=Paper=
{{Paper
|id=Vol-3831/paper18
|storemode=property
|title=Explaining Predictions of Hypertension Disease through Anchors
|pdfUrl=https://ceur-ws.org/Vol-3831/paper18.pdf
|volume=Vol-3831
|authors=Gabriella Casalino,Giovanna Castellano,Katarzyna Kaczmarek-Majer,Pietro Giovanni Rizzo,Gianluca Zaza
|dblpUrl=https://dblp.org/rec/conf/explimed/CasalinoCKRZ24
}}
==Explaining Predictions of Hypertension Disease through Anchors==
https://ceur-ws.org/Vol-3831/paper18.pdf
Explaining Predictions of Hypertension Disease
through Anchors
Gabriella Casalino1,* , Giovanna Castellano1 , Katarzyna Kaczmarek-Majer2 ,
Pietro Giovanni Rizzo1 and Gianluca Zaza1,*
1
Computer Science Department, University of Bari Aldo Moro Bari, Italy
2
Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland
Abstract
Hypertension is a disease that stresses the arteries and can cause damage to vital organs. It is often
asymptomatic, and timely diagnosis and management are crucial to prevent complications and mitigate
the risks associated with the disease. Photoplethysmography has proven to be effective in capturing
variations in blood volume within vessels and holds the potential for continuous monitoring of heart-
related diseases to be adopted in real-time systems [1]. Using automated processing on “high-risk” medical
data requires careful attention to regulations. The emergence of Explainable Artificial Intelligence (XAI)
is especially important in this context because it can provide explanations that clarify the reasoning
behind the results produced by automatic processing. This paper introduces the application of an agnostic
algorithm called Anchors for explaining predictions related to hypertension levels through the use of
concatenations of logic statements. This algorithm has been selected based on its ability to produce easily
understandable explanations, which is particularly valuable in the medical domain, where the primary
stakeholders are physicians and patients. Additionally, it has been chosen for its ability to balance
classification and explanation accuracy. Furthermore, we have investigated the impact of varying the
number of features utilized in the explanations on the quantitative measures. This exploration involved
the application of diverse feature selection methods, and their outcomes were systematically compared.
Experiments showed that reducing the number of features does not harm classification performance and
significantly improves the quality of explanations.
Keywords
Explainable Artificial Intelligence, XAI, Hypertension, classification, Decision Support System, Photo-
plethysmography, Feature selection,
1. Introduction
Explainable Artificial Intelligence (XAI) has gained a lot of attention in recent years due to
AI’s incredible and sometimes overwhelming capabilities. The increasing power of AI has
made it necessary to establish regulations to ensure trustworthy, privacy-compliant, and ethical
AI practices. XAI specifically refers to automated methods that can represent, in a way that
EXPLIMED - First Workshop on Explainable Artificial Intelligence for the medical domain - 19-20 October 2024, Santiago
de Compostela, Spain
*
Corresponding author.
$ gabriella.casalino@uniba.it (G. Casalino); giovanna.castellano@uniba.it (G. Castellano);
k.kaczmarek@ibspan.waw.pl (K. Kaczmarek-Majer); p.rizzo7@studenti.uniba.it (P. G. Rizzo); gianluca.zaza@uniba.it
(G. Zaza)
000-0003-0713-2260 (G. Casalino); 0000-0002-6489-8628 (G. Castellano); 0000-0003-0422-9366
(K. Kaczmarek-Majer); 0000-0003-3272-9739 (G. Zaza)
© 2024 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
is understandable for humans, the hidden mechanisms guiding their processing [2]. The
importance of XAI extends across various domains, with a particular emphasis on areas like
healthcare. In such critical fields, understanding algorithms’ inner workings has become
essential [3]. Physicians and patients alike need insight into how specific results are generated by
an algorithm. This transparency is crucial for establishing trust in the technology and ensuring
that AI applications are accurate and understandable to end-users. This need for explainability
has become an absolute requirement in the medical domain, highlighting XAI’s pivotal role in
fostering trust and confidence in AI-driven decision-making processes [4]. Explainable methods
are broadly categorized into two groups: ante-hoc methods, which are inherently explainable
by design, and post-hoc methods, which are applied to the outcomes of a machine learning
method to extract explanations.
Depending on the type of data and methods employed, various XAI methods have been
proposed in the literature, and they have been effectively used in the medical domain [5]. Some
examples are: feature importance techniques such as SHAP (SHapley Additive exPlanations) [6]
and LIME (Local Interpretable Model-agnostic Explanations) [7], Counterfactual Explanations
[8], Layer-wise Relevance Propagation (LRP) [9], Rule-based Models [10, 11, 12, 13], Attention
Mechanisms [14], Surrogate Models [15, 16, 17].
