions. Explainability is another important pillar that consists
      </p>
      <p>
        Recently, the research community has agreed on the of understanding how ML/DL models come to their
conimportance of fairness, explainability, robustness, and clusions. When AI is used in high-risk fields, all
stakeholders should understand the main decision drivers. For
SafeAI2023: The AAAI’s Workshop on Artificial Intelligence Safety, human decision-making, trust can be gained by
explain*FeCborruraersypo1n3–d1in4g,2a0u2t3h,oWr.ashington, D.C. ing the underlying rationale. However, for AI, aspects
$ huertas@ifi.uzh.ch (A. Huertas Celdran); jan.kreischer@uzh.ch such as the algorithm class, features importance, or model
(J. Kreischer); melike.cilogluu@gmail.com (M. Demirci); complexity are some of the key aspects to explain
predicjoel.leupp@uzh.ch (J. Leupp); pedromigel.sanchez@um.es tions [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ]. In this context, the IBM AI Explainability 360
(P. M. Sanchez Sanchez); franco@ifi.uzh.ch (M. F. Franco); toolkit [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] contains a pool of algorithms and methods to
(gGer.oMmaer.tbinovezetP@earerzm);asstuiillsesre@.c hifi.u(Gzh. .cBhov(Bet.);Sgtirlleegro)rio@um.es explain model details and predictions. This toolkit also
0000-0001-7125-1710 (A. Huertas Celdran); 0000-0002-6444-2102 includes two metrics to evaluate the goodness of
expla(P. M. Sanchez Sanchez); 0000-0002-0208-0521 (M. F. Franco); nations. In addition, the literature has created various
0000-0002-4534-3483 (G. Bovet); 0000-0001-5532-6604 (G. Martinez libraries implementing local explanations methods like
Perez); 0000-0002-7461-7463 (B. Stiller)
      </p>
      <p>
        © 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License LIME or SHAPE [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]. Despite the contributions of these
CPWrEooUrckReshdoinpgs IhStpN:/c1e6u1r3-w-0s.o7r3g ACttEribUutRion W4.0oInrtekrnsahtioonpal (PCCroBYce4.0e).dings (CEUR-WS.org) solutions they only focus on explainability and do not
consider other important aspects of trusted AI like the • A Web application [
        <xref ref-type="bibr" rid="ref15">15</xref>
        ] that allows stakeholders
robustness of ML models. to use the proposed algorithm to compute and
      </p>
      <p>
        In this sense, robustness is the third pillar of trusted compare the trustworthiness level of their
superAI and refers to the model ability to deal with adver- vised ML/DL models.
sarial samples. Even in black-box approaches, where • A case study focused on models classifying
malmodel details are unknown to adversaries, it is possi- ware afecting Internet of Things (IoT) devices to
ble to cause unexpected predictions using adversarial at- demonstrate the suitability of the developed Web
tacks. Therefore, to ensure trusted ML/DL models, their application and proposed algorithm.
predictions must be stable and robust, even when
adversaries are present [
        <xref ref-type="bibr" rid="ref9">9</xref>
        ]. In this context, [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ] proposes The remainder of this paper is structured as follows.
a comprehensive taxonomy for adversarial robustness Section 2 analyzes previous works in the area of trusted
and discusses potential consequences of attacks consid- AI. Section 3 presents the pillars and metrics relevant for
ering data integrity, confidentiality, and privacy. From trusted AI. Section 4 introduces the design and
implea diferent perspective, the IBM Adversarial Robustness mentation of the trusted AI algorithm. While Section 5
Toolbox (ART) [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ] ofers a collection of adversarial at- presents the functionality of the Web application,
Sectack/defense implementations, run-time attack detection tion 6 validates the algorithm in a cybersecurity scenario.
methods, poisoning detection, and robustness metrics. Finally, Section 7 draws some conclusions and future
These metrics are very relevant to calculate the trustwor- work.
thiness level of AI models, but others dealing with the
methodology followed to train models are missing.
