=Paper= {{Paper |id=Vol-3121/paper8 |storemode=property |title=ConceptSuperimposition: Using Conceptual Modeling Method for Explainable AI |pdfUrl=https://ceur-ws.org/Vol-3121/paper8.pdf |volume=Vol-3121 |authors=Wolfgang Maass,Arturo Castellanos,Monica Chiarini Tremblay,Roman Lukyanenko,Veda C. Storey |dblpUrl=https://dblp.org/rec/conf/aaaiss/0002CTLS22 }} ==ConceptSuperimposition: Using Conceptual Modeling Method for Explainable AI== https://ceur-ws.org/Vol-3121/paper8.pdf
ConceptSuperimposition: Using Conceptual Modeling
Method for Explainable AI
Wolfgang Maass1,2 , Arturo Castellanos3 , Monica Chiarini Tremblay3 ,
Roman Lukyanenko4 and Veda C. Storey5
1
  Saarland University, Germany
2
  German Research Center for Artificial Intelligence (DFKI), Germany
3
  William & Mary, Williamsburg, VA, USA
4
  HEC Montréal, Montreal, Québec, Canada
5
  Georgia State University, Atlanta, GA, USA


                                         Abstract
                                         Many artificial intelligence (AI) applications involve the use of machine learning, which continues to
                                         evolve and address more and more complex tasks. At the same time, conceptual modeling is often applied
                                         to such real-world tasks so they can be abstracted at the right level of detail to capture and represent
                                         the requirements for the development of a useful information system to support an application. In
                                         this research, we develop a framework for progressing from human mental models of an application
                                         to machine learning models via the use of conceptual models. Based on the framework we develop a
                                         novel ConceptSuperimposition method for increasing explainability of machine learning models. We
                                         illustrate the method by applying machine learning to publicly available data from the Home Mortgage
                                         Disclosure Act database which contains the 2020 mortgage application data collected in the United States.
                                         The machine learning task is to predict whether a mortgage is approved. The results show how the
                                         explainability of machine learning applications can be improved by including domain knowledge in
                                         the form of a conceptual model that represents a mental model, instead of relying solely on algorithms.
                                         Preliminary results show that including such knowledge can help advance the explainability problem.

                                         Keywords
                                         Artificial Intelligence, Machine Learning, Conceptual Modeling, Model Performance, Mental Models,
                                         Framework for Mental Models and Conceptual Models for Machine Learning,, ConceptSuperimposition




1. Introduction
Machine learning consists of methods that use data and algorithms to build models that make
inferences about an application from provided examples [1]. Both the opportunities and limita-
tions of machine learning are rooted in its reliance on building models from data and, therefore
In A. Martin, K. Hinkelmann, H.-G. Fill, A. Gerber, D. Lenat, R. Stolle, F. van Harmelen (Eds.), Proceedings of the AAAI
2022 Spring Symposium on Machine Learning and Knowledge Engineering for Hybrid Intelligence (AAAI-MAKE 2022),
Stanford University, Palo Alto, California, USA, March 21–23, 2022.
$ wolfgang.maass@iss.uni-saarland.de (W. Maass); arturo.castellanosbueso@mason.wm.edu (A. Castellanos);
Monica.Tremblay@mason.wm.edu (M. C. Tremblay); roman.lukyanenko@hec.ca (R. Lukyanenko);
vstorey@bellsouth.net (V. C. Storey)
€ https://iss.uni-saarland.de (W. Maass)
 0000-0003-4057-0924 (W. Maass); 0000-0002-7477-7379 (A. Castellanos); 0000-0003-1289-6679 (M. C. Tremblay);
0000-0002-8735-1553 (V. C. Storey)
                                       © 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
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    Workshop
    Proceedings
                  http://ceur-ws.org
                  ISSN 1613-0073
                                       CEUR Workshop Proceedings (CEUR-WS.org)
on the quality of the data used to train and test the models [2]. As our society’s dependence
on machine learning grows, it is important to ensure that machine learning models perform
well and are interpretable and transparent. This is a tradeoff that is often augmented by opaque
transformations in the input data (i.e., feature engineering), which makes it challenging to
assess the effectiveness of the input data on the outcome [3]. Numerous challenges persist,
including biases, discrimination, lower performance, lack of transparency, and explainability.
While popular approaches have emerged for explaining predictions of classifiers (Layerwise
relevance propagation, Local Interpretable Model-Agnostic Explanations, and many others) [4],
there are criticisms about explanations being dependent on the choice of hyperparameters and
how these models have different explanations for similar instances in the data. The objective of
this research is to investigate how to improve machine learning explainability by incorporating
domain knowledge of the application. The contribution is to propose a framework for progress-
ing from human mental models to machine learning models through the use of conceptual
models. Based on the framework we develop a ConceptSuperimposition method for increasing
explainability of machine learning models. We illustrate the application of this method in the
home mortgage domain.


