{"id":388,"date":"2019-04-14T16:25:12","date_gmt":"2019-04-14T15:25:12","guid":{"rendered":"http:\/\/pageperso.math.univ-toulouse.fr\/statistics-geometry-and-topology\/?page_id=388"},"modified":"2019-04-14T16:54:11","modified_gmt":"2019-04-14T15:54:11","slug":"first-week","status":"publish","type":"page","link":"https:\/\/perso.math.univ-toulouse.fr\/statistics-geometry-and-topology\/accueil\/master-school-on-data-science-and-geometry\/first-week\/","title":{"rendered":"First week 2-5 July"},"content":{"rendered":"<p><span style=\"color: #ff99cc;font-size: 14pt\">Geometry Lecture (10h)\u00a0 <em>An Introduction to Riemannian Geometry<\/em><\/span><\/p>\n<p><span style=\"font-size: 14pt\">Paulo Carrillo Rouse<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 14pt\">Lecture 1 (2 hours) Differentiable manifolds, tangent spaces, vector fields.<\/span><\/li>\n<li><span style=\"font-size: 14pt\">Lecture\u00a0 2 (2 hours)\u00a0 Riemannian metrics and Riemannian connections.<\/span><\/li>\n<li><span style=\"font-size: 14pt\">Lecture 3 (2 hours) Geodesics; convex neighbourhoods.<\/span><\/li>\n<li><span style=\"font-size: 14pt\">Lecture\u00a0 4 (2 hours) Curvature. Ricci and scalar curvature. Tensors on Riemannian manifolds.<\/span><\/li>\n<li><span style=\"font-size: 14pt\">Lecture\u00a0 5 (2 hours) Jacobi fields. Morse Index theorem.<\/span><\/li>\n<\/ul>\n<p><span style=\"color: #ff99cc;font-size: 14pt\">Statistics Lecture (10h) <em>Probability\u00a0background for statistical learning<\/em><\/span><\/p>\n<p><span style=\"font-size: 14pt\">Cl\u00e9ment Pellegrini and Thierry Klein<\/span><\/p>\n<ul>\n<li><span style=\"font-size: 14pt\">Lecture 1 and 2 (4 hours) Convergence of random variables, SLLN, CLT Delta method and Slutsky lemma , Gaussian vectors, Classical concentration inequalities.<\/span><\/li>\n<li><span style=\"font-size: 14pt\">Lecture 3 (2 hours) Conditional expectation.<\/span><\/li>\n<li><span style=\"font-size: 14pt\">Lecture 4 (2 hours) Parameter estimation in statistics. Moments methods and maximum likelihood estimation. Confidence sets.<\/span><\/li>\n<li><span style=\"font-size: 14pt\">Lecture 5 (2 or 4 hours) Basic methods in statistical learning. PCA, Regression, k-nearest neighbours algorithm, theoretical study of the rate of convergence of the k-nearest neighbours algorithm.<\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Geometry Lecture (10h)\u00a0 An Introduction to Riemannian Geometry Paulo Carrillo Rouse Lecture 1 (2 hours) Differentiable manifolds, tangent spaces, vector fields. Lecture\u00a0 2 (2 hours)\u00a0 Riemannian metrics and Riemannian connections. Lecture 3 (2 hours) Geodesics; convex neighbourhoods. Lecture\u00a0 4 (2 hours) Curvature. Ricci and scalar curvature. Tensors on Riemannian manifolds. Lecture\u00a0 5 (2 hours) Jacobi [&hellip;]<\/p>\n","protected":false},"author":203,"featured_media":0,"parent":377,"menu_order":0,"comment_status":"closed","ping_status":"open","template":"template-full-width.php","meta":{"footnotes":""},"class_list":["post-388","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/perso.math.univ-toulouse.fr\/statistics-geometry-and-topology\/wp-json\/wp\/v2\/pages\/388","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/perso.math.univ-toulouse.fr\/statistics-geometry-and-topology\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/perso.math.univ-toulouse.fr\/statistics-geometry-and-topology\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/perso.math.univ-toulouse.fr\/statistics-geometry-and-topology\/wp-json\/wp\/v2\/users\/203"}],"replies":[{"embeddable":true,"href":"https:\/\/perso.math.univ-toulouse.fr\/statistics-geometry-and-topology\/wp-json\/wp\/v2\/comments?post=388"}],"version-history":[{"count":4,"href":"https:\/\/perso.math.univ-toulouse.fr\/statistics-geometry-and-topology\/wp-json\/wp\/v2\/pages\/388\/revisions"}],"predecessor-version":[{"id":410,"href":"https:\/\/perso.math.univ-toulouse.fr\/statistics-geometry-and-topology\/wp-json\/wp\/v2\/pages\/388\/revisions\/410"}],"up":[{"embeddable":true,"href":"https:\/\/perso.math.univ-toulouse.fr\/statistics-geometry-and-topology\/wp-json\/wp\/v2\/pages\/377"}],"wp:attachment":[{"href":"https:\/\/perso.math.univ-toulouse.fr\/statistics-geometry-and-topology\/wp-json\/wp\/v2\/media?parent=388"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}