      </p>
      <p>
        To measure the quality of the ML pipeline or method- 2. Related Work
ology used to train ML/DL models, the fourth main pillar First, it is important to mention that trust in AI is an
of trusted AI proposes to use accountability and trans- incipient field, and, to the best of our knowledge, there is
parency aspects. More in detail, train/test splitting strat- no solution automatically assessing the trustworthiness
egy, data pre-processing, normalization, or feature extrac- level of ML/DL models in multiple dimensions.
Howtion and selection are some aspects providing valuable ever, related work has proposed metrics and tools for
insights to trust AI systems. In this sense, [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ] proposes individual dimensions or pillars impacting model
trustthe creation of FactSheets as a form of AI documentation. worthiness. Therefore, this section reviews work dealing
Additionally, [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ] studies the documentation needed by with AI trustworthiness in terms of fairness,
explainabilstakeholders to trust AI. Finally, the IBM AI FactSheets ity, robustness, and accountability.
360 [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] provides a guide and tool for the manual prepara- Starting from fairness, the authors of [
        <xref ref-type="bibr" rid="ref16">16</xref>
        ] introduced
tions of factSheets. the notions of group fairness and individual fairness and
      </p>
      <p>
        Despite the valuable contributions of previous works, discussed how model developers could address the topic.
trusted AI is an emerging research field that needs more In the same direction, [
        <xref ref-type="bibr" rid="ref17">17</xref>
        ] proposed an algorithm for
efort. In particular, the state-of-the-art lacks a compre- fair classification that complied with the two previous
hensive and unified collection of relevant metrics per notions of fairness. To mitigate unfairness in AI, [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ]
pillar to identify and quantify trusted ML/DL models. proposed a novel de-biasing approach, called Fairness
Furthermore, existing solutions focus on detecting and GAN, capable of creating a new dataset that
approximitigating diferent issues per pillar. However, there is mates a given original biased one. Reviewing existing
no solution combining the pillars and computing a global tools and frameworks, IBM AI Fairness 360 toolkit [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ]
trustworthiness level of ML/DL models. Last but not contains a comprehensive set of fairness metrics such
least, IBM toolkits are helping data scientists to create as statistical parity, equal opportunity, or average odds
fair, explainable, robust, and transparent ML/DL mod- that can be used to detect bias in ML models and datasets.
els. Nevertheless, tools to quantify AI trustworthiness in Furthermore, the toolkit ofers algorithms capable of
mitiheterogeneous and real-world scenarios are still missing. gating bias during the pre-processing, in-processing, and
      </p>
      <p>
        To address the previous challenges, this article presents post-processing stages. Facebook internal Fairness Flow
the following contributions: toolkit [
        <xref ref-type="bibr" rid="ref18">18</xref>
        ] is another solution composed of a Python
• A taxonomy with the four main pillars of trusted library that provides a simple API that requires a data
AI (fairness, explainability, robustness, and ac- set of predictions, labels, and group membership. As
countability) and their most relevant metrics to an output, the API ofers informative metrics, statistical
quantify the trustworthiness level of supervised confidence, and how to interpret the results. Microsoft
ML/DL models. Fairlearn [
        <xref ref-type="bibr" rid="ref19">19</xref>
        ] is another open-source project that
com• An extensible, adaptive and parameterized algo- bines visualization capabilities with unfairness detection
rithm (available in [
        <xref ref-type="bibr" rid="ref14">14</xref>
        ]) to quantify the trustwor- and mitigation algorithms.
thiness level of supervised ML/DL models with Explainability is another important dimension for
tabular data according to the pillars and metrics trusted AI. In this sense, IBM AI Explainability 360
of the proposed taxonomy. toolkit [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] contains several algorithms and methods to
create explanations for ML models or make explainable
models like decision trees more accurate. It also includes
two proxy metrics to evaluate the goodness of
explanations. Compared to the work at hand, this toolkit does
not evaluate the level of model explainability but
provides explanation methods for diferent types of models.