2. Machine Learning and Conceptual Modeling
Supervised learning guides the learner in acquiring knowledge in a domain through examples,
so new cases can be handled in a manner most appropriate based on the knowledge learned
from similar cases. Modern supervised machine learning has been taking advantage of the
availability of data, and developing methods and techniques (e.g., deep learning neural networks,
reinforcement learning), which rely on large volumes of high-quality data for performance
improvement. The increase in the use of complex machine learning models has brought about
challenges in explaining the decision logic of these models. Transparency research in AI is a
growing societal concern and a growing research area [4, 5]. A generally overlooked approach
to explainability, however, is how to incorporate domain knowledge that a user or designer
might possess. This knowledge would manifest itself in mental models which contribute to the
development of conceptual models that support the interpretation of machine learning models
and outcomes. Conceptual modeling formally describes “some aspects of the physical and social
world around us for the purposes of understanding and communication” [6, p. 2]. Humans use
conceptualizations about domains for representing specific or abstract situations in domains.
Recent research has proposed combining conceptual modeling with artificial intelligence or,
specifically machine learning [7, 8, 9, 10, 11, 12, 13]. The main argument is that doing so can
provide reliable rules about the domain without being dependent on extracting them from
the data. Despite these efforts, conceptual models are rarely used in the process of machine
learning. At the same time, machine learning invariably relies on human mental models –
representations of reality in the minds of data scientists or users of machine learning models,
who either develop or interpret machine learning solutions, in light of their mental models.
Unlike conceptual models, mental models are not explicit, and hence may contain biases.
   Research in psychology and other disciplines (e.g., philosophy, cognitive science), dealing
with decision-making, has argued that, when making decisions, humans construct one or more
                    Implicit/tacit knowledge                                                                  Explicit knowledge

                       Data Scientists                                    Conceptualizations                                   ML-based Information systems


                        Mental Models                                         Conceptual Models                                                   AI/ML Models

                     Subjective/Acquired                                          Shared                                                            AI / ML
                         knowledge                                             understanding                                                    representations


                      Doyle & Ford 98
                      - Conceptual                                       Wand & Weber 02                                               -   Incl. feature engineering
                        (vs. mental image)                               - Grammar, method, script, context                            -   Architecture design
                      - Representation                                   - Ontologies                                                  -   Model selection and optimization
                        (vs. cognitive processes)                                                                                      -   Performance evaluation




                                                        Entities and                                          Data (representations)
                                                          events                                              of entities and events

