Instructor: Thierry Denoeux

Description: This is an introductory course on belief functions, with focus on data analysis, machine learning and statistical inference.

Course outline

1. Belief functions on finite frames
2. Decision analysis
3. Evidential k-NN classifier
4. Evidential neural network classifier
5. Predictive belief functions for categorical and ordinal variables
6. Random sets and belief functions in a general mathematical framework
7. Possibility theory and epistemic random fuzzy sets
8. Statistical prediction using belief functions: application to linear and logistic regression
9. The ENNreg model
10. Uncertain data and the evidential EM algorithm

Slides

1. Belief functions on finite frames. Dempster's rule
2. Decision analysis and classification
3. Multinomial predictive belief functions
4. Statistical inference

Exercises

1. Exercises on Chapter 1
   1. Solutions
2. Exercises on Chapter 2
   1. Solutions
3. Exercises on classification
   1. Solutions
4. Exercise on multinomial predictive belief functions
   1. Solutions
5. Exercises on statistical inference
   1. Solutions
6. Projects
   1. Solutions

Papers

1. T. Denoeux. A k-nearest neighbor classification rule based on Dempster-Shafer theory. IEEE Transactions on Systems, Man and Cybernetics, 25(05):804-813, 1995. pdf
2. T. Denoeux. A neural network classifier based on Dempster-Shafer theory. IEEE Transactions on Systems, Man and Cybernetics A, 30(2):131-150, 2000. pdf
3. T. Denoeux. Constructing belief functions from sample data using multinomial confidence regions. International Journal of Approximate Reasoning, Vol. 42, pages 228-252, 2006. pdf
4. O. Kanjanatarakul, T. Denoeux and S. Sriboonchitta. Prediction of future observations using belief functions: a likelihood-based approach. International Journal of Approximate Reasoning, Vol. 72, pages 71-94, 2016. pdf
5. Thierry Denoeux. Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models. Fuzzy Sets and Systems, Vol. 453, pages 1–36, 2023. pdf
6. T. Denoeux. Quantifying Prediction Uncertainty in Regression using Random Fuzzy Sets: the ENNreg model. IEEE Transactions on Fuzzy Systems (to appear), 2023. pdf
7. T. Denoeux. Maximum likelihood estimation from Uncertain Data in the Belief Function Framework. IEEE Transactions on Knowledge and Data Engineering, Vol. 25, Issue 1, pages 119-130, 2013. pdf
8. B. Quost, T. Denoeux and S. Li. Parametric Classification with Soft Labels using the Evidential EM Algorithm. Linear Discriminant Analysis vs. Logistic Regression. Advances in Data Analysis and Classification, Vol. 11, Issue 4, pp 659–690, 2017. pdf

Data

1. Globalization data (2000, 2014)
2. Globalization dataset (full)
3. GDP data
4. Credit approval dataset