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  <front>
    <journal-meta>
      <journal-title-group>
        <journal-title>L. Marconi); r.matamorosaragon@campus.unimib.it (R. A. M. A.);
r.matamorosaragon@campus.unimib.it (F. Epifania)</journal-title>
      </journal-title-group>
    </journal-meta>
    <article-meta>
      <title-group>
        <article-title>Discovering the Unknown Suggestion: a Short Review on Explainability for Recommender Systems</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Luca Marconi</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Ricardo A. Matamoros A.</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Francesco Epifania</string-name>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Department of Informatics</institution>
          ,
          <addr-line>Systems and Communication</addr-line>
          ,
          <institution>University of Milano - Bicocca</institution>
          ,
          <addr-line>Milan</addr-line>
          ,
          <country country="IT">Italy</country>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Social Things SRL</institution>
          ,
          <country country="IT">Italy</country>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2022</year>
      </pub-date>
      <volume>000</volume>
      <fpage>0</fpage>
      <lpage>0002</lpage>
      <abstract>
        <p>Artificial Intelligence and in particular machine learning and deep learning models are normally considered to be fast and high performing, but in general there is a lack of transparency and interpretability. The issues related to explainability and its consequences are becoming more and more relevant in the whole broad scenario of Artificial Intelligence. To address this issue, explainable AI emerged, as a set of Artificial Intelligence techniques able to make their own decision more transparent and interpretable, so as to let users understand the specific reasons why the system provided its outcome, decision, or, in the case of recommender systems, its suggestions. Explainable Artificial Intelligence is deeply needed in heterogeneous domains and contexts, as the need for transparency, interpretability and even accountability of the Artificial Intelligence-based systems is a big necessity, as confirmed by the recent right to explanation in the 2018 General Data Protection Regulation by the European Union. Due to the difusion of recommender systems in many applicative domains and situations in everyday life and business ifelds, there is an emerging necessity for systems not only able to provide human decision-makers with suggestions and ease the decision-making processes in organizations, but also to give the right motivations of their recommendations. This paper summarizes the results of the study of the state of the art for Explainable Artificial Intelligence for Recommender Systems. We will follow the main reviews in literature to present the main work, kinds of explanainable recommendations and methods.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;Machine Learning</kwd>
        <kwd>Recommender Systems</kwd>
        <kwd>Artificial Intelligence</kwd>
        <kwd>eXplainable Artificial Intelligence</kwd>
        <kwd>eXplainable Recommender Systems</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Nowadays, Artificial Intelligence (AI) is becoming more and more important in our professional
and personal life. According to the International Data Corporation (IDC) the global investment
on AI will reach almost 118 billion U.S. dollars in 2022 and even surpass 300 billion U.S. dollars
by 2026 [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]. Moreover, the statistics portal Statista forecasts that revenues from the AI market
worldwide will grow from 10.1 billion U.S. dollars in 2018 to 126 billion U.S. dollars by 2026 [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ].
Gartner identifies AI as a fundamental technology in most of the the Gartner Top 10 Strategic
Technology Trends for 2023 [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. In the context of the current fourth industrial revolution,
overlapping waves of breakthroughs in computing, artificial intelligence, nanotechnology and
material science, 3D-printing, molecular biology (gene sequencing), robotics and other evolving
and emergent technologies are reshaping life, business models and ecosystems, according
to [
        <xref ref-type="bibr" rid="ref4">4</xref>
        ] In this scenario, AI is strongly emerging as transversal and powerful technological
paradigm, due to its ability not only to deal with data and big data, but especially because it
produces and manages knowledge. Andrew Ng, former chief scientist at Badu and Co-founder
at Coursera, said in a keynote speech at the AI Frontiers conference in 2017 that AI is really
the new electricity: a disruptive, pervasive and enabling technology, empowering technologies
and processes in potentially any field or domain. AI and in particular Machine Learning (ML)
and Deep Learning (DL) models are normally considered to be fast and high-performing, but
in general there is a lack of transparency and interpretability [
        <xref ref-type="bibr" rid="ref5 ref6">5, 6, 7</xref>
        ]: it’s hard work to get
insights from their internal mechanisms when trying to understand why the system provided
its outcome or decision. To address this issue, explainable AI (XAI) emerged, as a set of AI
techniques able to make their own decision more transparent and interpretable, so as to let
users understand the specific reasons why the system provided its outcome, decision, or, in
the case of recommender systems, its suggestions [
        <xref ref-type="bibr" rid="ref5 ref6">5, 6, 7</xref>
        ]. Explainable AI is deeply needed in
heterogeneous domains and contexts, as the need for transparency, interpretability and even
accountability of the AI-based systems is a big necessity, as confirmed by the recent right to
explanation in the 2018 General Data Protection Regulation (GDPR) by the European Union [8].