                                                    Application Domain                                        (Raw) Data on Being


                                                     Physical World                                              Data Sphere




Figure 1: Framework for Mental Models and Conceptual Models for Machine Learning


mental models of a domain [14, 15]. A mental model is a representation of a possible state of
affairs in reality [15]. Mental models are the central mechanism for coping with diversity and
change, allowing someone to act in an informed and effective manner. In a typical machine
learning scenario, we may encounter different customers purchasing goods or services from
a store. However, we can reduce this complexity by constructing a handful of mental models
that segment customers (e.g., loyal repeat customer, high volume customers, one-time buyer).
Mental models, are important for problem-solving, including in ML contexts, but are also prone
to bias and error. If left unchecked, the biases arising from the suboptimal formation and
use of mental models, could affect the judgment of machine learning developers, and result
in a variety of machine learning problems. Hence, we seek to augment mental models with
conceptual models so the representations will be more formal and externalized and better
equipped at mitigating the cognitive biases inherent in mental models. If, in reality, mental
models are inconsistent, or even contradictory, with the machine learning model or the data, it
is possible that: (1) subjects have selected inadequate conceptual statements for a situation, (2)
perception and measurement about reality are distorted, or (3) conceptual statements are flawed.
In this paper we, therefore, propose improving explainability of complex machine learning
models based on the externalizing the mental models via conceptual models. Mental models
[14] can represent components, states and structural relations, basic operational rules and on
general scientific principles, events and processes, and ontological knowledge. They represent
individual knowledge extracted from either physical or abstract domains that is used for various
cognitive tasks, including understanding, communication, navigation, and decision making.
Mental models are often understood as surrogate models used for simulation and prediction as
well as a means for constructing advanced mental models [16]. Conceptual models are shared
representations expressed in various forms, such as texts and graphics. According to model
theory, conceptual models are projected and abbreviated representations made by human experts
and used for a purpose [17]. In contrast, machine learning models are statistical abstractions
derived by algorithmic fitting mathematical functions to data according to a purpose given
by an objective functions. Data used for model fitting and also for construction of conceptual
models are representations of domains themselves. In essence, mental models are individually
constructed, conceptual models are socially constructed, and machine learning models are
algorithmically constructed. Designing information systems means that all three model types
are synchronized and balanced by negotiation for finding a satisfiable equilibrium between
these models. (See Figure 1). A gap exists between mental models and conceptual models
versus machine learning models because internal representations of machine learning models
are generally inaccessible. Thus, research is needed on interpretability and explainability of
machine learning models as a means for alignment of all three model types.


3. ConceptSuperimposition Method
Following the Framework for Mental Models and Conceptual Models for Machine Learning
(cf. Figure 1), we advance a new method – ConceptSuperimposition. This is a method which
extends our early work on Superimposition method. Superimposition adds structural semantic
information to the outputs of machine learning to support explainability [10]. While this
information is absent in current ML practice, it is routinely employed by humans to understand
their day-to-day experiences.
   As per our Framework, a machine learning model is a model of some domain (e.g., credit card
fraud, image classification, online auctions). The machine learning model is a set of rules for
estimating a value of interest or discriminating among the cases of interest based on previously
provided domain examples.
   Superimposition maps the output of machine learning models (i.e., the features, rules and
transformation functions) onto a conceptual model of the domain. The method suggests indi-
cating inside the conceptual model information about the rules of the machine learning models.
This step depends on the type of machine learning model. For example, if a regression model is
used, these rules can be represented as feature weights or feature coefficients. These coefficients
can be appended to the attributes in the conceptual model, or the attributes can be highlighted
differently to indicate the different relative importance of each attribute. Features are conceived
and defined based on domain knowledge. For instance, the feature 𝑝𝑟𝑜𝑝𝑒𝑟𝑡𝑦_𝑣𝑎𝑙𝑢𝑒 is necessary
for evaluating a loan application. A conceptual model clusters features into concepts (e.g., classes,
entity types). The relations (e.g., association, type of, part of) provide connections between the
concepts. Generally, concepts that are directly connected via a relation are semantically closer
to each other than indirectly connected concepts.
   The final step of the Superimposition method involves analyzing the resulting conceptual
model to gain a clearer understanding of the underlying rules machine learning models use
to makes its decisions, and to identify opportunities to improve the machine learning model
further.
   A key limitation of the early version of the Superimposition method is in the lack of rep-
resentation of concepts and their relationships. The method merely attached feature weights
to the conceptual model. Yet, the understanding of the impact of the concepts (e.g., entity
types) on the target is also of critical importance. Furthermore, the early formulation of the
Superimposition lacked formalization. We address both shortcomings in the formalized and
holistic ConceptSuperimposition method. We propose a ConceptSuperimposition method for
assessing the alignment between conceptual models and machine learning models. This method
consists of three steps:
   1. Marginal contribution: determination of Shapley values for predicting features
   2. Feature Contribution: local contribution of outcome features associated with outcome
      concepts.
   3. Concept Contribution: local contributions on outcome concepts.

