[{"command":"insert","method":null,"selector":".course-modal-ajax-placeholder-962042","data":"\u003Cdiv class=\u0022container content-rte\u0022\u003E\n  \u003Cdiv class=\u0022row\u0022\u003E\n    \u003Cdiv class=\u0022box col-md-6 bg-primary text-white\u0022\u003E\n      \u003Ch2 class=\u0022h1 text-left\u0022\u003E  Mathematical Basis for Communication and Learning\n\u003C\/h2\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EECTS :\n          4\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                  \u003Cdiv class=\u0022field-spacing\u0022\u003E\n        \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ESemestre calendaire :\n          Semestre 1\n        \u003C\/div\u003E\n      \u003C\/div\u003E\n                    \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ELangue d\u0026#039;enseignement\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EAnglais\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EEnseignement \u00e0 distance\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003Enon\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n    \u003Cdiv class=\u0022box col-md-6\u0022\u003E\n                    \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EProgramme \/ plan \/ contenus\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EPart I\u0026nbsp;\u003Cbr\u003E\n- Introduction to probabilities on events.\u003Cbr\u003E\n- Probabilities on a finite or countable space\u003Cbr\u003E\n- Random variables on continuous space (R). Independent random variables and characteristic functions.\u003Cbr\u003E\n- Multivariate distributions (Gaussian distribution).\u003Cbr\u003E\n- Different convergences (Central Limit Theorem and the Laws of Large Number).\u003Cbr\u003E\n- Introduction to parameter estimation and confidence areas\u003Cbr\u003E\n- Concept of sufficient statistics\u003Cbr\u003E\n- UMVU (Uniformly Minimum-Variance Unbiased) estimators\u003Cbr\u003E\n- Cram\u00e9r-Rao bound, Fisher information\u003Cbr\u003E\n- Maximum Likelihood estimator, asymptotic efficiency\u003Cbr\u003E\n- Bayesian estimators (MMSE, L1 Norm, MAP)\u003Cbr\u003E\n- Posterior Cram\u00e9r-Rao bound\u003Cbr\u003E\n- Detection: Neyman-Pearson lemma\u003Cbr\u003E\n- Bayesian detection.\u003C\/p\u003E\n\u003Cp\u003EPart II\u003C\/p\u003E\n\u003Cul\u003E\n\u003Cli\u003EReview of fundamental notions of set theory and topology\u003C\/li\u003E\n\u003Cli\u003EUnconstrained optimization\u003C\/li\u003E\n\u003Cli\u003EConstrained optimization\u003C\/li\u003E\n\u003Cli\u003EKKT conditions\u003C\/li\u003E\n\u003Cli\u003EThe important case of convex optimization, global optimality, duality principle\u003C\/li\u003E\n\u003Cli\u003EA short note on optimization in dynamical systems: the dynamic programming principle (Viterbi algorithm example), HJB equation\u003C\/li\u003E\n\u003Cli\u003ENumerical methods for optimum design\u003C\/li\u003E\n\u003Cli\u003EDistributed optimization in communication networks\u003C\/li\u003E\n\u003Cli\u003EBasic notions of games and learning\u003C\/li\u003E\n\u003C\/ul\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EObjectifs d\u0026#039;apprentissage\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EThe aim of the first part of this course is refreshing basic notions in probability theory and providing students with sound knowledge in estimation (decision) theory. In the second part of the course, the purpose is to introduce fundamental tools which are used in typical optimization problems encountered in the analysis and design of communications and learning systems.\u0026nbsp; Many examples of use of the aforementioned tools in telecommunications and learning will be provided.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EOrganisation g\u00e9n\u00e9rale et modalit\u00e9s p\u00e9dagogiques\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003EThe course is divided into two parts: i) probability and estimation theory, and ii) optimization theory and numerical methods. The course is composed of lectures and sessions reserved for solving problems sets.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n                        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003EBibliographie\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003E\u003Cp\u003E[1] JACOD, J. AND PROTTER, P.E., Probability Essentials, Springer Verlag, 2003\u0026nbsp;\u003C\/p\u003E\n\u003Cp\u003E[2] BREMAUD, P., An Introduction to Probabilistic Modeling, Springer, 1988\u0026nbsp;\u003C\/p\u003E\n\u003Cp\u003E[3] CHUNG, K.L., A Course in Probability Theory, Academic Press, 2001\u0026nbsp;\u003C\/p\u003E\n\u003Cp\u003E[4] FELLER, W., An Introduction to Probability Theory and its Applications, Vol I \u0026amp; II - John Wiley \u0026amp; Sons, Wiley Series in Probabilities and Statistics, 1968\u0026nbsp;\u003C\/p\u003E\n\u003Cp\u003E[5] LEHMANN E.L., and CASELLA, G., Theory of Point Estimation, Springer Texts in Statistics, 2003\u0026nbsp;\u003C\/p\u003E\n\u003Cp\u003E[6] LEHMANN, L., and ROMANO, J.P., Testing Statistical Hypotheses, Springer Texts in Statistics, 2006 [\u003C\/p\u003E\n\u003Cp\u003E[7] ARORA, J. A, Introduction to Optimum Design, Elsevier Academic Press, 2nd edition, 2004.\u0026nbsp;\u003C\/p\u003E\n\u003Cp\u003E[8] BOYD, S., and VANDENBERGHE, L., Convex Optimization, Cambridge University Press, 2004.\u0026nbsp;\u003C\/p\u003E\n\u003Cp\u003E[9] HIRIART-URRUTY, J.-B., and LEMARECHAL C., Convex Analysis and Minimization Algorithms I and II, Springer-Verlag, 1993.\u0026nbsp;\u003C\/p\u003E\n\u003Cp\u003E[10] HADJISAVVAS, N. et al, Handbook of Generalized Convexity and Generalized Monotonicity, Springer, 2005.\u0026nbsp;\u003C\/p\u003E\n\u003Cp\u003E[11] ENGWERDA, J. C., LQ Dynamic Optimization and Differential Games, Wiley, 2005.\u003C\/p\u003E\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n        \u003Cdiv class=\u0022field-spacing\u0022\u003E\n      \u003Cdiv class=\u0022field__label h3 dash\u0022\u003ENature de l\u0026#039;\u00e9valuation\u003C\/div\u003E\n                        \u003Cdiv class=\u0022mt-5 text-justify\u0022\u003E\n                                      \u003Cspan\u003EEvaluation Continue non Int\u00e9grale\u003C\/span\u003E\n                      \u003C\/div\u003E\n                  \u003C\/div\u003E\n      \u003C\/div\u003E\n  \u003C\/div\u003E\n\u003C\/div\u003E\n","settings":null}]