Due to the difusion of Recommender Systems (RSs) in many applicative domains and situations
in everyday life and business fields, there is an emerging necessity for systems not only able to
provide human decision-makers with suggestions and ease the decision-making processes in
organizations, but also to give the right motivations of their recommendations [9, 10]. A good
way to classify eXplainable Recommender Systems (XRSs) was proposed by Zhang et al. in 2014
[11]: it essentially deals with two dimensions: the information source or display style of the
explanations (e.g., textual sentence explanation, or visual explanation): it represents the
humancomputer interaction perspective of explainable recommendation research; the model itself,
representing the machine learning perspective of explainable recommendation research. XRSs
can be evaluated both by qualitative, user-centered and quantitative evaluation methods. The
evaluation can be either related to the performance of the system or to its explainability. In both
cases, experiments can be designed wher real users are involved, or without the contribution of
human users in the experimental setting. When it comes to evaluating the explainability of the
RSs, methods can regard online, ofline evaluation or user studies [12], while other classifications
have been proposed in the literature. Overall, the evaluation of explainability sufers from a
lack of a unified, precise and widely accepted formal definition of explainability, which implies
the use of complementary qualitative and quantitative methodologies to completely strive to
evaluate such systems.
      </p>
      <p>This paper summarizes the results of the study of the state of the art for XRSs. We will follow
the main reviews in literature to present the main work, kinds of explainable recommendations
and methods. Thus, the aim of this paper is to provide a short and compact macro-review of the
mostly difused and used methods and systems reported in the literature. The rise, evolution,
adaptation and modifications of models are definitively ongoing processes in the state-of-the-art,
thus getting a comprehensive and complete classification is challenging. Given the ongoing
evolution of the field, as well as the increasing number of potential applications, the aim of this
paper is definitively not to provide a comprehensive and complete review of the large panorama
of such discipline. Rather, we report a limited and carefully circumscribed set of fundamental
concepts and methods to get a general picture for later understanding and appreciate the many
potential applications and uses of for heterogeneous business and industrial domains. Given
the increasing need of explainable, interpretable and thrustworthy systems in business and
organizational Therefore, the proposed survey is intended to provide a general overview of
the growing scenario of the XRSs, with the aim to help researchers, practitioners and
decisionmakers to orient themselves to exploit the many potentialities of explainability in recommender
systems for business and industrial applications.</p>
    </sec>
    <sec id="sec-2">
      <title>2. The context of Explainable AI</title>
      <p>
        Actually, the explanation problem is definitively not new in the literature: the term started to
be used in 2004 [13], though the problem itself has existed since the mid-1970s, specifically in
the field of expert systems [ 14], with the first rise of AI in the literature. Though, a greater
interest in this theme started to grow with the evolution of machine learning methodologies
and techniques, particularly with the growth of its performances in the last years. In the
literature, the need for explainable AI is motivated mainly by three reasons: the need for trust,
for interaction and for transparency [7]. It’s worth to notice that, consequently, explainable AI
is strictly related to responsibility and transparency [
        <xref ref-type="bibr" rid="ref6">7, 12, 6</xref>
        ]. Consequently, explainability is
definitively becoming a key conceptual elements for the present and incoming AI systems, as it
is also explicitly required in the European General Data Protection Regulation (GDPR) [15],
where also the key related concepts of fairness and transparency in automated decision-making
are highlighted.
