InvestigationintoExplainableRegressionTreesforConstructionEngineeringApplications.pdf

Investigation into Explainable Regression Trees for
Construction Engineering Applications

Serhii Naumets1 and Ming Lu, M.ASCE2

Abstract: The logic of an artificial intelligence (AI) model derived from machine learning algorithms and domain-specific data is analogous
to an expert’s perception of a complex problem. Human insight based on know-how and experience also provides the best clue to verify such
analytical models generalized from data. To facilitate the acceptance and implementation of AI by industry professionals, we explored the
least complicated form of model that still is sufficient to represent the complexities of real-world problems. This research established
a framework to apply the M5P model tree in the context of producing explainable AI for practical applications. The explanatory information
derived from M5P (a decision tree with linear regressions at leaf nodes) is instrumental in explaining how the more complicated AI model
reasons for the same problem, illuminating the sufficiency of problem definition and data quality, and distinguishing valid submodels from
invalid ones in the obtained model tree. A steel fabrication labor cost–estimating case and a concrete strength development case were given
for method validation and application demonstration. DOI: 10.1061/(ASCE)CO.1943-7862.0002083. © 2021 American Society of Civil
Engineers.

Introduction

The most challenging and crucial undertaking in construction en-
gineering and management is planning the execution of an activity
in the field within limited budgets while maximizing gains in pro-
ductivity and cost-efficiency (Halpin and Riggs 1992). Planning
entails the prediction of crew performances in terms of time and
cost that is a subject to activity-specific contexts and constraints.
Thus, regression-type model development for input–output map-
ping based on historical data in a particular application problem is
warranted in support of making decisions in construction engineer-
ing. Conventional regression techniques and emerging artificial in-
telligence (AI), such as artificial neural networks (ANNs), have
been applied to generalize hidden patterns and implicit relation-
ships from historical data, ultimately resulting in a valid prediction
model to assist the planner in the analysis of new cases in the prob-
lem domain. In construction engineering applications, in addition
to the prediction result that is sufficiently accurate, the decision
maker also demands the revelation of an AI model’s reasoning
logic in to cross-check personal experiences and gut feeling.
In addition, the historical data used for AI modeling in reality are
almost certain to contain noise (i.e., incomplete or inconsistent data
collected from the real world due to human errors or system errors).

In practice, the construction plan (i.e., a cost budget for a given
scope of work) ultimately is presented to the operations personnel
as a baseline to control field execution. To turn over the plan to the
operations personnel, the planner (i.e., the estimator) needs to ex-
plain and communicate (1) how the plan was derived, i.e., how the

AI model reasoned in relating the input factors to the predicted out-
put, (2) how much noise was present in the learning data that could
lower the prediction performance of the AI model, and (3) given
a specific context of the problem, the trustworthiness of a partic-
ular prediction compared with the overall averaged accuracy of
the AI model. Therefore, without a doubt, the explainability of an
AI model in support of decision making in construction engineer-
ing and management is important for its acceptance and successful
implementation.

Explainable artificial intelligence (XAI) is formalized in com-
puting research in an attempt to develop a second model to explain
the precise logic in the problem domain based on learning, while
still delivering sufficient predicting accuracy as the primary AI
model (Gunning 2016). It is a new AI application paradigm in con-
struction engineering and management.

Classification models are used more frequently in application
fields such as medicine, justice, social media, and advertisement
(Rudin 2019). In the computer vision field, in which AI has found
successful applications, explanations of derived AI models usually
are presented in the form of saliency maps to identify the parts of an
image that significantly impact the image classification. Currently,
the majority of XAI frameworks have been developed to enable pat-
tern recognition and classification, whereas XAI for regression-type
models has yet to be addressed. In the construction field, opportu-
nities abound for the use of AI algorithms to address regression-type
problems such as predicting the labor cost of steel fabrication or the
compressive strength of concrete in curing (which are the two ap-
plications addressed in this research). To explore the explainability
of AI and to promote its applications in the construction field, we
enhanced the model tree made of regressions in to interpret
the performance of each submodel and validate the model’s reason-
ing logic.

