Actionable Explainable AI (AxAI): A Practical Example with Aggregation Functions for Adaptive Classification and Textual Explanations for Interpretable Machine Learning
Abstract
:1. Introduction and Motivation
2. Preliminaries of Classification by Rule-Based Systems, Neural Networks and Ordinal Sums
2.1. Classification by Rule-Based Systems
- IF A is LOW and B is LOW, then C is no
- IF A is LOW and B is HIGH, then C is maybe
- IF A is HIGH and B is LOW, then C is maybe
- IF A is HIGH and B is HIGH, then C is yes
- where A and B are atomic or compound attributes.
2.2. Classification by Neural Networks
2.3. Classification of Ordinal Sums of Conjunctive and Disjunctive Functions
- 1.
- if , ,
- 2.
- if , ,
- 3.
- if
- 4.
- if
3. Learning Parameters from Data for Classifying by Ordinal Sums of Conjunctive and Disjunctive Functions Expressed by Nilpotent Functions
- For data points in the ML model learns parameters for strict or nilpotent conjunction to classify into class no
- For data points in the ML model learns parameters for strict or nilpotent disjunction to classify into class yes
- For data points in the ML model learns parameters for power means to classify into class maybe
4. A New Dissimilarity Function for Classifying by XOR into Classes Yes, No and Maybe
- (QD1) ;
- (QD2) ;
- (QD3) ;
- (QD4) whenever ;
- (QD5) and whenever .
- , ;
- ;
- .
5. Parameter Learning in Classification by Ordinal Sums with Evolutionary Algorithm and Reinforcement Learning
5.1. Parameter Learning for Conjunctive and Averaging Functions
- —Clear no
- —Very significant inclination to no
- Avg—Averaging functions with possible inclination to no or yes
- —Very significant inclination to yes
- —Clear yes
5.1.1. Averaging Behaviour for Class Maybe
- : Neutral
- : Optimistic—A bit inclination to yes
- : Pessimistic—A bit inclination to no
5.1.2. Conjunctive Behaviour for Class No
- For area : and
- For area :
- : Linear case, i.e.,
- : More restrictive, for instance , for
- : Less restrictive, for instance , for
5.1.3. Implementation of Parameter Estimation from Synthetically Generated Noisy Data with an Evolutionary Algorithm
5.1.4. Implementation of Parameter Estimation from Synthetically Generated Noisy Data with Reinforcement Learning
6. Experiment on Medical Data for Classification by Ordinal Sums
6.1. Dataset Information
6.2. Data Preprocessing
6.3. Tool Navigation
6.4. Fitting Parameters
- m: 0.2
- n: 0.7
- x axis: [age, cp, trestbps, fbs, restecg, exang, oldpeak, slope, ca]
- y axis: [sex, chol, thalach, thal]
6.5. Adjusting and r
6.6. Interpretation of the Visualisation
7. Discussion and Future Works
8. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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1.25 | 1.25 | 1.25 | 1.25 | 0.75 | 1.25 | 1.25 | 1.25 | 1.25 | 1.25 | |
x | 0.01 | 0.25 | 0.26 | 0.23 | 0.25 | 0.27 | 0.05 | 0.49 | 0.22 | 0.48 |
y | 0.41 | 0.48 | 0.39 | 0.34 | 0.35 | 0.30 | 0.49 | 0.49 | 0.06 | 0 |
solution | 0 | 0.22 | 0.12 | 0 | 0.12 | 0 | 0.03 | 0.47 | 0 | 0 |
1.25 | 1.25 | 1.25 | 0.75 | 1.25 | 1.25 | 1.25 | 1.25 | 1.25 | 1.25 | |
x | 0.50 | 0.39 | 0.03 | 0.20 | 0.09 | 0.25 | 0.40 | 0.11 | 0.10 | 0.35 |
y | 0.13 | 0.39 | 0.20 | 0.30 | 0.20 | 0.09 | 0.49 | 0.50 | 0.10 | 0.07 |
solution | 0.13 | 0.27 | 0 | 0.05 | 0 | 0 | 0.38 | 0.11 | 0 | 0 |
1 | 1.25 | 1.25 | 1.25 | 1.25 | 1.25 | 1.25 | 1 | |||
