UMR CNRS 7253

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en:bf [2022/09/02 16:03] tdenoeuxen:bf [2023/10/21 05:38] (current) tdenoeux
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-====== Introduction to belief functions ======+====== Theory of belief functions: Application to machine learning and statistical inderence======
  
 **Instructor:** Thierry Denoeux **Instructor:** Thierry Denoeux
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 Description: This is an introductory course on belief functions, with focus on data analysis, machine learning and statistical inference.   Description: This is an introductory course on belief functions, with focus on data analysis, machine learning and statistical inference.  
  
 +** Course outline **
 +  - Belief functions on finite frames
 +  - Decision analysis
 +  - Evidential k-NN classifier
 +  - Evidential neural network classifier
 +  - Predictive belief functions for categorical and ordinal variables
 +  - Random sets and belief functions in a general mathematical framework
 +  - Possibility theory and epistemic random fuzzy sets
 +  - Statistical prediction using belief functions: application to linear and logistic regression
 +  - The ENNreg model
 +  - Uncertain data and the evidential EM algorithm
  
  
 **Slides** **Slides**
  
-  - {{ :en:bf2022_lecture1.pdf |Belief functions on finite frames. Dempster's rule}} +  - {{ :en:bf2023_lecture1.pdf |Belief functions on finite frames. Dempster's rule}} 
-  - {{ :en:bf2022_lecture2.pdf |Decision analysis}} +  - {{ :en:bf2023_lecture2.pdf |Decision analysis and classification}} 
-  - {{ :en:bf2022_clustering.pdf |Evidential clustering}}+  - {{ :en:bf2023_lecture3.pdf |Multinomial predictive belief functions}} 
 +  - {{ :en:bf2023_lecture4.pdf |Statistical inference}} 
 + 
  
-**Lecture notes** 
-  - {{ :en:book_bf.pdf |Lecture notes on belief functions (draft)}} 
- 
-**Videos** 
- 
-  - [[https://filesender.utc.fr/filesender/?s=download&token=062a0156-4763-4545-8911-be55624f5963|Lecture 1]] 
-  - [[https://filesender.utc.fr/filesender/?s=download&token=ea2f08fe-987d-403f-8113-a832d6d5f4ce|Lecture 2]] 
-  - [[https://filesender.utc.fr/filesender/?s=download&token=07b3497b-1c31-400f-b672-1289465e1a28|Lecture 3]] 
-  - [[https://filesender.utc.fr/filesender/?s=download&token=1a169949-8070-4d73-842a-188a2fae7b52|Lecture 4]] 
-  - [[https://filesender.utc.fr/filesender/?s=download&token=e061df39-4fb6-48f0-a8b4-a24a54f13b52|Lecture 5]] 
-  - [[https://filesender.utc.fr/filesender/?s=download&token=b4cb8613-dcdb-4adf-86b7-9484fb5c2725|Lecture 6]] 
-  - [[https://filesender.utc.fr/filesender/?s=download&token=1dddf2ac-caa5-4902-9452-3bd01b88484a|Lecture 7]] 
  
 **Exercises** **Exercises**
  
-  - {{ :en:bf2022_ex_lecture1.pdf |Exercises of lecture 1}} +  - {{ :en:bf2023_ex_lecture1.pdf |Exercises on Chapter 1}} 
-    - {{ :en:bf2022_ex_lecture1sol.pdf |Solutions}} +    - {{ :en:bf2023_ex_lecture1sol.pdf |Solutions}} 
-  - {{ :en:bf2022_ex_lecture2.pdf |Exercise of lecture 2}} +  - {{ :en:bf2023_ex_lecture2.pdf |Exercises on Chapter 2}} 
-    - {{ :en:bf2022_ex_lecture2sol.pdf |Solution}} +    - {{ :en:bf2023_ex_lecture2sol.pdf |Solutions}} 
-  - {{ :en:bf2022_ex_lecture3.pdf |Project of lecture 3}} +  - {{ :en:bf2023_ex_classification.pdf |Exercises on classification}} 
-  - {{ :en:bf2022_ex_clustering.pdf |Project on clustering}} +    - {{ :en:bf2023_ex_classif_sol.pdf |Solutions}} 
-    - {{ :en:clustering_ts.pdf |Solution}}+  - {{ :en:bf2023_ex_pbf.pdf |Exercise on multinomial predictive belief functions}} 
 +    - {{ :en:bf2023_ex_pbf_sol.pdf |Solutions}} 
 +  - {{ :en:bf2023_ex_inference.pdf |Exercises on statistical inference}} 
 +    - {{ :en:bf2023_ex_inference_sol.pdf |Solutions}} 
 +  - {{ :en:bf2023_projets.pdf |Projects}} 
 +    - {{ :en:bf2023_projects_sol.pdf |Solutions}}
    