The steel fabrication labor hour prediction problem was identi-
fied jointly with an industry partner as a practical application case,
which warranted the implementation of the proposed XAI frame-
work. Over the last 3 years, data set preparation and model verifi-
cation and validation were conducted through a collaborative
research effort engaging the partner company. The research had
proven that the enhanced model tree algorithm provided effective

1Ph.D. Candidate, Dept. of Civil and Environmental Engineering, Univ.
of Alberta, 116 St. and 85 Ave., Edmonton, AB, Canada T6G 2R3. ORCID:
https://orcid.org/0000-0001-8653-0667. Email: [email protected]

2Professor, Dept. of Civil and Environmental Engineering, Univ. of
Alberta, 116 St. and 85 Ave., Edmonton, AB, Canada T6G 2R3 (corre-
sponding author). ORCID: https://orcid.org/0000-0002-8191-8627. Email:
[email protected]

Note. This manuscript was submitted on June 16, 2020; approved on
January 22, 2021; published online on May 31, 2021. Discussion period
open until October 31, 2021; separate discussions must be submitted for
individual papers. This paper is part of the Journal of Construction En-
gineering and Management, © ASCE, ISSN 0733-9364.

© ASCE 04021084-1 J. Constr. Eng. Manage.

J. Constr. Eng. Manage., 2021, 147(8): 04021084

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https://doi.org/10.1061/(ASCE)CO.1943-7862.0002083

https://orcid.org/0000-0001-8653-0667

mailto:[email protected]

https://orcid.org/0000-0002-8191-8627

mailto:[email protected]

http://crossmark.crossref.org/dialog/?doi=10.1061%2F%28ASCE%29CO.1943-7862.0002083&domain=pdf&date_stamp=2021-05-31

XAI for practical applications such as structural steel labor-cost es-
timating in the bidding stage.

To further demonstrate the application of the developed scheme,
a second construction engineering problem (concrete strength pre-
diction during the curing process) is presented. The data set was
taken from the University of California, Irvine machine learning
repository (UCI 2020) that is well established for benchmarking
AI algorithm performance. The model tree was calibrated by ap-
plying the proposed framework to serve as the XAI for interpreting
the models previously developed from computing research.

The remainder of this paper is structured as follows. The section
“Literature Review” first delves into the mechanisms of four pre-
dictive methods and further discusses trends in AI applications. The
following section describes performance metrics selected for evalu-
ating regressions and AI models. The section “How M5P Works”
explains the model tree algorithm in layman terms. The section
“Steel Fabrication Labor-Cost Estimating” describes the data collec-
tion process for the case study, attribute selection, and the interpret-
ability of each evaluated model, and elaborates on the three-color
enhancement scheme. The section “Concrete Strength Prediction:
Case Study” is provided next, followed by the Conclusion. Appen-
dixes I and II contain seven samples of the steel fabrication data set.

Literature Review

Predictive Methods

Rosenblatt (1961) pioneered the research of analytically model-
ing the human brain as perceptron, a machine designed for image
recognition (the term perceptron can be compared with neurons,
i.e., the unit cells of nerves). Since then, researchers in a wide range
of scientific fields have adopted this artificial neural network ap-
proach for teaching a machine to recognize the output based on
a set of inputs. A significant departure from Rosenblatt’s percep-
tron occurred when Vapnik and Cortes (1995) combined Vapnik’s
optimal hyperplanes developed in 1965 (Vapnik and Kotz 2006)
with an ANN design into the concept of the support vector ma-
chine (SVM). ANNs and SVMs usually perform better than simpler
models such as multiple linear regression or decision trees. For ex-
ample, SVM defines categories in a high-dimensional space (simply
put, SVM clusters points in unlimited dimensions). In contrast,

ANNs are adept at distinguishing data that are not linearly separable
(Kantardzic 2011). Fig. 1 illustrates an ANN function and a SVM
function. To a certain degree, attempting to explain how these neural
nets reason is analogous to trying to explain the mechanisms of
thought process and consciousness in the human brain.