In this work, we used the Anchors algorithm. It is a model-agnostic technique used for
generating explanations that are both easy to understand and reliable. It focuses on creating
simple and clear conditions (anchors) that explain a model’s prediction for a specific instance
(local explanations). By analyzing each instance, the algorithm identifies a set of features that,
when present, are highly likely to lead to the model’s prediction. These anchor conditions are
combined using a disjunction (OR combination) to form a complete explanation. This makes it
easy for end-users to understand and accept the reasons behind a model’s decision. Moreover,
Anchors attempts to balance precision and recall, ensuring that the generated conditions are
accurate and cover a significant portion of the decision space [18].
The quality and correctness of explanations are closely related to the number of features
used to describe the data. To investigate how the number of features influences the accuracy
of explainability, we compared four different feature selection methods. The objective of this
comparison was twofold: to identify the most effective algorithm and to determine which subset
of features were the most relevant for the predictive task.
In this paper, a case study on predicting hypertension is used to demonstrate deriving
explainable predictions for enhancing decision support systems.
Hypertension is a heart condition with increased blood pressure, increasing the likelihood of
cerebral, cardiac, and renal events. Doctors often prescribe antihypertensive drugs to lower
blood pressure and reduce the risk of cardiovascular problems. However, many patients still
have uncontrolled hypertension and related risk factors. To prevent major cardiovascular
events, monitoring blood pressure continuously is crucial [19]. According to the World Health
Organization (WHO), cardiovascular diseases (CVDs) are one of the leading causes of death1 .
Hypertension programs have proven effective in reducing the incidence of coronary heart disease
and stroke, especially at the primary care level. However, these programs can be expensive,
1
WHO:https://www.who.int/news-room/fact-sheets/detail/cardiovascular-diseases-(cvds) (last accessed on May 5,
2024
(a) (b)
Figure 1: Dataset information: (a) the statistics of the feature values and (b) the occurrence values of
the target class.
requiring medical staff and resources to manage. To address these challenges, machine learning
methods have emerged as useful tools to support medical decision-making [20], particularly in
hypertension diagnosis [21].
In this scenario, photoplethysmography (PPG) emerges as a valuable tool for the continuous
monitoring of vital sign parameters [22, 23]. Specifically, it finds widespread application in
heart rate monitoring by utilizing light reflection due to blood variations in vessels [24]. The
present study utilizes a dataset of patient information and vital signs obtained from photo-
plethysmographic signals related to hypertension [25]. There are various methods proposed in
scientific works for explaining hypertension, such as in [26, 27, 28, 29], just to mention a few.
However, none of them concentrate on the accuracy of the explanation. We can provide local
explanations for previously unseen samples using the Anchors algorithm. At the same time, we
can study the balance between coverage and precision of the explanations derived.
The main findings of this work are as follows:
• a study decision support systems for hypertension that takes into account both the
classification and explanation accuracy;
• a study on the more effective subset of features useful for accurate predictions
• a study on the more effective subset of features useful for accurate and easy-to-understand
explanations.
The paper is organized as follows. Section 2 describes the data, the Anchors algorithm, and
adopted feature selection algorithms. Section 3 presents quantitative and qualitative results to
evaluate accuracy in terms of classification performance and explainability. In Section 4, we
summarize our findings, draw conclusions, and outline future work.
2. Materials and methods
The work aims to apply an explainable model, such as Anchors, to analyze tabular data on
hypertension risk. The Anchors method, along with the hypertension dataset to be analyzed, is
described in detail. Additionally, a brief overview of the feature selection methods is provided.
2.1. Data
We utilized a dataset containing the values of patients’ photoplethysmographic (PPG) signals
correlated with their respective physiological information. The study in [25] aimed to find
a possible correlation between the two sets of information collected. The dataset included
219 subjects (115 female and 104 male) aged between 21 and 86, with an average age of 58.
In our research, we considered a subset of 8 input features, namely Sex, Age, Height, Weight,
Systolic Blood Pressure (SBP), Diastolic Blood Pressure (DBP), Heart Rate (HR), and Body Mass
Index (BMI). Our selection was guided by identifying the most influential features in classifying
hypertension. Consequently, we excluded the features 𝑁 𝑢𝑚 and 𝑆𝑢𝑏𝑗𝑒𝑐𝑡_𝐼𝐷 as they did not
contribute significantly to this classification. Figure 1(a) displays the box plots describing the
input features. The plots show uniformly distributed feature values in the dataset for even
representation in model processing. Finally, we can also observe that there are outlier points, as
they fall outside the range defined by the box plot’s whiskers. We found this problem consistent
in Weight, Diastolic Blood Pressure, and BMI. The dataset contains four target classes, the healthy
class Normal, and three classes representing the various disease states of hypertension, namely,
Prehypertension, Stage 1, and Stage 2. As depicted in Figure 1(b), the dataset reveals a slight
imbalance between the Normal and Prehypertension and the classes Stage 1 hypertension and
Stage 2 hypertension classes, underscoring the challenge in the research and the need for a
robust model.