x | 0.25 | 0.46 | 0.46 | 0.50 | 0.21 | 0.50 | 0.11 | 0.19 | ||
y | 0.44 | 0 | 0.03 | 0.24 | 0.24 | 0.03 | 0.32 | 0.35 | ||
solution | 0.19 | 0 | 0 | 0.24 | 0 | 0.03 | 0 | 0.04 |
r | 0.75 | 0.75 | 0.75 | 0.75 | 0.75 | 1.25 | 0.75 | 0.75 | 0.75 | 0.75 |
x | 0.42 | 0.37 | 0.26 | 0.10 | 0.29 | 0.29 | 0.42 | 0.32 | 0.36 | 0.35 |
y | 0.80 | 0.57 | 0.95 | 0.55 | 0.67 | 0.70 | 0.98 | 0.78 | 0.99 | 0.63 |
solution | 0.70 | 0.43 | 0.65 | 0.13 | 0.44 | 0.51 | 0.88 | 0.57 | 0.82 | 0.46 |
r | 1 | 0.75 | 0.75 | 0.75 | 0.75 | 0.75 | 1.25 | 0.75 | 0.75 | 0.75 |
x | 0.0 | 0.14 | 0.31 | 0.36 | 0.37 | 0.47 | 0.12 | 0.38 | 0.34 | 0.44 |
y | 1.0 | 0.69 | 0.96 | 0.60 | 0.92 | 0.57 | 0.59 | 0.78 | 0.57 | 0.73 |
solution | 0.5 | 0.28 | 0.73 | 0.45 | 0.76 | 0.53 | 0.23 | 0.64 | 0.40 | 0.66 |
r | 0.75 | 0.75 | 0.75 | 1 | 0.75 | 0.75 | 0.75 | 0.75 | 0.75 | |
x | 0.46 | 0.50 | 0.36 | 0.20 | 0.01 | 0.17 | 0.45 | 0.47 | 0.02 | |
y | 0.56 | 0.50 | 0.74 | 0.80 | 0.63 | 0.56 | 0.71 | 0.68 | 0.98 | |
solution | 0.51 | 0.50 | 0.58 | 0.50 | 0.07 | 0.21 | 0.65 | 0.64 | 0.33 |
Label | Min Limit | Max Limit | Description |
---|---|---|---|
age | 40 | 65 | Age in years |
sex | 0 | 1 | Sex |
cp | 2 | 1 | Chest pain type |
trestbps | 120 | 140 | Resting blood pressure in mm Hg |
chol | 180 | 300 | Serum cholesterol in mg/dL |
fbs | 0 | 1 | Fasting blood sugar |
restecg | 0 | 2 | Resting electrocardiographic results |
thalach | 160 | 120 | Maximum heart rate during exercise electrocardiogram. |
exang | 0 | 1 | Exercise-induced angina |
oldpeak | 0 | 4.4 | ST depression relative to rest (mV) |
slope | 1 | 3 | The slope of the peak exercise ST segment (1 = upsloping, 2 = flat, 3 = downsloping) |
ca | 0 | 3 | Number of major vessels coloured by fluoroscopy |
thal | 3 | 7 | Thallium scintigraphic defects (3 = normal, 6 = fixed defect, 7 = reversible defect) |
num | Presence of disease |
Patients without disease in the no section | 97 |
Patients with disease in the no section | 13 |
Patients without disease in the yes section | 7 |
Patients with disease in the yes section | 52 |
Patients without disease in the maybe section | 56 |
Patients with disease in the maybe section | 73 |
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Saranti, A.; Hudec, M.; Mináriková, E.; Takáč, Z.; Großschedl, U.; Koch, C.; Pfeifer, B.; Angerschmid, A.; Holzinger, A. Actionable Explainable AI (AxAI): A Practical Example with Aggregation Functions for Adaptive Classification and Textual Explanations for Interpretable Machine Learning. Mach. Learn. Knowl. Extr. 2022, 4, 924-953. https://doi.org/10.3390/make4040047
Saranti A, Hudec M, Mináriková E, Takáč Z, Großschedl U, Koch C, Pfeifer B, Angerschmid A, Holzinger A. Actionable Explainable AI (AxAI): A Practical Example with Aggregation Functions for Adaptive Classification and Textual Explanations for Interpretable Machine Learning. Machine Learning and Knowledge Extraction. 2022; 4(4):924-953. https://doi.org/10.3390/make4040047
Chicago/Turabian StyleSaranti, Anna, Miroslav Hudec, Erika Mináriková, Zdenko Takáč, Udo Großschedl, Christoph Koch, Bastian Pfeifer, Alessa Angerschmid, and Andreas Holzinger. 2022. "Actionable Explainable AI (AxAI): A Practical Example with Aggregation Functions for Adaptive Classification and Textual Explanations for Interpretable Machine Learning" Machine Learning and Knowledge Extraction 4, no. 4: 924-953. https://doi.org/10.3390/make4040047