Breiman et al. (1984) developed analytical algorithms of the de-
cision tree model for classification and regression (CART). This
model acts like an upside-down tree, growing its branches from the
root node down to the leaf nodes at the bottom. Each split in a branch
represents a numeric or categorical condition. The expansion of the
tree ends at leaf nodes (Fig. 2). The interpretability of this model is
high, butit has some serious drawbacks. According to Tibshirani and
Friedman (2008), “trees have one aspect that prevents them from
being the ideal tool for predictive learning, namely inaccuracy.”

As an enhanced version of a decision tree, the random forest
(RF) was developed by Ho (1995). This algorithm builds as many
random trees as possible. A RF model arbitrarily categorizes data
points using decision trees and simple yes/no conditions (Fig. 3).
After all trees are grown, each is evaluated using the data reserved
for testing. Based on this evaluation, the RF model chooses the
most accurate tree as the final solution. The forest is trained on a
bootstrapped data set which is of the same size as the original data
set but consists of randomly selected samples from the original data
set and their duplicates. The duplicates usually account for up to
30% of the training data set, which essentially creates an unnatural
data set (Fan and Zhang 2009).

Another parallel endeavor to embellish decision tree had re-
sulted in integration with regression algorithms. The M5P model
tree was designed by Quinlan (1992) and then enhanced by Wang
and Witten (1997). M5P grows a decision tree–like CART; instead
of providing one value at a leaf node, it builds a linear regression
based on the instances of data that reach the particular node (Fig. 4).

Current AI Trend

Machine learning algorithms for data-driven predictive analytics, in-
cluding ANN, SVM, and RF, have been utilized widely by research-
ers in the last couple of decades. According to the recent discussion
by Emmert-Streib et al. (2020), such statistical models and machine
learning methods have been introduced due to the lack of general
theoriesoutsideofphysics.Innearlyeveryapplieddomain,historical
data are abundant, and big data is emerging due to technological

Fig. 1. Abstract illustration of ANN and SVM: ANN function is the result of learning from training data analogous to nonlinear regression; SVM
function clusters data into classes using hyper plane (star—class A, circle—class B).

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Fig. 2. Abstract illustration of decision tree: Clustering based on splitting attributes and certain criteria, e.g., yes/no in the current example
(star—class A, circle—class B, square—class C).

Fig. 3. Abstract illustration of random forest: Clustering based on random splitting attributes and certain criteria, e.g., yes/no in the current example
(star—class A, circle—class B, square—class C, triangle—class D).

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advancements. AI has been applied widely as effective computing
means to extract hidden signals and uncover nonobvious patterns
from the data, while also making reliable predictions of the outcome
expected in unseen cases. Adeli (2001) conducted a review of the
journal Computer-Aided Civil and Infrastructure Engineering from
1989 (the first publication on the ANN topic) to 2000 and found over
180 ANN use cases, not counting alternative standalone algorithms
such as decision tree or fuzzy logic. A review by Kulkarni et al.
(2017) covered over 70 ANN applications in construction manage-
mentalone.Althoughscholarskeepwideningtheboundariesofwhat
machines can learn, AI applications remain rare in practice. Many of
the best-performing methods feature highly complex mathematical
algorithms, thus prohibiting a straightforward explanation of the
obtained results in simple terms (Emmert-Streib et al. 2020).
Nonetheless, for professionals who make high-stakes decisions,
these explanations are worth their weight in gold. The user’s trust
in a computer program is analogous to trust in a co-worker: if there
is no understanding, there is no trust; if there is no trust, there is no
cooperation.