3.1. Marginal contribution
Machine learning (ML) models are globally fitted to datasets. Often, ML models are black boxes
without direct access to feature contributions to outcomes. Therefore, simpler models (surrogate
models) are locally fitted ex-post to ML models. Surrogate models provide information on
local contribution of features to outcomes (e.g., LIME or SHAP [18]). SHAP (Shapley Additive
Explanation) values are Shapley values of a conditional expectation function of the machine
learning model, i.e., the fitted model is used for determining local contribution of single features
to an outcome.
    Shapley values formalize coalition games and determine additive marginal contributions of
single players to an overall payoff of the coalition of players. They are defined by an operator 𝜑
that assigns for each game 𝑣 a vector of payoffs 𝜑(𝑣) = (𝜑1 , ..., 𝜑𝑛 ). 𝜑𝑖 (𝑣) is player i’s marginal
and additive contribution to the outcome of a game over all permutations with all other players
[19]. Shapley values are locally accurate, i.e. match the original model 𝑓 (𝑥), is not affected
by missing values and are consistent wrt. unequality relation between two models 𝑓 (𝑥) and
𝑓 ′ (𝑥) [18]. The Shapley value of a feature 𝑖 is a weighted mean of its marginal value of feature
𝑖, averaged over all possible subsets of features:
                           ∑︀              |𝑆|!(|𝐹 |−|𝑆|−1)!
                    𝜑𝑖 =        𝑆⊆𝐹 ∖{𝑖}          |𝐹 |!      [𝑓𝑆∪{𝑖} (𝑥𝑆∪{𝑖} ) − 𝑓𝑆 (𝑥𝑆 )]

   with 𝐹 the set of all features and 𝑓𝑆∪{𝑖} with a model trained with feature 𝑖 and 𝑓𝑆 (𝑥𝑆 )
without. SHAP values determine additive contributions of input features 𝑋 on the prediction
of an output feature 𝑦, i.e., 𝑦 = 𝑓 (𝑋), agnostic to the machine learning model used with 𝑓 the
original model and Φ a vector of all Shapley value 𝜑𝑖 for all independent features. Input feature
𝑥 ∈ 𝑋 is transformed into simplified vector 𝑧 ∈ 𝑍 with 𝑧 ∈ {0, 1}, i.e., SHAP value 𝜑𝑖 𝑧𝑖 is
zero if feature 𝑧𝑖 is missing and 𝜑𝑖 carries the whole marginal contribution of a feature to an
outcome otherwise.

3.2. Feature contribution
We now use marginal contributions for defining conceptually generalized contributions of input
features. Given a conceptual model 𝐶𝑀 with a bidirectional mapping of concepts to all features
in 𝑂. For each concept 𝑐 in 𝐶𝑀 , a n-ary concept contribution vector 𝑔𝑐𝑜 is constructed by
Hadamard product of Shapley vector Φ and input vector 𝑥𝑐 for an output feature 𝑜 in output
concept 𝑂. 𝑥𝑐 has only feature values associated with concept 𝑐 and value 0 everywhere else.
Vector 𝑔𝐶𝑜 is the contribution of all input concepts on an outcome feature 𝑜.


                                  𝑔𝑐𝑜 = Φ ∘ 𝑥𝑐 and 𝑔𝐶
                                                    𝑜 =Π     𝑜
                                                        𝑐∈𝐶 𝑔𝑐 ∘ 1𝑛
   First the average of all SHAP values per input feature is calculated. 𝑔¯𝑜𝑐 is the normalized value
for all 𝑔𝑐𝑜 , ie., relative contribution of feature to an outcome feature.
   By normalization over all input data 𝑋, 𝑔¯𝑜𝑐 is determined that provides relative contributions
of each feature of concept 𝑐 with respect to output feature 𝑜, ie. input features are superimposed
on 𝑐 relative to 𝑜.