2.2. Explainable algorithm
The Anchors algorithm is designed to provide explanations for the predictions made by any black-
box classification model. This is done by identifying a decision rule that effectively describes
the prediction process. Anchors [18] uses a perturbation-based strategy for predictions made
by black-box machine learning models. This produces easily understandable IF-THEN rules,
known as anchors, that precisely define the instances to which they apply, even for those that
may not have been previously observed. A rule anchors a prediction when changes in feature
values have no effect on the prediction itself.
For each instance being considered, perturbations are created and evaluated, allowing the
approach to bypass the structural and internal parameters of the black-box model. As a result,
Anchors are model-agnostic, enabling their application across diverse classes of models. Anchors
uses reinforcement learning techniques alongside a graph search algorithm to reduce the
computational costs and avoid local optima.
An anchor is formally defined as:
E𝒟𝑥 (𝑧|𝐴) [1𝑓^ (𝑥)=𝑓^ (𝑧) ] ≥ 𝜏, 𝐴(𝑥) = 1 (1)
where 𝑥 represents the instance being explained; 𝐴 is a set of features, namely the resulting
rule; 𝑓 indicates the classification model to be explained; 𝒟𝑥 (𝑧|𝐴) indicates the distribution of
neighbors of 𝑥, corresponding to 𝐴; 0 ≤ 𝑡 ≤ 1 specifies a precision threshold (only rules that
achieve a local fidelity of at least 𝑡 are considered a valid result).
In [18], the coverage is introduced to determine the quality of rules. Coverage refers to
identifying a set of rules that apply to a significant portion of a model’s input space. This means
Table 1
Feature selection settings.
Algorithm Parameter #Features Acronym
62.5% 5 FI1
50% 4 FI2
Feature Importance
37.5% 3 FI3
25% 2 FI4
65.5% 5 RFE1
50% 4 RFE2
Recursive Feature Elimination
37.5% 3 RFE3
25.5% 2 RFE4
62.5% 5 IG1
50% 4 IG2
Information Gain
37.5% 3 IG3
25% 2 IG4
0.7 6 CB1
0.6 5 CB2
Correlation based
0.5 4 CB3
0.3 3 CB4
that it calculates the probability of an anchor applying to its neighbors, which represents its
perturbation space. The goal is to find a rule that has the highest coverage among all eligible
rules that meets the precision threshold according to the probabilistic definition.
cov(𝐴) = E𝒟(𝑧) [𝐴(𝑧)]. (2)
Rules with more predicates are typically more precise than those with fewer predicates.
On the other hand, a rule with many features is excessively specific and only applicable to a
few instances, leading to low coverage values. Therefore, finding the right balance between
precision and coverage is essential to identify the most significant rules that describe a larger
portion of the model.
2.3. Feature selection methods
To strike a balance between precision and coverage, reducing the number of features is necessary.
To achieve this, we employed four different feature selection algorithms, namely Feature
Importance, Recursive Feature Elimination, Information Gain, and Correlation-Based. Each
algorithm was tested with four different parameter settings, resulting in variations in the number
of features considered, ranging from 2 to 6. Table 1 summarises the sixteen different settings.
3. Results
A set of experiments was carried out to achieve two objectives: firstly, to evaluate the effec-
tiveness of the Anchors algorithm in explaining hypertension data while altering the number
of features employed to represent the data, and secondly, to investigate the influence of fea-
ture reduction on classification performance. The primary goal is to identify the best feature
selection configuration that leads to favorable results in both explainability and classification
performance. A value 0.95 was used for the Anchors’ threshold 𝑡, resulting in highly precise
rules. Empirical evaluation of this algorithm parameter has shown that this default value was
optimal. The results were evaluated both quantitatively and qualitatively. The dataset was
split into 33% for testing and the rest for training. A random forest classifier was implemented
using the Scikit-learn library2 with default parameters. We selected this classifier based on
its performance demonstrated in a previous study [30]. In that work, it outperformed other
classification algorithms, including the perceptron, support vector machine, and neuro-fuzzy
systems. Additionally, it exhibited stability when subjected to variations in data splits and
feature numbers. Indeed, in that study, classifiers were compared using only two features. This
was done to simplify the set of explanations returned from transparent models, such as fuzzy
neural networks, making it easier for physicians to interpret. In this work, we take a step
forward by utilizing a post-hoc explanation method that leverages natural language to explain
the decision-making process that led to a given result with a black-box algorithm. However,
even in this case, a high number of features compromises the clarity and effectiveness of the
explanations. Therefore, we have reduced the number of features.