 +
 **Papers** **Papers**
  
-  - 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. {{en:revues: smc95.pdf|pdf}} +  - 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. {{ :en:smc95_final.pdf |pdf}}
-  - L. M. Zouhal and T. Denoeux. An evidence-theoretic k-NN rule with parameter optimization. IEEE Transactions on Systems, Man and Cybernetics - Part C, 28(2):263-271,1998. {{en:revues:smc96.pdf|pdf}}+
   - T. Denoeux. A neural network classifier based on Dempster-Shafer theory. IEEE Transactions on Systems, Man and Cybernetics A, 30(2):131-150, 2000. {{en:revues: smc2000.pdf|pdf}}   - T. Denoeux. A neural network classifier based on Dempster-Shafer theory. IEEE Transactions on Systems, Man and Cybernetics A, 30(2):131-150, 2000. {{en:revues: smc2000.pdf|pdf}}
-  - T. Denoeux, SSriboonchitta and OKanjanatarakul. Evidential clustering of large dissimilarity data. Knowledge-Based Systemsvol106, pages 179-195 2016. {{:en:publi:evclus_kbs_v2_clean.pdf|pdf}} +  - T. Denoeux. Constructing belief functions from sample data using multinomial confidence regionsInternational Journal of Approximate ReasoningVol42, pages 228-2522006. {{ :en:pbf_final.pdf |pdf}} 
-  - TDenoeux. NN-EVCLUS: Neural Network-based Evidential Clustering. Information SciencesVol. 572, Pages 297-330, 2021. {{ :en:publi:nn_evclus_insv2.pdf |pdf}} +  - OKanjanatarakul, T. Denoeux and SSriboonchitta. Prediction of future observations using belief functionsa likelihood-based approach. International Journal of Approximate Reasoning, Vol. 72, pages 71-942016. {{ :en:ijar_2016_final.pdf |pdf}} 
-  - T. Denoeux. Calibrated model-based evidential clustering using bootstrapping. Information Sciences, Vol. 528, pages 17-45, 2020. {{ :en:publi:bootclus_v2_clean.pdf |pdf}} +  - Thierry Denoeux. Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy setsgeneral framework and practical modelsFuzzy Sets and Systems, Vol. 453pages 1–362023. {{ :en:rfs2_final.pdf |pdf}} 
-  - T. Denoeux. Likelihood-based belief function: justification and some extensions to low-quality data. International Journal of Approximate Reasoning, Volume 55, Issue 7, pages 1535–15472014. {{en:publi:likelihood_v2.pdf|pdf}} +  - T. Denoeux. Quantifying Prediction Uncertainty in Regression using Random Fuzzy Setsthe ENNreg modelIEEE Transactions on Fuzzy Systems (to appear)2023. {{ :en:publi:ennreg_tfs_final.pdf |pdf}}
-  - N. Ben Abdallah, N. Mouhous-Voyneau and T. Denoeux. Combining statistical and expert evidence using belief functionsApplication to centennial sea  level estimation taking into account climate changeInternational Journal of Approximate Reasoning, Vol. 55Issue 1, Part 3, pages 3413542014. {{en:publi:belief_ijar_v2.pdf|pdf}} +
-  - O. Kanjanatarakul, T. Denoeux and S. Sriboonchitta. Prediction of future observations using belief functionsa likelihood-based approachInternational Journal of Approximate ReasoningVol. 72, pages 71-94, 2016. +
-  - Ph. Xu, F. Davoine, H. Zha and T. Denoeux. Evidential calibration of binary SVM classifiers. International Journal of Approximate Reasoning, Vol 72, pages 55-70, 2016. {{:en:publi:evidentialcalibration_final.pdf|pdf}}+
   - 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. {{en:publi:tkde2011.pdf|pdf}}   - 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. {{en:publi:tkde2011.pdf|pdf}}
-  - 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. {{:en:publi:adac2017_v3.pdf|pdf}} +  - 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. {{ :en:adac2017_final.pdf |pdf}}
-  - Thierry Denoeux. Reasoning with fuzzy and uncertain evidence using epistemic random fuzzy sets: general framework and practical models. Fuzzy Sets and Systems (to appear), 2022. {{ :en:publi:random_fs_v2clean.pdf |pdf}} +
- +
  
 **Data** **Data**
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   -{{:en:globalization_2017_short.xlsx.zip|Globalization dataset (full)}}   -{{:en:globalization_2017_short.xlsx.zip|Globalization dataset (full)}}
   -{{ :en:gdp.csv.zip |GDP data}}   -{{ :en:gdp.csv.zip |GDP data}}
 +  -{{ :en:credit_approval.zip |Credit approval dataset}}
    

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