3.3. Concept contribution
Concept contributions depend on the type of outcome features, i.e. application of classification
or regression. For binary classification, we define 𝑓𝑂 (𝑋) as the sum of contributions of all
feature contributions of input concepts on a feature 𝑜 in output concept 𝑂 except contributions
of features in 𝑂 due to implicit strong collinearity with the output feature 𝑜:

                                                        ¯𝑜⊤
                                              ∑︀
                                  𝑓𝑂 (𝑋) =      𝑐∈𝐶∖{𝑂} 𝑔 𝑐 · 1𝑛

  For regression, feature contributions are evaluated relative to features of concept 𝑂. The
mean of output features except outcome feature 𝑜 are calculated (𝜔). Only those input features
are considered with a larger feature contribution than 𝜔.

                                                   ¯𝑜⊤
                                         ∑︀
                              𝑓𝑂 (𝑋) =     𝑐∈𝐶∖{𝑂} 𝑔 𝑐 · (1/𝜔𝑛 − 1)

  Concept contributions are the weighted summation of all summed up feature contributions.
The weight 𝑤 is the count of all features minus selected features plus 1. This accounts for
decreasing feature contribution values with the number of features. Only features with strong
feature contributions are selected. If, for instance, only one input feature is selected, feature
contributions are not affected while a large 𝑤 will reduce feature contributions on concept
contributions.
                                                    ∑︀
                                  𝜅𝑂 (𝑋) = 1/𝑤 *       𝑜∈𝑂 𝑓𝑂 (𝑥)

   It shall be noted, that 𝜅𝑂 (𝑋) depends on the type of prediction. Values for 𝜅𝑂 (𝑋) for
classifications can be compared with one another and for regression respectively but 𝜅𝑂 (𝑋)
cannot be compared between classification and regression.
   𝜅𝑂 is determined for permutations over all homogeneous concepts 𝑐 ∈ 𝐶, i.e., 𝜅𝑂 is deter-
mined for all concepts 𝑐 ∈ 𝐶. This provides a measure for local contributions of input concepts
on a homogeneous concept given input 𝑥. Concept contributions on heterogeneous concepts
requires a functional model that integrates features 𝑜 ∈ 𝑂.
   A concept 𝑐 with little concept contribution 𝜅𝑂 (𝑋) on an output concept 𝑐𝑝 has a weak
conceptual relation with 𝑐𝑝 , i.e., the outcome is only weakly affected by the presence of 𝑐𝑖 .
Conceptual relations are directed form 𝑐𝑖 to 𝑐𝑝 due to the game-theoretic construction of Shapley
values. The semantics of conceptual relations are constrained by the concepts.
Figure 2: ConceptSuperimposition


3.4. ConceptSuperimposition
Feature contributions provide a directed similarity measure between input features and output
features analog to local similarity measures in social networks (e.g., [20]). Feature contributions
are consistent with the properties of additive feature attribution methods, ie. local accuracy,
missingness and consistency [18].
   Concept contribution abstracts from features to concepts and determines directed contri-
butions between directly connected concepts (cf. Game 1 [21]). Additive feature attribution
properties are not maintained because lack of output values on concept level. Therefore, concept
contribution is a score that measures directed local contribution of one concept to another
derived by feature contributions.
   We call the attribution of concepts by concept contributions ConceptSuperimposition. It closes
a cycle between conceptual models, data and ML models that consists of three steps. First,
conceptual models provide constraints on data that is considered for ML model development.
Second, data is used for constructing ML models. Concept contributions elevate patterns found
by ML models to a conceptual level that is fed back to conceptual models. Thus, concept contri-
butions can be used for confirmation of conceptual models, i.e., for evaluation whether identified
patterns from data are consistent with conceptual models and, thus, shared understanding of
actors involved.