3.1. Quantitative results
Quantitative evaluation of the classification performance was carried out using standard classifi-
cation metrics, such as accuracy, precision, recall, and F1 score, on different subsets of data. The
outcomes of this evaluation, along with the number of features obtained from four feature selec-
tion methods, each having four different parameter settings, are presented in Table 2. Sixteen
distinct subsets of data were generated through various configurations of feature selections,
resulting in a range of features from 2 to 6. Additionally, we examined the scenario involving
all features to assess whether reducing the number of features affects accuracy negatively or,
conversely, leads to performance enhancement by reducing noise in the data.
Qualitative results confirm the robustness of random forest to the reduction of the number
of features. The results remain consistent across different feature selection settings. In fact,
reducing the number of features leads to an improvement in the classification performance.
This indicates that some features contribute to noise and are not required for classification. A
detailed analysis of the subsets of features will be conducted in the following paragraph.
As previously discussed, Anchors provides coverage and precision for each explanation,
enabling us to quantify its performance. Table 3 presents the average values of coverage and
precision across samples for each feature selection setting, along with the number of returned
features. We can observe a high value of precision, confirming the previous discussion. Moreover,
for all the feature selection methods, we observe an increase in coverage as the number of
adopted features is reduced, while still preserving classification performance. This analysis
suggests that a lower number of features is preferable because it improves coverage values, and
shorter explanations are easier to understand than longer ones. In particular, regarding the
algorithm that returned the best performance in terms of explainability, all the algorithms with
two features gave a coverage of 27%, which is the best. Thus, the quantitative analysis of the
explanations is not able to identify the best setting of feature selection methods, but suggests
that a lower number of features is better.
2
Python’s Scikit-Learn library: https://scikit-learn.org/
Table 2
Quantitative results of the classifier, for different subsets of data, varying the number of the selected
features.
#F Acc. Prec Rec F1
N P S1 S2 N P S1 S2 N P S1 S2
No FS 8 93% 90% 92% 100% 100% 100% 88% 93% 86% 95% 90% 96% 92%
FI1 5 99% 100% 96% 100% 100% 100% 100% 100% 86% 100% 98% 100% 92%
FI2 4 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100%
FI3 3 97% 100% 93% 100% 100% 100% 100% 93% 86% 100% 96% 96% 92%
FI4 2 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100%
RFE1 5 97% 96% 96% 100% 100% 100% 96% 100% 86% 98% 96% 100% 92%
RFE2 4 99% 100% 96% 100% 100% 100% 100% 100% 86% 100% 98% 100% 92%
RFE3 3 95% 96% 89% 100% 100% 100% 96% 86% 86% 98% 93% 92% 92%
RFE4 2 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100%
IG1 5 99% 100% 96% 100% 100% 100% 100% 100% 86% 100% 98% 100% 92%
IG2 4 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100%
IG3 3 97% 96% 96% 100% 100% 100% 96% 100% 86% 98% 96% 100% 92%
IG4 2 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100% 100%
CB1 6 93% 100% 90% 85% 100% 100% 100% 79% 71% 100% 95% 81% 83%
CB2 5 99% 96% 100% 100% 100% 100% 96% 100% 100% 98% 98% 100% 100%
CB3 4 99% 96% 100% 100% 100% 100% 96% 100% 100% 98% 98% 100% 100%
CB4 3 41% 58% 36% 0% 0% 54% 62% 0% 0% 56% 45% 0% 0%
Table 3
Average values of precision and coverage for different subsets of data, varying the number of the selected
features.
#Feature AvgPrec AvgCov
No FS 8 89% 13%
FI1 5 87% 16%
FI2 4 85% 17%
FI3 3 85% 18%
FI4 2 84% 27%
RFE1 5 88% 16%
RFE2 4 85% 16%
RFE3 3 83% 20%
RFE4 2 84% 27%
IG1 5 87% 16%
IG2 4 83% 18%
IG3 3 86% 19%
IG4 2 83% 27%
CB1 6 88% 13%
CB2 5 86% 13%
CB3 4 81% 15%
CB4 3 72% 7%
3.2. Qualitative results
The qualitative evaluation aims to better understand the influence of different feature selection
settings on the explanations. We reported the explanations obtained with Anchors without
using feature selection and with the FI2 feature selection setting, along with the features selected
by the different settings.