      </p>
      <p>
        Additionally, various python libraries implemented local
explanations methods like LIME or SHAPE [
        <xref ref-type="bibr" rid="ref8">8</xref>
        ]. All those
solutions aim to explain the decisions of models but not
to classify models on their explainability level, as the
paper at hand does.
      </p>
      <p>
        Robustness against adversarial attacks is something
well-studied in the literature. The authors of [
        <xref ref-type="bibr" rid="ref10">10</xref>
        ]
presented a comprehensive taxonomy with explanations for
existing attacks and defenses. They also discussed the
potential consequences of adversarial attacks in terms of
data integrity, confidentiality, and privacy. However, the
authors did not analyze metrics measuring the models
robustness. In terms of metrics, the literature focuses
mainly on intrinsic and post-hoc explainability
methods. In terms of existing tools, IBM ART [
        <xref ref-type="bibr" rid="ref11">11</xref>
        ] is an
opensource Python library that collects adversarial robustness
techniques on ML models. It consists of adversarial
attack/defense implementations, run-time attack detection
methods, poisoning detection, and robustness metrics.
      </p>
      <p>This toolbox implements multiple attack detection and
defense techniques. Similar to the work at hand, ART
also gathers possible robustness metrics.</p>
      <p>
        Dealing with accountability, [
        <xref ref-type="bibr" rid="ref12">12</xref>
        ] proposed a
methodology for creating factsheets. Factsheets provide
information regarding ML models, such as training data, model
type, or training methodology. All stakeholders involved
in the AI lifecycle contribute to the Factsheet creation,
and it covers the expertise gap between AI producers and
consumers. The authors of [
        <xref ref-type="bibr" rid="ref13">13</xref>
        ] studied the necessities of
developers and other stakeholders to understand what
content to include in factsheets. They highlighted the
importance of documenting how a model was structured,
what training data was used, and how features were
engineered. In terms of existing tools, IBM AI FactSheets
360 [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] provides a guide for preparing factsheets.
Transparent and well-documented communication between
model creator and model operator increases trust and
enables more eficient integration of pre-trained models.
      </p>
      <p>One limitation of the previous works is that the creation
of factsheets requires a lot of manual efort. The paper
at hand automates this process as much as possible.</p>
      <p>In conclusion, despite the contributions made by the
previous works, there is no automatic tool or solution
combining diferent pillars and metrics to compute the
trustworthiness level of supervised ML models.
3. Main Pillars &amp; Metrics of</p>
      <p>Trustworthy AI
This section describes the pillars and metrics identified
by this work as the most relevant to quantify the
trustworthiness of supervised ML/DL models (see Figure 1).
ML/DL models can be classified as unfair due to diferent
reasons such as i) biased training data, ii) unbalanced or
lack of training data, or iii) discrimination of protected
groups, among others. The concept of protected group
refers to a set of samples sharing a common property or
feature value. For instance, in a job application, women
could be a protected group to avoid gender
discrimination. Considering these reasons, this work proposes the
following metrics to quantify the fairness level of
supervised ML/DL models.</p>
      <p>• Underfitting : detects if the model is unable to
learn the relationship between inputs and
outputs accurately. In this work, Eq (1) calculates
underfitting as the diference between the model
accuracy with train data and a baseline threshold
(established according to the expected accuracy
of the selected application scenario).</p>
      <p>(ˆ = 1| = 0)|
   =  −  (1)
• Overfitting : measures the model generalization
capabilities. In this work, Eq (2) calculates
overfitting as the diference between the model accuracy
with train and test datasets.</p>
      <p>=  −</p>
      <p>(2)
• Class Balance: measures the ratio of samples
belonging to diferent classes in the training dataset.</p>
      <p>Class imbalance is a problem for predicting tasks
of infrequent classes with few samples. In this
work, the class balance is computed by using Eq.