      </p>
      <p>
        In general, XAI is strongly needed for justifying and interpreting the results, so as to ensure
that they were not made erroneously [
        <xref ref-type="bibr" rid="ref6">7, 6</xref>
        ]. Moreover, the possibility to explain the results
would help to improve the way the results are obtained, control the systems dynamics and
facilitate new ways to gain knowledge [7].
      </p>
      <p>In a broader perspective, the difusion of XAI methods and techniques is a crucial step
in the current and future evolution of AI systems. Such methods can significantly be grouped
into the so-called third wave of AI, as defined by DARPA. Thus, XAI strives to realize the big
challenge of contextual adaptation, i.e. the construction of progressively explanatory methods
for classes of real-world phenomena. The further steps in the design and development of such
new and empowered AI systems is the ability to foster continuous learning by the inclusion of
synergetic learning techniques, as well as the progressive empowerment of the interaction with
human decision-makers [7]. Eventually, the last mile of this ambitious evolution is the quest
for reaching or emulating the human intelligence [7].</p>
      <p>In the literature, there are diferent ways to classify the XAI models: among them, there are
classifications distinguishing algorithms for their global or local interpretability, and classifications
taking into considerations the diferences between model-specific or model-agnostic methods,
thus related with the possibility to apply explainable techniques only to specific models or not.
We present the main useful concepts for our work, as well as the main classification reported in
the literature, in the case of XRS.</p>
    </sec>
    <sec id="sec-3">
      <title>3. Explainable Recommendations</title>
      <p>In this context, explainable AI in the field of RSs is aimed at providing intuitive explanations for
the suggestions and recommendations provided by the algorithms [12, 19]. Basically they try
to address the problem of why certain recommendations are suggested by the models. As they
are part of the big world of the XAI, explainable recommendations can either be model-intrinsic
or model-agnostic: in the former case, the output model is intrinsically interpretable, meaning
that the decision mechanism is completely transparent providing explainability; in the latter
case, instead, the output model provides the so-called post-hoc explanations, without any
modification of the model itself. It is interesting this two approaches can be conceptually linked
to a cognitive psychological root [12]: in this perspective, the model-intrinsic models would be
similar to the human minds rational decisions taken after some reasoning process, while the
model-agnostic ones would somehow resemble the intuitive ways of deciding, followed by
some search of the explanations.</p>
      <p>In other words, as in the general case of XAI, XRSs, based on explainability-aware ML
techniques, can generally be categorized into two main groups [18]:
1. Systems providing an explanation of their predictions in a way that is interpretable by
the user. These types of methods usually only justify their output by the means of an
added explanations, but without providing an in depth understanding of the underlying
algorithm. This is typical in the case of post-hoc explanations.
2. Explainable systems directly incorporating interpretable models in the construction of
the automated systems. Model intrinsic and, specifically, white-box models, such as DTs,
can be categorized in this group.</p>
      <p>XRSs started formally to be defined, conceived and used in recent years. The term explainable
recommendation was formally introduced by Zhang et al. in 2014 [11], but there were earlier
works in personalized recommendation research. An extensive review of the first historical
stages of explainable recommendation and how it was focused especially on collaborative
ifltering methods in RSs is in Zhang et al., 2018 [12].</p>
    </sec>
    <sec id="sec-4">
      <title>4. Classification of Explainable Recommender Systems</title>
      <p>A good way to classify XRS was proposed by Zhang et al. in 2018 [12]: it essentially deals with
two dimensions:
1. the information source or display style of the explanations (e.g., textual sentence
explanation, or visual explanation): it represents the human-computer interaction perspective of
explainable recommendation research;
2. the model itself, representing the machine learning (ML) perspective of explainable
recommendation research.</p>
      <p>A somehow generalized taxonomy, focused on the specific classification of interpretability
methods, is provided in the review by Linardatos in 2021 [66], which depicts and highlights the
major concepts and dimensions involved in the analysis of interpretable models. It proves to be
useful to get a complete picture of the most significant conceptual perspectives involved.</p>