4. Example
To illustrate the application of ConceptSuperimposition, we use publicly avail-
able data (10 GB) from the Home Mortgage Disclosure Act (HMDA) website
(https://www.consumerfinance.gov/data-research/hmda/). This data contains the 2020
mortgage application data collected in the U.S. under the Home Mortgage Disclosure Act. The
dataset consists of a sample of 3,481,348 applications for single-family, principal residence
Figure 3: Conceptual Model for the HMDA loan dataset


purchases, i.e. 5% of the HMDA dataset. The data is comprised of 99 variables including
payment history, credit history, credit mix, demographics, income, and characteristics of the
loan (e.g., purpose of the loan, interest rate, total loan costs), and census data (e.g., census tract,
tract population).The target variable is to predict whether a mortgage is originated (target = 1)
or denied (target = 0). Of the sample applications in the dataset, 44.3% of the applications were
for refinancing, 32.42% were for home purchase, 14.96% for cash-out refinancing. 83.56% of the
applications were approved. 69.99% of the applications belonged to White applicants and 6.15%
to Black or African American applicants (approval rate for Whites was 85.33% and Blacks was
71.51%). (see Figure 3 with a fragment of the conceptual model).
   For comparison of concept contributions, data needs to be standardized. Categorical features
are transformed by one-hot-encoding except output feature 𝑦. After data engineering, the
dataset contains 52 features from which 20 are associated to the concept applicant, 14 to the
concept loan and 18 to the concept 𝑙𝑜𝑎𝑛_𝑎𝑝𝑝𝑙𝑖𝑐𝑎𝑡𝑖𝑜𝑛.

4.1. Feature Contribution
All five concepts are used for making a binary decision on loan applications, i.e. concept Decision
with a feature 𝑎𝑐𝑡𝑖𝑜𝑛_𝑡𝑎𝑘𝑒𝑛. We use XGBoost Classification for predicting 𝑎𝑐𝑡𝑖𝑜𝑛_𝑡𝑎𝑘𝑒𝑛.
Performance metrics for the model on the test dataset are: accurary (0.995), precision (0.999),
recall (0.995), F-measure (0.997).
  For all three concepts, i.e., Applicant, Loan and LoanApplication, we determined feature
contributions on the concept Decision modeled by a single feature (𝐴𝑐𝑡𝑖𝑜𝑛𝑇 𝑎𝑘𝑒𝑛) and three
permutations, i.e. (1) LoanApplication and Loan on Applicant, (2)) Applicant and Loan on
LoanApplication and (3) Applicant and LoanApplication on Loan.

4.2. Concept contributions
For each input concept (here: applicant, loan application, and loan), concept contributions are
determined. As a result, 𝑎𝑝𝑝𝑙𝑖𝑐𝑎𝑛𝑡 provides a strong concept contribution 𝜅𝑎𝑝𝑝𝑙𝑖𝑐𝑎𝑛𝑡 (𝑋) of
0.610 to LoanApplication while 𝑙𝑜𝑎𝑛𝑎𝑝𝑝𝑙𝑖𝑐𝑎𝑡𝑖𝑜𝑛 provides a relatively high concept contribution
𝜅𝑙𝑜𝑎𝑛𝑎𝑝𝑝𝑙𝑖𝑐𝑎𝑡𝑖𝑜𝑛 (𝑋) of 3.177 to 𝑙𝑜𝑎𝑛 (cf. Table 2). We only used one feature per outcome concept
for simplicity.
  For the HDMA dataset, concept contributions indicate a strong directed connection from
applicant to 𝑙𝑜𝑎𝑛_𝑎𝑝𝑝𝑙𝑖𝑐𝑎𝑡𝑖𝑜𝑛 (cf. Figure 4). This supports the establishment of a relation
between these two concepts. Same holds for 𝑙𝑜𝑎𝑛𝑎𝑝𝑝𝑙𝑖𝑐𝑎𝑡𝑖𝑜𝑛 to 𝑙𝑜𝑎𝑛 and 𝑙𝑜𝑎𝑛 to 𝑎𝑝𝑝𝑙𝑖𝑐𝑎𝑛𝑡.
The latter concept contribution is not captured by the original conceptual model (cf. Figure 3).
                                                                                            Loan
 Concepts                                 Decision (C)              Applicant (C)           Application      Loan (R)
                                                                                            (R)
                  Features
                  (total 21)               ActionTaken               PurchaseType           PropertyValue   LoanAmount