(3) and chi-square (2) distribution. It performs a
statistical test that checks the deviation between
a perfect samples distribution () for all classes
() and the actual distribution ().</p>
      <p>2 = Σ 
( − )2</p>
      <p>
        • Statistical Parity Diference : computes the spread
between the percentage of samples belonging to
the majority group receiving a favorable outcome
compared to a protected group [
        <xref ref-type="bibr" rid="ref20">20</xref>
        ]. This
metric and the following three detect discrimination
in predictions using samples of diferent groups.
      </p>
      <p>Eq. (4) measures the Statistical Parity Diference
(SPD) between both groups. ˆ = 1 represents a
favorable prediction and  (ˆ = 1| = ) is
the probability of receiving a favorable prediction
if the sample belongs to the protected minority
( = 1) or the unprotected majority ( = 0). If
SPD is close to zero, the classifier has statistical
parity.</p>
      <p>(ˆ , ,  ) = | (ˆ = 1| = 1)−
(3)
(4)</p>
      <sec id="sec-1-1">
        <title>Fairness</title>
      </sec>
      <sec id="sec-1-2">
        <title>Explainability</title>
      </sec>
      <sec id="sec-1-3">
        <title>Robustness</title>
      </sec>
      <sec id="sec-1-4">
        <title>Accountability</title>
        <p>Trusted AI
Taxonomy
Confidence
Score</p>
        <p>DT, RF,
GBDT
Clique
Method
Class
Balance
Statistical</p>
        <p>Parity</p>
        <p>Difference
Legend
Overfitting
Underfitting
Equal</p>
        <sec id="sec-1-4-1">
          <title>Opportunity Average Odds</title>
        </sec>
        <sec id="sec-1-4-2">
          <title>Difference Difference</title>
          <p>Disparate
Impact
Model Size
Correlated
Features
Algorithm
Class
Feature
Relevance
FactSheet</p>
        </sec>
        <sec id="sec-1-4-3">
          <title>Normalization Missing Data Completness</title>
        </sec>
        <sec id="sec-1-4-4">
          <title>Train/Test Regularization</title>
          <p>Split
NN, LG,
SVM
ER Fast
Gradient</p>
          <p>NN
Pillars</p>
          <p>Metrics</p>
          <p>Algorithms</p>
          <p>ER Carlini
Wagner</p>
          <p>ER
DeepFool</p>
          <p>Loss
Sensitivity</p>
          <p>
            CLEVER
Score
• Equal Opportunity Diference : measures the 3.2. Explainability Pillar
spread between true positive rate (TPR) and false
positive rate (FPR) of protected and unprotected Explainable artificial intelligence focuses on enabling a
groups [
            <xref ref-type="bibr" rid="ref21">21</xref>
            ]. Eq. (5) calculates the Equal Opportu- deeper understanding of the inner workings of ML/DL
models. To quantify the explainability of models and
nity Diference (EOD).  {ˆ = 1| = 0,  = their predictions, the following metrics (which assume
0u}nparnodtecte{dˆan=d1p|rot=ect1e,dgr=ou0p}s,arreestpheecFtPivReloyf. tabular data format) are used.
          </p>
          <p>Additionally,  {ˆ = 1| = 0,  = 1} and
 {ˆ = 1| = 1,  = 1} are the TPR of
unprotected and protected groups.
(ˆ ,  ) =  {ˆ = 1| = 1,  = }−
 {ˆ = 1| = 0,  = },  ∈ 0, 1</p>
          <p>
            (5)
• Average Odds Diference : calculates the mean
absolute diference in TPR and FPR between
protected and unprotected groups [
            <xref ref-type="bibr" rid="ref22">22</xref>
            ]. Eq. (6)
measures the Average Odds Diference (AOD)
as 1/2[(   −   ) +
(   −   )]
(ˆ , ,  ) = Σ  ∈{0,1}| {ˆ = 1| = 1,
 = } −  {ˆ = 1| = 0,  = }|
          </p>
          <p>2
• Disparate Impact: measures the ratio of a
protected group receiving a favorable prediction
divided by the ratio of an unprotected group
receiving a favorable outcome. Eq (7) calculates
the Disparate Impact (DI) and uses the previously
defined variables.</p>
          <p>
            (ˆ , ,  ) =  {ˆ = 1| = 1}
 {ˆ = 1| = 0}
(6)
(7)
• Algorithm Class: indicates the model
explainability degree according to the algorithm type and its
complexity. This work defines a predefined and
configurable score for each algorithm, which is
inspired by the literature.