Widman and Loparo (1990) pointed out that the credibility of an
AI program frequently depends on its ability to explain its conclu-
sions. Dhar and Stein (1997) argued that because neural network
(NN) algorithms such as the back-propagation NN are nonlinear,
high-dimensional functional equations featuring parallel distributed
data processing, it is hard to interpret explicitly which parameters
cause which behavior in the NN model. Although mathematical and
operational methods do exist for the analysis of neural networks, the
methods are fairly convoluted and are less than satisfying because
of their theoretical assumptions. Dhar and Stein (1997) stated that
“unlike most statistical methods, it can be difficult to say, even in
general, which variables are significant in what respect.” Research to
decipher those nonexplainable AI models has made inroads in spe-
cific application domains. For example, Lu et al. (2001) created a
tornado-like sensitivity graph that was able to analyze the sensitivity
of ANN input parameters and measure their impact on the output.
Domain experts could use this visual aid to interpret and validate the
ANN model based on their experience and common sense. Ruping
(2006) investigated how to interpret a SVM and how to measure the
interpretability of the machine learning algorithm itself. Ruping ar-
gued that in for a model to be comprehensible to the user, it
must be accurate and efficient so that interpretability does not
become a performance bottleneck.

The fact that explainability often is mandatory for an AI model
to be of practical value led the United States Defense Advanced
Research Projects Agency (DARPA) to initiate a new field called

explainable artificial intelligence (Gunning 2016). The computing
research community recently has developed multiple explainability
techniques, including model simplification approaches, feature rel-
evance estimators, text explanations, local explanations, and model
visualizations (Arrieta et al. 2019). Most XAI endeavors have fo-
cused on problems and data sets relevant to the areas of sociology
and image, text, or sound recognition, or at the corporate level have
been used to explain to users how the black box of AI software
functions (Rudin 2019). Nevertheless, developing and validating a
second non-black-box model, which is built to interpret the black
box of the primary model, presents a special dilemma: if the ex-
planation is completely faithful to the computation of the primary
model, one would not need the primary model, but only the explan-
ation resulting from the XAI model (Rudin 2019). From the per-
spective of applied research, XAI is a new AI application paradigm
in construction engineering. It remains unclear which algorithm can
be the proper fit in delivering XAI in a general sense or whether this
XAI paradigm is practically feasible.

Efforts to hybridize decision trees with artificial neural networks
to enhance the interpretability of the latter were made well before
DARPA coined the term XAI. Ivanova and Kubat (1995) used
decision trees to initialize the weights, hidden layers, and the
neurons in these layers, with the goal of making ANN setup less
trial-and-error and more systematic. Boz (2000) thought that the
understandability problem of neural networks could be material-
ized by extracting decision rules or decision trees from the trained
neural network and thus increasing the valuation of the algorithm.
In the field of deep learning, Wan et al. (2020) created neural-
backed decision trees that break down image classification into
a sequence of intermediate decisions. This sequence of decisions
then can be mapped to more-interpretable concepts to reveal in-
formative hierarchical structures in the underlying classes. In addi-
tion to efforts to explain neural networks by means of decision
trees, Lundberg et al. (2019) studied the explainability of decision-
based trees themselves. They argued that by combining many local
explanations of feature importance and feature interactions with
separate samples, the global structure of the model could be re-
vealed. Their TreeExplainer used the SHapley Additive exPlanation
(SHAP) value (Lundberg and Lee 2017) to extract such local ex-
planations and to monitor the model. All the aforementioned en-
deavors were attempts to explain the classification mechanism of
prediction models. To our best knowledge, no application frame-
works are available for developing regression-type XAI models
for commonly encountered data-driven prediction problems in the
domain of construction engineering and management. This research

Fig. 4. Abstract illustration of model tree (M5P): Clustering based on splitting attributes and certain criteria, e.g., yes/no in the current example;
a regression function is built for each class (star—class A, circle—class B, square—class C).

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proposes such a framework leading to the generation of XAI models
based on regression trees.