      <sec id="sec-4-1">
        <title>4.1. Information Source for Explanations</title>
        <p>The first dimension of this classification model is the information source for explanations,
also called display style: namely, explanations are pieces of information related to the
recommendations given by the algorithm. Recommendations can come from diferent
information sources and can be displayed in several ways: some examples include textual
sentences, word clouds or visual explanations. In the following paragraphs we provide a short
summary of the diferent types of recommendation explanations and we give some examples of
relevant related work.</p>
        <sec id="sec-4-1-1">
          <title>Explanations based on Relevant Users or Items</title>
          <p>This comes from the first stages of recommendation explanation research. User-based
explanations are especially used by collaborative filtering RSs, thus when the recommendation
is based on the ratings or interests of ”similar” users. [12] reports the example of Herlocker et
al. [20], comparing the efectiveness of diferent display styles for explanations in user-based
collaborative filtering. Instead, for item-based explanations, the measure of similarity comes
from the user’s past liked items. Zhang and Chen [12] argue that relevant-item explanations
are more intuitive for users than user-based explanations due to the familiarity of the user with
the items more than with other potential users: nevertheless, this problem could be solved by
another kind of explanations, the so-called social explanation.</p>
        </sec>
        <sec id="sec-4-1-2">
          <title>Feature-based Explanations</title>
          <p>This kind of explanations are especially related to content-based recommendation methods
[12]. CB-RSs elaborate suggestions according to a specific match between users’ proles and
content features of candidate items. In this case it is more intuitive to base the recommendations
on the specific features of the items, and then to display them in the best explanation style:
for example in Vig et al. [21] the recommendations are provided adopting movie tags as features.</p>
        </sec>
        <sec id="sec-4-1-3">
          <title>Textual Sentence Explanations</title>
          <p>This kind of explanations is very useful for getting relevant benefits from user-generated
content, such as e-commerce reviews and social media posts [12]. Sentences could come
from pre-defined templates or be directly generated based on natural language generation
models. Zhang and Chen [12] classify such approaches between aspect-level and sentence-level
approaches, based on the display style of the explanations. It is worth to notice some sort of
similarity between aspect-level textual explanations and feature-based explanation: though,in
the former case the aspects addressed are usually not directly available in an item or user prole.
In fact,they come from textual information usually related to and users opinions or textual
feedback about specific items. This is what happens in [ 11], where explanations are presented
as aspect-opinion wordclouds based on large-scale user reviews.</p>
        </sec>
        <sec id="sec-4-1-4">
          <title>Visual Explanations</title>
          <p>They help users to get precise and intuitive suggestions. Visually explainable recommendation
are still a relatively new topic in research, thus the integration of visual information and images
into recommender systems is far from being optimized in terms of both explainability and
performance [12]. For example, in [16] visually explainable recommendation are based on
personalized region-of-interest high-lights.</p>
        </sec>
        <sec id="sec-4-1-5">
          <title>Social Explanations</title>
          <p>The involvement of friends in the recommendation process implies a higher level of
personalization into the suggestions themselves, while solving the typical trustworthiness and privacy
problems of relevant-user explanations. Examples include the studies and applications in music
[17], and in product recommendations [22].</p>
        </sec>
      </sec>
      <sec id="sec-4-2">
        <title>4.2. Explainable Recommendation Models</title>
        <p>The second dimension of the classification model proposed by Zhang and Chen [ 12] regards the
specific models used for producing the explanations: namely, explanations given by diferent
types of algorithms. As always, explainable recommendations can either be model-intrinsic or
model-agnostic. In the following paragraphs we provide a short summary of the major types of
explainable recommendation models and we give some examples of relevant related work.</p>
        <sec id="sec-4-2-1">
          <title>Factorization Models</title>
          <p>Latent Factor Models based on Matrix Factorization is a classical ML model for recommender
systems [26]. It learns latent factors to predict the missing ratings in a user-item rating matrix.