• Correlated Features: measures the percentage
of highly correlated features. High correlation
among features might lead to biases in most
explanation techniques. This work calculates the
number of highly correlated features (&gt;= 95%)
and predefines configurable thresholds to
compute the metric score.
• Feature Relevance: calculates the percentage of
irrelevant features for a set of predictions. The
lower irrelevant features, the better, as they
would only make explanations more complex
without being relevant [
            <xref ref-type="bibr" rid="ref23">23</xref>
            ]. As in the previous
metric, this work calculates the number of
irrelevant features (relevance &lt;= 3% ) for the model
and predefines configurable thresholds to
compute the metric score.
• Model Size: indicates the number of parameters
used by models. In this work, this metric
considers predefined thresholds that are used to
evaluate the model comprehensibility, which inversely
correlates with the model degrees of freedom
determined by the number of parameters.
3.3. Robustness Pillar
To trust ML/DL models, their predictions should be
stable and robust. If small changes in the input data cause
significant deviations in the output, adversarial
perturbations can be used to generate undesired outcomes. This
work proposes using the following metrics to measure
the robustness of supervised ML/DL models.
(, ,  ) =
1 ∑︁ || () − ||
|| ∈
||||
          </p>
          <p>
            (10)
3.4. Accountability Pillar
Accountability fosters trust in AI by documenting,
validating, and notifying the creation, evaluation, and
main• Confidence Score : measures the probability of cor- tenance of ML/DL models. This work identifies the
folrectly predicting samples. It calculates the stabil- lowing metrics as relevant to evaluating the
accountability of predictions, the more stable the predictions, ity of supervised ML/DL models. The following
metthe more robust the model [24]. Eq (8) calculates ric scores are calculated using predefined configurable
the confidence score as the mean over all the pre- thresholds that can be found in [
            <xref ref-type="bibr" rid="ref14">14</xref>
            ].
cision scores for all thresholds. Where  are the
labels, and  ℎ are the probabilities that one
vector is classified correctly.
• Train/Test Split: measures the ratio between the
number of samples used for training and testing.
          </p>
          <p>If the training and testing dataset do not contain
enough representative data, the model will not
perform well, it will not be able to generalize, and
the predictions will not be reliable.
• Missing Data: evaluates how missing values of
features of the training dataset are handled. If the
model is trained on a dataset containing many
missing values, the model will not be reliable.
• Normalization: evaluates if some models have
been trained with normalized or non-normalized
data. It helps mitigating the efects of outliers and
ensures that features values are in the same range
[29].
• Regularization: measures if the ML/DL model
used generalization techniques during training. It
avoids model parameters taking extreme values,
and it is necessary to avoid memorization during
training NN with millions of parameters.
• FactSheet Completeness: measures if the FactSheet
includes all necessary information that
stakeholders need in order to trust the model and its
predictions. A FactSheet summarizes important
metadata regarding the steps followed to train a model,
purpose, algorithm, and data, among others.</p>
          <p>1  
  = | ℎ| Σ    +   +</p>
          <p>(8)
• Loss Sensitivity: calculates the largest variation
of the output of a Neural Network (NN) under a
small change in its input. Overall, it quantifies
the smoothness of a model [24]. The smaller the
variation in the output, the smoother the model.</p>
          <p>Eq (9) calculates Loss sensitivity (g), where ℒ is
the loss function.</p>
          <p>= ⃦⃦⃦⃦ ℒ ⃦⃦⃦⃦ 1</p>
          <p>
            (9)
• Cross Lipschitz Extreme Value for Network
Robustness (CLEVER) Score: measures the minimal
perturbation that is needed to change the
classification outcome [25] using the local Lipschitz
constant [
            <xref ref-type="bibr" rid="ref11">11</xref>
            ]. It is applicable to NN.
• Clique Method: finds the exact minimal
adversarial perturbation or a guaranteed lower bound of it
[26]. It is applicable to Decision Trees (DT),
Random Forests (RF), and Gradient Boosted Decision
          </p>
          <p>
            Trees (BGDT).
• Empirical Robustness: measures the average
minimal perturbation that needs to be introduced 4. Algorithm Quantifying
to change the model prediction [
            <xref ref-type="bibr" rid="ref11">11</xref>
            ]. Empirical Trustworthy AI
robustness (ER) is applicable to NN, Logistic
Regression (LG), and Support Vector Machine (SVM) This section presents a novel, extensible, and
algorithms. Eq. (10) calculates ER, where  is a parametrized algorithm able to quantify the
trusttrained classifier,  is an untargeted attack,  worthiness level of supervised ML/DL models. Figure 2
is the test data. First adversarial inputs  () shows the algorithm schema and lifecycle.
are crafted and the classifier is tested against First, for each pillar, the algorithm computes the
metthem. In the equation only the adversarial in- rics explained in the previous section. For that, each
puts which successfully fooled the model are be- metric receives as an input the i) training and testing
ing considered. So only the indices  ∈ 1, 2,  datasets, ii) trained ML/DL model, and iii) FactSheet with
where () ̸= ( ()) must be taken. Select- the metadata of the training methodology. Then, the
aling attacks is a challenging task, and this work gorithm evaluates if the inputs fulfill the conditions of
considers the success ratio and calculation speed each metric. If so, each metric is independently
calcuof each attack to select Fast Gradient [
            <xref ref-type="bibr" rid="ref9">9</xref>
            ], Carlini lated according to its formula and input data. Table 1
&amp; Wagner [27], and DeepFool [28] attacks. shows for each metric, its inputs, conditions, and output.
          </p>
          <p>Input
Input
Inputs
Inputs
Inputs</p>
          <p>Metric 1
Metric 2
MMeettrriicc 3n
MMeettrriicc 4n
MMeettrriicc nn</p>
          <p>Output
Output
Outputs</p>
          <p>Score 1
Score 2</p>
          <p>Scores
Outputs</p>
          <p>Scores
Outputs</p>
          <p>Scores</p>
        </sec>
      </sec>
      <sec id="sec-1-5">
        <title>Explainability</title>
      </sec>
      <sec id="sec-1-6">
        <title>Score</title>
      </sec>
      <sec id="sec-1-7">
        <title>Robustness</title>
      </sec>
      <sec id="sec-1-8">
        <title>Score</title>
      </sec>
      <sec id="sec-1-9">
        <title>Accountability</title>
      </sec>
      <sec id="sec-1-10">
        <title>Score</title>
        <p>Mapping FuPnilcl atiroAnggregation FuncGtiolonbsal Aggregation FunTcrutisotnScore</p>
        <p>The metrics outputs cannot be interpreted as trust
scores because they have diferent data types, scales, and
meanings. Therefore, each metric output must be
interpreted and translated into a standard trust score using a
mapping function. The proposed trust score for all
metrics ranges from one to five, where one corresponds to the
worst score, and five represents the best score. The
mappings from metrics outputs to trust scores are predefined
according to good practices indicated in the literature.</p>
        <p>However, this process could involve some arbitrary
decisions adding biases. To avoid it, the mapping function
is parameterized and can be fine-tuned by stakeholders
according to the data domain, metric, or scenario.</p>
        <p>The next step consists of aggregating all the metrics
scores of each pillar and calculating a score per pillar. The
algorithm proposes a weighted approach where each
metric has particular importance in the pillar score. It is up
to discuss whether all metrics are equally important and
how weighted they should be. Because of that, default
weights for every metric are defined, but stakeholders can
modify them according to the scenario characteristics.</p>
        <p>Finally, the four pillar scores are aggregated into a
global trust score, which is the return value of the
algorithm. Computing the global trust score is done analog
to calculating the pillars scores. Independent weights are
assigned to each pillar, and the global trust score is the
weighted average of each pillar. Since the importance
of each pillar depends on the scenario, the predefined
configuration of the algorithm (equal importance per
pillar) can be modified by stakeholders. Algorithm 1 shows
the pseudocode implementing the previous steps of the
proposed Trusted AI algorithm.</p>
        <p>Algorithm 1 Trusted AI Algorithm
1: function Trusted_AI(, , ,  ℎ,  ,  ℎ)
2: _ ← 0
3:  ←  , , , 
4: _ ←  
5: for    do
6:  ← 0
7: _ ←  
8:  ← _()
9: for    do
10:  ←  []
11: _[] ← _()
12:
13:
14:
15:
16:
17:
18:
19:
 ←  ℎ[]
 ←  +  * 
_[] ←</p>
        <p>
          for ( ∈ ,  ∈ )  _ do
for ( ∈ ,  ∈ )  _ do
 ←  ℎ[]
_ ← _ +  * 
return _
5. Web Application
This section presents a Web-based application hosting
the proposed algorithm and allowing stakeholders to
calculate the trustworthiness level of supervised ML/DL
models [
          <xref ref-type="bibr" rid="ref15">15</xref>
          ] in an intuitive way. To understand the
application functionality, it is important to introduce the
concepts of scenario and solution. Firstly, a scenario is the
application context where supervised ML/DL models are
created to solve a particular task. Classifying malware in
IoT devices, or fraud in credit cards are two examples of
scenarios. Secondly, a solution is a combination of i) the
training &amp; testing data, ii) a trained supervised ML/DL
model, and iii) a FactSheet solving a given scenario task.
        </p>
        <p>Thus, the Web application allows stakeholders to:
• Create scenarios and upload solutions for existing</p>
        <p>scenarios.
• Calculate and graphically see the trustworthiness</p>
        <p>level of a solution.
• Re-calculate the trustworthiness level of a given</p>
        <p>solution according to customized parameters.
• Compare the trustworthiness levels of two
solutions, explaining the meaning and results of each
metric and pillar.</p>
        <p>The Python framework dash 2.1.0 was used to
implement the Web application backend and frontend
components. The backend implements the algorithm and
a database to store the input data needed by the
algorithm. The frontend provides stakeholders with a
graphical interface composed of the following four pages. The
Appendix contains one screenshot of each page.
5.1. Web Application Functionality
The main functionality of the proposed Web application is
organized in the following main pages: scenario, upload,
analyze, and compare. Below, more details about them
are given.</p>
        <p>Scenario Page. This page allows stakeholders to
create new scenarios with their descriptions.</p>
        <p>Upload Page. Stakeholders use it to upload their
solutions for a previously created scenario. In particular,
the following aspects are needed:
• Scenario &amp; Solution.
• Description: Brief description of the solution
(op</p>
        <p>tional).
• Training &amp; Testing data: Two datasets (format:</p>
        <p>csv or pickle).
• Protected Feature: Protected features of the
Train</p>
        <p>ing data (optional).
• Protected values: Protected values for the
pro</p>
        <p>tected features (optional).
• Target Column: Column of the training dataset to</p>
        <p>be predicted.
• ML/DL model: Supervised ML/DL model of the</p>
        <p>solution (format: pickle).
• FactSheet: Methodological steps (format: json)
with the following fields.</p>
        <p>– Model Name (optional);
– Purpose: Supervised ML/DL model goal</p>
        <p>(optional).
– Domain: Where the model is used
(op</p>
        <p>tional).
– Data: Description of the data and the
pre</p>
        <p>
          processing techniques (optional).