Model Performance Metrics

Effective and straightforward metrics are selected based on those
commonly applied to evaluate regression models. For the researcher,
it is not very important which evaluating metrics to use because in
most practical situations the best numeric prediction method still is
the best no matter which error measure is used (Witten and Frank
2011). On the other hand, for practitioners, these metrics need to
indicate whether the model is valid and acceptable. Thus, selecting
proper metrics for model accuracy evaluation is vital. This section
elaborates three general types of errors for evaluating regression or
classification algorithms: absolute or mean errors, relative errors,
and correlation coefficients.

Absolute Errors

Absolute errors are the most intuitive. For example, mean absolute
error is an average of the differences between actual and predicted
values. Mean absolute percentage error indicates by how much, on
average, the model under- or overpredicts the target value. In prac-
tical applications, the percentage error usually is avoided because it
tends to be distorted by outliers.

Relative Errors

Relative errors can be good metrics to compare AI algorithms. The
error is normalized by the error of the simple predictor (the differ-
ences between actual values and the mean of actuals) that always
predicts the mean. Furthermore, squared relative error and root rel-
ative squared error often result in higher numerical values than ab-
solute errors. A complete set of equations and their interpretation
was given in Section 5.8 of Witten and Frank (2011).

R-squared

The R-squared is a widely used metric to estimate the accuracy of a
model. Ironically, this coefficient often is confusing and can be mis-
used. In statistics, R-squared refers to the coefficient of determina-
tion, and is simply the square of the Pearson correlation coefficient
(PCC). The PCC measures the linear correlation between two var-
iables, and ranges between −1 and þ1. Mathematicians square the
PCC and derive Eq. (1) to explain the percentage of variation be-
tween two variables. Eq. (1) is given only to facilitate the interpre-
tation of R-squared and should not be used to calculate the Pearson
correlation coefficient (Witte and Witte 2017)

R2 ¼ Variancemean − Varianceðactual;predictedÞ
Variancemean

ð1Þ

In machine learning, R-squared also refers to the coefficient of
determination that indicates how much variation of the target value
is explained by the predicted value [Eq. (2)]. In other words, if R2 is
equal to 0.78, we can say that the model account for only 78% of
the variation, and 22% remains hidden

R2 ¼
P

ibaseline error
2
i −

P
ierror

2
iP

ibaseline error
2
i

ð2Þ

where:

errori ¼ actuali − predictedi ð3Þ
baseline errori ¼ actuali − actualmean ð4Þ

Eqs. (1) and (2) essentially are identical. The other interpretation
of Eq. (2) can be put in the following way: if R2 is equal to 0.78.
then the model performs 78% better than a zero-rule predictor (a
model which always predicts the mean); or if R2 is equal to −0.11,
one can suggest that the model performs 11% worse than a zero-
rule predictor. This version of the R-squared definition can be neg-
ative ðR2 ∈ ð−∞; 1�Þ in the case of poor prediction performance
(error is much higher than baseline error). Hence, this metric can
be of great value to the user for evaluating model performance. The
name, however, can be changed to coefficient of explained varia-
tion to avoid confusion.

Pearson Correlation Coefficient

As mentioned previously, the Pearson correlation coefficient mea-
sures the statistical correlation between two variables, and is de-
noted R ∈ ½−1; 1�. In other words, this coefficient can tell whether
the dependency between two parameters is weak ðR → 0Þ or strong
(R → −1 or R → 1)

R ¼ Covarianceactual;predictedffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Varianceactual

p
·

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Variencepredicted

p ð5Þ

Despite the great value of PCC to statisticians, it causes confu-
sion in machine learning. This metric is scalable, meaning that if we
multiply all predicted values by any number and leave the actual
values intact, the correlation remains the same [Figs. 5(b and c)].

This implies the possibility that if an algorithm consistently
underperforms on all the predictions by a considerable margin, the
correlation coefficient can remain high. An intuitive indicator of
ideal prediction accuracy is the correlation line intersecting the
x- and y-axes at the origin with a 45° tilt angle [Fig. 5(a)]. Thus,
it is advisable to apply the correlation coefficient to justify a model’s
prediction performance only if it is supported by graphical visuali-
zation of the tilt angle of the correlation line.