                  income                       -0.014                   -0.014                      0.161      0.387
                  purchaser_type                0.266                    0.265
 Applicant
                  age                                                                               0.449
                  loan_term                    0.081                    -0.081
                  origination_charges          0.073                     0.073                                 0.868
 Loan
                  loan_type                    0.034                     0.034                                 0.567
 Application
                  property_value               0.037
                  loan_product_type                                                                            1.742
                  loan_amount                  -0.025                   -0.026
 Loan             rate_spread                  -0.026                   -0.026
                  total_loan_costs              0.160                    0.160                                -0.838
Table 1
Feature contributions for two outcome concepts based on classification (C) and two by regression (R)

                 𝜅𝑐 (𝑥)               Applicant (C)             LoanApplication (R)         Loan (R)
                 Applicant                  1                         0.610                  0.387
                 LoanApplication         0.0262                         1                    3.177
                 Loan                    0.108                         mc                      1
Table 2
Concept contributions 𝜅𝑐 (𝑥)


                          APPLICANT           LOAN_APPLICATION                            LOAN

                    ApplicantID             ApplicantID                          LoanID
                    applicant_sex           Loan_term                            Loan_amount
                    Income                  Origination_charges                  Rate_spread
                    purchaser_type          Loan_type                            Total_loan_costs
                    age                     Property_value
                                            Loan_product_type




Figure 4: ConceptSuperimposition onto HMDA conceptual model


   This is an example how concept contributions 𝜅𝑝 can be leveraged for automatically scru-
tinization of conceptual models associated with datasets and database implementations. In
this example, we found support for a revised conceptual model with relations between loan
towards applicant. It shall be noted that concept contributions do not provide link semantics,
such as cardinalities or type of links. Proposals for revisions based ConceptSuperimposition
help domain experts and ML developers and business analysts to align conceptual models with
data and ML models.
5. Conclusion
This research proposes that ML models and conceptual models can be used effectively for
analyzing prior conceptual knowledge used for data selection. A conceptual model represents
agreed-upon domain knowledge. In this work we first provide a theoretical basis for using
conceptual models in the domain of explainable AI. Within use the Mental Models Framework
to develop a formalized and holistic ConceptSuperimposition method. The method is formalized
and its utility is demonstrated in the application to the home mortgage domain.
   The new ConceptSuperimposition method can be used to improve ML explainability and
should be especially effective for situations where there is insufficient data to extract all relevant
domain knowledge in a data-driven manner. Future work is needed to apply the framework
and method to other examples in other domains. In future studies we hope to evaluate the
increased transparency due to the new method by conducting interviews, focus groups, and
laboratory experiments with the stakeholders looking to understand the decision logic behind
machine learning models. We also plan to investigate the benefit of this method together with
other existing approaches to explainability. We do not position this method as an alternative,
rather, we believe it could complement existing methods by extrapolating their outputs onto
the conceptual models.
   In future work, we will address the integration of concept contributions for classification and
regression.


