# MIS-IMH research school on Mathematics of Data

# This School has been cancelled

### MIS-IMH research school on Mathematics of Data

Hanoi, 4-13 March, 2020

**AIM AND OBJECTIVE**

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- Science is relying increasingly on large data sets. They provide important resources, and we have ever more powerful computational devices to treat them, but we often lack good prior theories to make sense of them or hypotheses to test on them. We therefore need novel formal methods to identify and extract meaningful structures in large and intransparent data sets. This is a challenge and an opportunity for mathematics. In fact, ideas from very different mathematical disciplines have been used to provide new tools for data analysis. Topological data analysis uses methods from algebraic topology, manifold learning is inspired by Riemannian geometry, compressed sensing uses Banach space theory, hierarchical decompositions utilize tensor algebra, network analysis has inspired graph theory and currently moves towards hypergraphs, to name but a few examples. In particular, statistics faces new problems, either of large data sets without good model classes or conversely models with many more free parameters than available observations.

This is an exciting situation for mathematics. We want to introduce the participants of this school to those problems and to a wide range of new mathematical techniques, and to prepare them to pursue novel mathematical research. - At this school, we want to provide a stimulating intellectual environment for researchers from Vietnam and neighboring countries in Asia to learn about recent developments in mathematical data science, acquire background knowledge from the relevant mathematical disciplines and interact with leading researchers on concrete topics of mathematical data analysis and statistics.

**CONCRETE TOPICS WILL INCLUDE**

- Deep learning theory
- Statistical/probabilistic/optimization foundation for data
- Graph theory and neural networks
- Information complexity

**SCHOOL LOCATION**

Institute of Mathematics, Hanoi (IMH), Vietnam Academy of Science and Technology (VAST).

Address: 18 Hoang Quoc Viet Road, Cau Giay disctrict, 10307 Ha Noi, Vietnam.

Contact

Email: misimh2020@math.ac.vn

**ORGANIZING INSTITUTIONS**

- Max Planck Institute for Mathematics in the Sciences (MIS)- Germany
- Institute of Mathematics, Vietnam Academy of Science and Technolgy, Vietnam.

**SCIENTIFIC ORGANIZERS**

- Jürgen JOST, Max Planck Institute for Mathematics in the Sciences, Germany (chair)
- Duc Hoang LUU, Institute of Mathematics, VAST, Vietnam & Max Planck Institute for Mathematics in the Sciences, Germany.

**LOCAL ORGANIZERS**

- Duc Hoang LUU, Institute of Mathematics, VAST, Vietnam & Max Planck Institute for Mathematics in the Sciences, Germany.
- Hung Viet PHAM, Institute of Mathematics, VAST, Vietnam.

**Lecturer 1**: **Jürgen JOST, Max Planck Institute for Mathematics in the Sciences**

Course title: **Geometric, topological and analytical methods of data analysis**

*Abstract:* This series of lectures will introduce a variety of mathematical approaches for finding and exploiting structure in data. Topological data analysis investigates how topological invariants based on the proximity of data points change as the scale of resolution varies.

Manifold learning can detect intrinsically low-dimensional smooth data sets that extrinsically may span a huge number of dimensions. Spectral analysis and discrete invariants can reveal qualitative properties of networks. When relations involve more than two items, as for instance in chemical reaction networks, we can model that by simplicial complexes or hypergraphs, and we shall also develop the corresponding mathematical methods systematically.

**Lecturer 2: Nihat AY, Max Planck Institute for Mathematics in the Sciences**.

Course title: * Artificial Neural Networks and Machine Learning: Theoretical Foundations*.

*Abstract*: This course will provide a review of core ideas within the fields of neural networks and machine learning. It will be structured in line with the historical developments of artificial intelligence. Particular emphasis will be but on various mathematical concepts and methods related to universal approximation, natural gradient, deep neural networks, statistical learning theory, and support vector machines.**Lecturer 3: Hồng Vân Lê, Institute of Mathematics of ASCR, Czech Republic**

Course title: *Mathematical foundations of Machine Learning*

* Abstract*: Machine learning is an interdisciplinary field in the intersection of mathematical statistics and computer sciences.

Machine learning studies statistical models and algorithms for deriving predictors and meaningful patterns from empirical data.

Machine learning techniques are applied in search engine, speech recognition and natural language processing, image detection, robotics etc. In our course we discuss mathematical models of learning mathematical principles in supervised learning, unsupervised learning and Baysean machine learning. The course consists of six lectures which cover the following topics:

mathematical models of supervised learning and unsupervised learning, generalization ability of machine learning, support vector machine,

kernel machine, neural networks and Bayesian networks.

**Recommended Literature**:

1. S. Shalev-Shwart and S. Ben-David, Understanding Machine Learning:

From Theory to Algorithms, Cambridge University Press, 2014

2. