UMR CNRS 7253

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en:bf [2017/07/21 04:28] 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:cmu_2017_lecture1.pdf|Lecture 1 Representation and combination of evidence}}+  - {{ :en:bf2023_lecture1.pdf |Belief functions on finite frames. Dempster's rule}} 
 +  {{ :en:bf2023_lecture2.pdf |Decision analysis and classification}} 
 +  - {{ :en:bf2023_lecture3.pdf |Multinomial predictive belief functions}} 
 +  - {{ :en:bf2023_lecture4.pdf |Statistical inference}}
    
 +
 +
 **Exercises** **Exercises**
  
-  - {{:en:ex_lecture1.pdf|Lecture 1}}+  - {{ :en:bf2023_ex_lecture1.pdf |Exercises on Chapter 1}} 
 +    - {{ :en:bf2023_ex_lecture1sol.pdf |Solutions}} 
 +  - {{ :en:bf2023_ex_lecture2.pdf |Exercises on Chapter 2}} 
 +    - {{ :en:bf2023_ex_lecture2sol.pdf |Solutions}} 
 +  - {{ :en:bf2023_ex_classification.pdf |Exercises on classification}} 
 +    - {{ :en:bf2023_ex_classif_sol.pdf |Solutions}} 
 +  - {{ :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. Constructing Belief Functions from Sample Data Using Multinomial Confidence RegionsInternational Journal of Approximate ReasoningVol. 42, Issue 3Pages 228-2522006. {{en:revues: ijar2006.pdf|pdf}} +  - T. Denoeux. A k-nearest neighbor classification rule based on Dempster-Shafer theoryIEEE Transactions on SystemsMan and Cybernetics25(05):804-8131995. {{ :en:smc95_final.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: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 O. Kanjanatarakul. Evidential clustering of large dissimilarity dataKnowledge-Based Systems, vol106, pages 179-195,  2016. {{:en:publi:evclus_kbs_v2_clean.pdf|pdf}}+  - T. Denoeux. Constructing belief functions from sample data using multinomial confidence regions. International Journal of Approximate ReasoningVol42, pages 228-252, 2006. {{ :en:pbf_final.pdf |pdf}} 
 +  - O. Kanjanatarakul, TDenoeux and S. Sriboonchitta. Prediction of future observations using belief functions: a likelihood-based approachInternational Journal of Approximate Reasoning, Vol. 72, pages 71-94, 2016. {{ :en:ijar_2016_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, Vol453, pages 1–362023. {{ :en:rfs2_final.pdf |pdf}} 
 +  - T. Denoeux. Quantifying Prediction Uncertainty in Regression using Random Fuzzy Sets: the ENNreg model. IEEE Transactions on Fuzzy Systems (to appear), 2023. {{ :en:publi:ennreg_tfs_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}}
-  - OKanjanatarakul, T. Denoeux and S. SriboonchittaPrediction of future observations using belief functions: a likelihood-based approachInternational Journal of Approximate Reasoning, Vol. 72pages 71-942016. {{:en:publi:ijar_belief2014_v3.pdf|pdf}}+  - BQuost, T. Denoeux and S. LiParametric Classification with Soft Labels using the Evidential EM AlgorithmLinear Discriminant Analysis vs. Logistic Regression. Advances in Data Analysis and Classification, Vol. 11Issue 4pp 659–690, 2017. {{ :en:adac2017_final.pdf |pdf}}
  
 +**Data**
  
-**R code** +  -{{:en:global2000_2014.txt|Globalization data (2000, 2014)}} 
- +  -{{:en:globalization_2017_short.xlsx.zip|Globalization dataset (full)}} 
-  -{{:en:example1.txt|Behrens-Fisher example}} +  -{{ :en:gdp.csv.zip |GDP data}} 
 +  -{{ :en:credit_approval.zip |Credit approval dataset}}
    
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