– Model information: Information about the
model (optional).
stage, it is worth mentioning that the mapping function
and weights per pillar and metric of the algorithm are
not shown for the sake of simplicity and room.
However, they can be found on the compare page of the Web
application [
          <xref ref-type="bibr" rid="ref15">15</xref>
          ] once both solutions are selected.
        </p>
      </sec>
    </sec>
    <sec id="sec-2">
      <title>7. Conclusions</title>
      <p>This article introduced a novel, adaptive, and
parameterized algorithm able to quantify the trustworthiness level
of supervised ML/DL models with tabular data. The
algorithm considers twenty-three metrics grouped into four
pillars of trusted AI (fairness, explainability, robustness,
and accountability). It combines the metrics outputs to
compute a global trustworthiness score of supervised
ML/DL models according to their training and testing
data, model, and FactSheet. Also, the algorithm was
deployed on a Web application where a cybersecurity
scenario demonstrates the practical applicability of the
algorithm. In conclusion, this work outlines the
importance of considering not only traditional performance
metrics but also the trustworthiness level of ML/DL
models.</p>
      <p>Future work plans to improve the limitations of the
current solution with the support of unsupervised models
and the inclusion of suggestions to improve the
trustworthiness level of ML/DL models. Finally, the Web
application will be redesigned to reduce computation time.</p>
      <p>Acknowledgments
This work has been partially supported by (a) the Swiss
Federal Ofice for Defense Procurement (armasuisse) with
the CyberTracer and RESERVE (CYD-C-2020003) projects
and (b) the University of Zürich UZH.
tion models, SN Applied Sciences 3 (2021) 1–12.
[24] F. Y. et al, Interpreting and evaluating neural
network robustness, in: 2019 International Joint
Conferences on Artificial Intelligence, 2019, pp. 4199–
4205. URL: https://www.ijcai.org/proceedings/2019/
0583.pdf .
[25] T.-W. Weng, H. Zhang, P.-Y. Chen, J. Yi, D. Su,</p>
      <p>Y. Gao, C.-J. Hsieh, L. Daniel, Evaluating the
robustness of neural networks: An extreme value theory
approach, arXiv preprint arXiv:1801.10578 (2018).
[26] H. Chen, H. Zhang, S. Si, Y. Li, D. Boning, C.-J.</p>
      <p>Hsieh, Robustness verification of tree-based
models, Advances in Neural Information Processing</p>
      <p>Systems 32 (2019).
[27] N. Carlini, D. Wagner, Towards Evaluating the</p>
      <p>Robustness of Neural Networks, in: 2017 IEEE
symposium on security and privacy, IEEE, 2017, pp.</p>
      <p>39–57.
[28] S. Moosavi-Dezfooli, A. Fawzi, P. Frossard,
Deepfool: a simple and accurate method to fool deep
neural networks, in: 2016 IEEE Conference on
Computer Vision and Pattern Recognition, 2016,
pp. 2574–2582.
[29] T. Jayalakshmi, A. Santhakumaran, Statistical
normalization and back propagation for classification,
International Journal of Computer Theory and
Engineering 3 (2011) 1793–8201.</p>
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Choose File no file selected Drag and Drop or Select File
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          <article-title>MSeuGlpikpeEosrtSNVvceEctoRrCAlasLsifieIr N01 Contact In5formation melike</article-title>
          .
          <source>demirci@uzh.ch WGAGelcliocogbubhartlalecdy 00..8855 Precision 00..8855 PPrreecciissiioonn WWeeiigghhtteedd 00..8855 WWeeiigghhtteedd 5500..8855 FGRG1ellocobabalall FF131 Score 00..8855 0.85 3.1/5 4 Figure 7: Compare55Page withinPgerformance Metrics acne d Tessrustworthin55ess Scores of Two Solutions.rence 2</source>
          .5/5 p le p
          <string-name>
            <surname>le E X P L A I N A B I L I T Y</surname>
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      </ref>
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