References
 [1] P. McCorduck, C. Cfe, Machines who think: A personal inquiry into the history and
     prospects of artificial intelligence, CRC Press, 2004.
 [2] V. S. Sheng, F. Provost, P. G. Ipeirotis, Get another label? improving data quality and
     data mining using multiple, noisy labelers, in: Proceedings of the 14th ACM SIGKDD
     international conference on Knowledge discovery and data mining, 2008, pp. 614–622.
 [3] M. C. Thrun, A. Ultsch, Swarm intelligence for self-organized clustering, Artificial
     Intelligence 290 (2021) 103237.
 [4] A. Adadi, M. Berrada, Peeking inside the black-box: a survey on explainable artificial
     intelligence (xai), IEEE access 6 (2018) 52138–52160.
 [5] A. B. Arrieta, N. Díaz-Rodríguez, J. Del Ser, A. Bennetot, S. Tabik, A. Barbado, S. García,
     S. Gil-López, D. Molina, R. Benjamins, et al., Explainable artificial intelligence (xai):
     Concepts, taxonomies, opportunities and challenges toward responsible ai, Information
     Fusion 58 (2020) 82–115.
 [6] J. Mylopoulos, Conceptual modeling and telos, in: P. Loucopoulos, R. Zicari (Eds.),
     Conceptual Modeling, Databases, and CASE: An Integrated View of Information Systems
     Development, Editors John Wiley & Sons, 1992, pp. 49–68.
 [7] W. Maass, V. C. Storey, Pairing conceptual modeling with machine learning, Data &
     Knowledge Engineering (2021) 101909.
 [8] U. Reimer, D. Bork, P. Fettke, M. Tropmann-Frick, Preface of the first workshop models in
     ai., in: Modellierung (Companion), 2020, pp. 128–129.
 [9] D. Bork, A. Garmendia, M. Wimmer, Towards a multi-objective modularization approach
     for entity-relationship models., in: ER Forum/Posters/Demos, 2020, pp. 45–58.
[10] R. Lukyanenko, A. Castellanos, V. C. Storey, A. Castillo, M. C. Tremblay, J. Parsons, Super-
     imposition: augmenting machine learning outputs with conceptual models for explainable
     ai, in: International Conference on Conceptual Modeling, Springer, 2020, pp. 26–34.
[11] R. Lukyanenko, A. Castellanos, J. Parsons, M. C. Tremblay, V. C. Storey, Using concep-
     tual modeling to support machine learning, in: International Conference on Advanced
     Information Systems Engineering, Springer, 2019, pp. 170–181.
[12] W. Maass, I. Shcherbatyi, Inductive discovery by machine learning for identification of
     structural models, in: J. Trujillo, K. C. Davis, X. Du, Z. Li, T. W. Ling, G. Li, M. Lee (Eds.),
     Conceptual Modeling - 37th International Conference, ER 2018, Xi’an, China, October
     22-25, 2018, Proceedings, volume 11157 of Lecture Notes in Computer Science, Springer,
     2018, pp. 545–552.
[13] W. Maass, I. Shcherbatyi, Data-driven, statistical learning method for inductive confir-
     mation of structural models, in: T. Bui (Ed.), 50th Hawaii International Conference on
     System Sciences, HICSS 2017, Hilton Waikoloa Village, Hawaii, USA, January 4-7, 2017,
     ScholarSpace / AIS Electronic Library (AISeL), 2017, pp. 1–10.
[14] D. Gentner, A. L. Stevens, Mental models, Psychology Press, 2014.
[15] P. N. Johnson-Laird, Mental models: Towards a Cognitive Science of Language, Inference,
     and Consciousness, Harvard Univ Press, Cambridge, MA, 1983.
[16] P. N. Johnson-Laird, Comprehension as the construction of mental models, Philosophical
     Transactions of the Royal Society of London. B, Biological Sciences 295 (1981) 353–374.
[17] H. Stachowiak, Allgemeine modelltheorie, Springer, 1973.
[18] S. M. Lundberg, S.-I. Lee, A unified approach to interpreting model predictions, in:
     Proceedings of the 31st international conference on neural information processing systems,
     2017, pp. 4768–4777.
[19] L. S. Shapley, A value for n-person games, in: H. W. Kuhn, A. W. Tucker (Eds.), Contribu-
     tions to the Theory of Games (AM-28), Volume II, Princeton University Press, 2016, pp.
     307–318.
[20] L. Lü, T. Zhou, Link prediction in complex networks: A survey, Physica A: statistical
     mechanics and its applications 390 (2011) 1150–1170.
[21] T. P. Michalak, K. V. Aadithya, P. L. Szczepanski, B. Ravindran, N. R. Jennings, Efficient
     computation of the shapley value for game-theoretic network centrality, Journal of
     Artificial Intelligence Research 46 (2013) 607–650.