Figure 2 illustrates the features selected from each setting. We can observe that, except for
the correlation-based algorithm, which behaves completely differently, the other algorithms
Figure 2: Comparison of the features selected by the different feature selection settings.
agree that the two most important features are Systolic and Diastolic blood pressure. When
more features are added, they do not completely agree about the most important ones, but
overall, age seems to be an important feature, as well as heart rate. Almost all the settings agree
that height and weight are useless, as well as the BMI for most of them. The correlation-based
algorithm returns completely different results; indeed, it is the only algorithm selecting sex and
age as relevant other than the systolic blood pressure and the heart rate. Surprisingly, it does
not select the diastolic blood pressure in any setting, resulting still in a good performance as
previously discussed. These differences need further studies, so we will focus on the first three
algorithms for the analysis of the explanations.
Figure 3 illustrates anchors generated for four instances belonging to the four classes: normal,
Prehypertension, Stage 1 hypertension, and Stage 2 hypertension. Specifically, Figure 3(a)
displays the explanations obtained without feature selection, while Figure 3(b) showcases the
explanations after applying the feature selection setting FI2. When feature selection is applied,
we observe an increase in coverage for all classes while the precision remains comparable or
even increases. It was found that for the Normal class, only one feature, Systolic blood pressure,
was enough to describe the class. However, very complex explanations were generated for
the disease classes without feature selection. But, when feature selection was applied, the
explanations became clear and easy-to-understand, with a reduced number of anchors. The
(a)
(b)
Figure 3: Examples of explanations obtained from the Anchors algorithm, for the four classes Normal,
Stage 2 Hypertension, Stage 1 Hypertension, Prehypertension, without feature selection (a), and with
the feature importance method FI 2 (b).
algorithm also identified differences between samples belonging to the three classes, where
even if the two features involved were the same, the values of these features varied across
classes. Similar results have been observed with the other feature selection settings.
4. Conclusion
This study aimed to assess the effectiveness of the Anchors algorithm in explaining hypertension
data. To do this, we used a dataset that included patient personal information and vital signs
obtained through photoplethysmography.
Previously, we used explainable algorithms to generate IF-THEN rules for classification
explanations, which yielded lower results than black-box models. For this study, we used a
post-hoc method that derives IF-THEN rules to explain a black-box model’s decisions.
Our results showed that the Anchors algorithm was sensitive to the number of features
in the data. An increased number of features led to decreased rule reliability (coverage). We
compared sixteen different feature selection settings to understand this impact on classification
performance and explainability. The results indicated that our chosen classification algorithm
(random forest) remained robust even with reduced features.
Interestingly, only two out of eight features in the original data space yielded the best coverage
values. This suggests a preference for concise explanations both quantitatively and qualitatively.
Qualitative analysis also highlighted the agreement among feature selection algorithms, except
for the correlation-based algorithm, regarding the importance of photoplethysmographic signal-
derived features, specifically Systolic Blood Pressure and Diastolic Blood Pressure. Moreover,
the anchors generated for the hypertension data with feature selection are more compact and,
thus, more understandable than those generated without feature selection. Additionally, the
algorithm was able to correctly identify differences among the four classes and explain them in
terms of conjunctions of anchors.
Overall, Anchors proved to be a viable solution for explaining black-box models in natural
language, facilitating comprehension for humans. However, its effectiveness relies on a limited
number of features. Therefore, the adoption of feature importance methods becomes essential
when utilizing Anchors.
Future research will delve into exploring the impact of various feature selection settings on
Anchors using different datasets. This investigation aims to determine whether any feature
selection algorithm outperforms others or if an optimal approach exists for maximizing Anchors’
effectiveness.
5. Acknowledgments
Giovanna Castellano and Gianluca Zaza acknowledge the support of the PNRR project FAIR -
Future AI Research (PE00000013), Spoke 6 - Symbiotic AI (CUP H97G22000210007) under the
NRRP MUR program funded by the NextGenerationEU. The research objectives of this paper
are in partial fulfilment of the project EXPLICIT (CUP H93C23000890005). Gabriella Casalino
acknowledges funding from the European Union PON project Ricerca e Innovazione 2014-2020,
DM 1062/2021. G. Casalino and G. Castellano are with the CITEL - Centro Interdipartimentale
di Telemedicina, University of Bari Aldo Moro. All authors are members of the INdAM GNCS
research group. This paper has been partially supported by the “INdAM – GNCS Project”,
CUP_E53C22001930001.
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