This study used (1) correlation coefficient (R), (2) coefficient of
explained variation (R2), and (3) mean absolute percentage error as
AI model performance evaluation metrics.

How M5P Works

Ensemble top-down trees usually are grown to the maximum size
and then pruned backward, replacing poor-performing subtrees
with leaves (Fig. 9). Then the smoothing procedure adjusts the per-
formance of each leaf node to compensate for sharp discontinuities
that inevitably would occur between adjacent linear models (Wang
and Witten 1997). These internal mechanisms are employed to
achieve the highest feasible prediction accuracy for the M5P model
as a whole.

Fig. 5. Illustration of the potential limitation of Pearson correlation
coefficient in checking regression quality.

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Growing Initial Tree

To build the upside-down tree, M5P uses a splitting criterion
[Eq. (6)] to find the attribute and the value at which to begin grow-
ing branches

Splitting criterion ¼ SDðoutputÞ − SDðoutputsplitÞweighted ð6Þ
where

SDðoutputsplitÞweighted

¼ SDðoutputsplit 1Þ ×
P joutputsplit 1j

numberinstances split 1
þ

þ SDðoutputsplit 2Þ ×
P joutputsplit 2j

numberinstances split 2
ð7Þ

The algorithm evaluates all possible splits and measures the
magnitude by which the standard deviation (SD) of the output is
reduced. The reduction is represented as the sum of the weighted
standard deviations of the output values of evaluated splits. For ex-
ample, if we have 2 attributes (one input and one output) and 12
instances, M5P would sort values for each attribute and find an
average between adjacent points (potential splitting values) (Fig. 6).
Then, Eq. (6) is calculated for each possible split (in this example,
11 splits), and a splitting value associated with the largest value of
the splitting criterion is chosen.

This procedure continues until the tree is grown to the maximum
size and the stopping condition is met. In the case of M5P, the tree
stops growing when the leaf node has less than three instances or
the standard deviation of the leaf’s output is less than 5% of the
standard deviation of the output of the entire set

SDðoutputleafÞ < 0.05 · SDðoutputÞ ð8Þ Pruning After the tree is grown, M5P builds multiple linear regressions for each leaf as well as each subtree using standard regression and greedy search attribute selection. Then the algorithm tests each in- stance (training process) and averages the difference between pre- dicted and actual values (expected error) for each leaf and subtree. The error of every entity then is multiplied by a compensation fac- tor [Eq. (9)] to account for the fact that the model is not tested on unseen cases. The lower the number of instances, more the error is expected to increase Compensation factor ¼ numberinstances þ numberattributes numberinstances − numberattributes ð9Þ The pruning itself is a process of comparing the expected error of the lower leaf nodes with the expected error of the upper subtree. If regression in the subtree performs better than the regressions in the leaf nodes, those leaf nodes are pruned and the subtree becomes a leaf node (bottom-up pruning). Smoothing Finally, smoothing is employed to calibrate the predicted value of the leaf by propagating it to higher subtrees and eventually to the root node. Eq. (10) is calculated at each level of the tree (from leaf to subtree, from subtree to next-level subtree, and so forth, to the root node). The goal is to combine the prediction power of the leaf with the prediction power of subtrees Predicted valueupper node ¼ Predicted valuenode × numberinstancecs þ predicted valuelower node × k numberinstances þ k ð10Þ where k is a constant, which in M5P is equal to 15; and numberinstances refers to the number of instances (training records) associated with the subtree which is denoted node (Fig. 7). Steel Fabrication Labor Cost: Case Study Data Collection Throughout the 3 years of joint industry–academia research efforts, we collected 935 separate pre-bid estimates of steel fabrication projects. Each estimate contained a take-off of the steel profiles (length, weight, and quantity) listed in a project. Additionally, we identified relevant …