1 An Introduction to Machine Learning: Methodologies and Practical Implementation

• Đối tượng người học - Audience: anybody in sciences and engineering, including anybody interested in Machine Learning, applied math, life sciences, computer science, electrical engineering, bioengineering, etc, including people outside of academia.
• Kiến thức cần có - Background: calculus, linear algebra, proficiency with some programming (python, MATLAB)
• Giảng viên:
  • Kevin Flores, Assistant Professor, Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University
  • Erica Rutter, Postdoctoral fellow, Department of Mathematics, Center for Research in Scientific Computation, North Carolina State University
  • Hien Tran, Alumni Distinguished Graduate Professor, Director Center for Research in Scientific Computation, Department of Mathematics, North Carolina State University
• Thời gian: June 17--21, 2019. Phòng học: Giảng đường 1, từ chiều Thứ ba: B11A
• Tóm tắt:
  • What is Machine Learning? “Machine learning teaches computers to do what come naturally to humans and animals: learn from experience. Machine learning algorithms use computational methods to “learn” information directly from data without relying on a predetermined equation as a model. The algorithms adaptively improve their performance as the number of samples available for learning increases” (from MathWorks, Natick, MA)
  • In this mini-lecture series, we will explore the core machine learning concepts and their computational implementation. Several real data, where applicable, will be used to test the numerical implementation.
  • Prerequisite: Participants need to bring their own laptops. Programming proficiency (Python, MATLAB)
• Course Timeline: Morning Lecture: 9:00 – 10:15 Break: 10:15 – 10:45 Lecture: 10:45 – 12:00 Afternoon Lecture: 2:00 – 3:15 Break: 3:15 – 3:45 Lecture: 3:45 – 5:00
• Course Topics:
  •  Monday:  ◦ AM (Hien): Bayesian Classifiers, Perceptron, Multilayer Perceptron (Neural Networks)
            ◦ PM (Erica): TensorFlow, UCI Machine Learning Repository: Iris and Diabetes Data Sets
  • Tuesday:  ◦ AM (Hien): Support Vector Machines (separable classes, nonseparable classes), Decision Tree
            ◦ PM (Erica): Tutorial: Scikit-Learn, Credit Card Approval Data Sets
  • Wednesday: (free day) No Lecture
  • Thursday: ◦ AM (Kevin): Convolutional Neural Networks, Computer Vision, Segmentation and Classification
            ◦ PM (Erica): MNIST Data Set, Imagenet, ISBI cell segmentation
  • Friday: ◦ AM (Kevin): Recurrent Neural Networks (RNN), Long Short-Term Memory (LSTM) Networks, Natural Language Processing (NLP), Time Series Data
            ◦ PM (Erica): Time series data, sentiment classification, NLP for translation
            ◦ Optional: Model Evaluation (confusion matrix, loss function, ROC, hypothesis testing), Multi-Class, Dimensionality Reduction (TSNE) – MNIST data last layer dimension reduction

2 Stochastic Models in Ecologie and Evolution: Pure jump Markov Processes in Continuous Time

• Giảng viên: Sylvie Méléard, Professor, CMAP, École Polytechnique, France
• Thời gian: July 15–19, 2019. Monday 9:00 - 11:45, Tuesday - Friday 8:45 - 11:30. Problem session by Dr. Hoàng Văn Hà: Monday, Wednesday, Friday, 13:30 - 16:00. Phòng F207
• Tóm tắt: In these lectures, we will give the structure of the pure jump Markov processes with countable values. The prototype is the Poisson process that we will study in details. We will define the infinitesimal generator and prove the Kolmogorov equations.  Then we will study two well-known examples, useful especially for applications in biology:  branching processes and birth and death processes describing population dynamics. In both cases, we will give criteria of existence and extinction. Finally, we will study  approximations of large populations, showing how these jump processes can be approximated in this case, either by dynamical systems or by stochastic differential equations.

• Tài liệu tham khảo:

  [1] Modèles aléatoires en écologie et évolution, Mathématiques et Applications 77, SMAI. Springer, 2016. (In French)

  Link download: http://www.cmap.polytechnique.fr/IMG/pdf/LIVRE07102013.pdf

  [2] L.J.S. Allen. An Introduction to Stochastic Processes with Applications to Biology, Second edition. CRC Press, Chapman & Hall/CRC, 2011.

  [3]  V. Bansaye, S. Méléard. Stochastic Models for Structured Populations. Mathematical Biosciences Institute Lecture Series 1.4. Springer 2015.

  Link download: https://arxiv.org/abs/1506.04165

  [4] Ross, Sheldon M. "Stochastic Processes. John Wiley& Sons." New York (1996).

3 An Introduction to Geometric Group Theory

• Giảng viên: Nhan-Phu Chung, Department of Mathematics, Sungkyunkwan University, Korea.
• Thời gian: August 12-14, 2019, 9:00-11:00.
• Tóm tắt: I will present finitely generated groups as viewpoints of metric spaces via word lengths and quasi-isometries. In this part, I will prove a result of Schwarzc-Milnor which is a fundamental observation of geometric group theory. In the second part of the course, I will introduce growth types of finitely generated groups. A landmark result in geometric group theory is Gromov’s theorem stating that a finitely generated group is virtually nilpotent if and only if it has polynomial growth. If time allows I will provide a sketch of Gromov’s proof.
• References
  1. Tullio Ceccherini-Silberstein and Michel Coornaert, Cellular automata and groups, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2010.
  2. Pierre de la Harpe, Topics in geometric group theory, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 2000.
  3. Mikhael Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53–73.