Factorization models for explainable recommendations have been proposed in order to explain
the specific latent factor acting user decisions. As an example, Explicit Factor Models [ 11]
links each latent dimension of matrix factorization with an explicit feature among the users
favorite ones. Thus, it can provide explicit recommendations based on the features. Instead,
other studies [27], focus on model-based approaches to generate relevant-user or relevant-item
explanations based on the user-item rating matrix.</p>
        </sec>
        <sec id="sec-4-2-2">
          <title>Topic Modeling</title>
          <p>This kind of explainable recommendations is still based on text information. Topic modeling
refers to a general methodology to classify semantics in documents according to topics clusters.
Explanations are generally displayed in the form of topical word clouds. McAuley and Leskovec
[28] proposed to use a model based on latent factor analysis to understand hidden topics
learned from reviews. Other studies [29] focused on other probabilistic graphic models. Wu
and Ester [29] created an hybrid model based on both collaborative filtering and aspect-based
opinion mining. The algorithm analyses users preferences on item aspects according to reviews
and then predicts the users ratings on diferent ones.</p>
        </sec>
        <sec id="sec-4-2-3">
          <title>Graph-based Models</title>
          <p>Graphs help to define relevant relations among information, so they can be specifically
useful to represent user-user or user-item relationships, especially in social recommendation
scenarios. For example, Park et al. [22] use a graph-based explainable recommendation
algorithm for providing interpretable suggestions thanks to rating and similar users. Other
authors exploited other kinds of graphs: in He et al. [30] a tripartite graph structure allows
to model user-item-aspect relations where an aspect is an item feature generally taken
from user reviews. These relations are constructed for the possible recommendations and
then aspects are ranked and explanations are given to the top-ranked aspects matching
the target user and the recommended item. Heckel et al. [31] instead created explainable
recommendations thanks to over-lapping co-clustering based on user-item bipartite graph [12]:
this approach allows to exploit both clusters of similar users and of items with similar properties.</p>
        </sec>
        <sec id="sec-4-2-4">
          <title>Deep Learning</title>
          <p>Given the higher and higher importance of deep learning techniques, there are many studies
and experiments to adopt a huge variety of them in the explainable recommendations scenario.
In Seo et al. [32] user preferences and item properties are represented through convolutional
neural networks upon review text, so as to attribute specific weights to words in the text
and highlight the relevant ones to provide explainable recommendations. Among the other
various typologies of neural networks used, it is worth to cite the work by Chen et al. [33],
where explainable sequential recommendation are extracted due to memory networks: they
have memory over previous items chosen, so each item in the users interaction history is in a
memory slot and predictions of the new behaviors can be made and explained subsequently, so
as to directly show the way the users previous choices influenced new predictions. That implies
the possibility to set dynamic explainable recommendations. Another interesting approach
comes from capsule networks, namely neural networks empowered with capsule structures
to manage hierarchies. Li et al. [34] use capsule networks to model item aspects and users
viewpoints as logic units, so as to get the users’ rating behaviors. Then, the algorithm, for
each user-item pair, extracts the informative logic units from the reviews so as to infer their
corresponding sentiments.</p>
        </sec>
        <sec id="sec-4-2-5">
          <title>Knowledge Graph-based</title>
          <p>As one of the classical ways to manage knowledge, knowledge graphs can be used for providing
better explanations for the recommended items thanks to their information about users and
items. Catherine et al. [35] proposed a method to provide explanations and recommendation
after producing a rank of the items thanks to information found in knowledge graphs. Instead,
Ai et al. [36] constructed a user-item knowledge graph, so as to get recommendations for a
user as the most similar item under the ”purchase” relation. In this way, they can establish a
series of relations between users and items to orient and explain recommendations.</p>
        </sec>
        <sec id="sec-4-2-6">
          <title>Data Mining</title>
          <p>Among the various possibilities and techniques, Zhang and Chen [12] report that the most
frequently used one is association rule mining. As an example, Davidson et al. [23] introduced
the YouTube video recommendation system, adopting association rule mining to create
associations between couples of videos co-watched within the same session. Then, explanations
are given considering the seed video and the the association rules themselves. The approach
for transparent, scrutable, and explainable recommendations suggested by Balog et al. [25] is
particularly interesting: given a set of tags or keywords characterizing user preferences, they
aimed at inferring preferences and recommendations by aggregating over items associated
with a tag. Consequently, item recommendations can be both transparent and explainable.
They chose to provide recommendations through sentence-level textual explanations, allowing
users to provide feedback on clear and scrutable suggestions. It is worth to mention that this
approach is a framework, which can be generalized to diferent machine learning models.</p>
        </sec>
        <sec id="sec-4-2-7">
          <title>Model Agnostic and Post Hoc</title>
          <p>These approaches are typically used when it is to dificult to include the explanability in
the recommendation model itself. Then, after the recommendations have been provided,
an explanation model generates the explanations according to the previously created
recommendations. As an example exploiting a data mining technique (thus related to the
previous paragraph), Peake and WanH [37] proposed an association rule mining approach. The
method considers the users’transaction history to explain the recommendation: namely, the
association rules help to associate the recommendations themselves with the users’ previous
choices, thus providing explanations to the recommendations.</p>
          <p>Overall, the literature makes a clear distinction among models that are interpretable by design,
and those that can be explained by means of external XAI techniques. This duality could also be
regarded as the diference between interpretable models and model interpretability techniques;
a more widely accepted classification is that of transparent models and post-hoc explainability.
In particular, local interpretation methods explain predictions individually from each
other. Among these [38] we have:
1. Individual conditional expectation (ICE) [39] curves underlie partial dependence plots
(PDPs) and describe how the change in a feature afects the change in the prediction.
2. Local surrogate models, as the Local Interpretable Model-agnostic Explanations model
(LIME) [40] explain a prediction by replacing the complex model with an interpretable
local surrogate.
3. Scoped rules (anchors) [41] are rules that describe which feature values allow the
prediction to be fixed.
4. Counterfactual explanations [42, 43] explain a prediction by examining which features
should be changed to achieve the desired prediction.
5. Shapley values [44] are an attribution method that assigns prediction equally to individual
features.
6. SHAP (SHapley Additive exPlanations) [45] is another computation method for Shapley
values, but unlike these it proposes global interpretation methods based on combining
Shapley values across data.</p>
        </sec>
      </sec>
      <sec id="sec-4-3">
        <title>4.3. Intrinsic, interpretable, white-box models</title>
        <p>Hereinafter, we recall the main interpretable models. We focus on such macro-category of
models due to the fact that the chosen approach for our XRS, DT models, is actually interpretable.
Therefore, we synthetically show the main characteristics of these models, as well as their main
advantages and disadvantages. Finally, we sketch the main motivations that lead us to orient
ourselves towards a decision-tree approach.</p>
        <sec id="sec-4-3-1">
          <title>Linear regression</title>
          <p>A linear regression model predicts the target as a weighted sum of the feature inputs [38].
Linear regression are particularly useful and significant in practice for their linearity. They
have long been used by statisticians, computer scientists, mathematicians and practitioners in
general [38]. They are usually exploited to model the dependence of a regression target  on
some features , and the predicted outcome of an instance is a weighted sum of its features,
where the optimal weights can be estimated by several methods.</p>
          <p>The main advantages of such methods are its linearity and the modeling of the predictions as
a weighted sum makes it transparent how predictions are produced [16]. The modeling of the
predictions as a weighted sum makes guarantees transparency on how predictions are created.
From the mathematic point of view, they are widely accepted and difused methods among
practitioners, and high level of collective experience and expertise is available in the scientific
community [38].</p>
          <p>Nevertheless, the are only useful for representing linear relationships, while any required
nonlinearity or interaction has to be hand-crafted and explicitly provided to the model
[38]. Moreover, they often have no good predictive performance, due to restricted ability to
represent reality in a purely linear way [38]. Finally, there is a possible unintuitive
interpretation of weights, due to the correlations and interactions with all the other involved features [38].</p>
        </sec>
        <sec id="sec-4-3-2">
          <title>Logistic regression</title>
          <p>Linear regression models the probabilities for classification problems with two outcomes. It’s
an extension of the linear regression model for classification problems [ 38]. Therefore, it shows
similar advantages and disadvantages than the linear regression models [38]. Also logistic
regression has been widely used by practitioners in diferent domains and application fields,
and it has issues with restrictive expressiveness and with dealing with interactions, as well
as with limitations in predictive performance. Moreover, logistic regression can sufer from
complete separation, namely the impossibility tobe trained in the case where there is a feature
that would perfectly separate the two classes.</p>
          <p>GLM and GAM
Generalized Linear Models (GLMs) and Generalized Additive Models (GAMs) are heterogeneous
generalization models of regression, useful for modeling real-life situations. They can be applied
in situations where the classical regression approaches fail or its assumptions are violated [38].
In the case of GLM, they can be applied where the input features do not follow a Gaussian
distribution, which concretely happens in many cases in reality [38]. Instead, GAMs deal with the
cases of nonlinearities, not tackled by the classical linear models. GAMs relax the restriction that
the relationship must be a linear weighted sum, assuming that the outcome can be modeled by
arbitrary functions that can be involved for each features [38]. Then, such models are generally .
In general, these models are highly flexible and useful for making predictions and
inferences in many application cases and contexts. These methods are highly difused in the
scientific community and updated methods are often released allowing to make inferences for
heterogeneous problems and applications [38]. Though, such models sufer from a significant
reduced interpretability, as compared with the classical linear models, and they strongly rely on
assumptions about the data generating process, which have to be respected for the validity of
the model and its interpretation of the weights [38].</p>
        </sec>
        <sec id="sec-4-3-3">
          <title>Decision-trees</title>
          <p>Already previously introduced in this Chapter, DT models are useful for solving many of the
presented issues, especially in the case of linear regression and logistic regression models,
which have problems in situations where the relationship between features and outcome is
nonlinear or where features interact with each other [38]. Tree-based models work through an
iterative process of multiple splitting of the dataset, according to certain cutof values in the
features. Thus, they are inherently interpretable due to the tree structure itself, while they are
also able to capture interactions between features in the data, as well as to efectively explain
and visualize their output results. The main disadvantages are related to their inability to deal
with linear relationships, as well as their lack of smoothness and unstability [38]. Moreover,
their interpretability is reduced in the case of a significant increase in the tree depth [38].</p>
        </sec>
        <sec id="sec-4-3-4">
          <title>Decision rules</title>
          <p>Decision rules are probably the most interpretable models. IF-THEN statement consist of a
condition (antecedent) and a prediction and, in simple cases, they semantically resembles natural
language [16]. Then, they are usually easy to interpret, expressive, robust and compact [38].
Nevertheless, in the literature they are used only for classification [ 38], resulting in applications
for restricted classes of problems. Moreover, they necessarily require categorical features and,
as in the case of decision-trees, they have issues in describing linear relationships.</p>
        </sec>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusions</title>
      <p>In this study we strived to provide an overview of Explainable AI in the field recommender
systems. We are aware that many other issues could have been addressed, specifically regarding
the pros and cons of the wide set of methods in the literature, as well as the many evaluation
techniques of both RS and explainability. As a general consideration to conclude our study, we
definitively agree that the evolution of such systems necessarily involve a synergy between the
empowerment of the models’ performances and the emergent human-AI interaction perspective.
We also conclude that much more work and efort should be dedicated to search and adopt a
widely accepted, pre-defined and formally circumscribed definition of explainability and its
related concepts. While there are several studies proposing both qualitative and quantitative
definitions, it should be necessary to both choose and apply them to the field of recommender
systems: this investigation could be the aim of a future study. Indeed, there are many further
challenges and possible future directions to explore for this fascinating topic: among them, the
issues related to the dificulties in quantiatively and formally measuring explainability, which
will be a key step to reach and exploit the full potentialities of explainable and interpretable
recommender systems for heterogeneous business and industrial domains. Moreover, the rise
of explainable intelligent recommender systems will increasingly require to further investigate
the broader impact of explainability on decision-making processes, so as to understand their
full influence in organizational context and applications. We hope that our work can contribute
to help researchers, scholars and practitioners to understanding the concept of explainable
recommendation, the main approaches in the literature and their potentialities for business or
industrial applications.
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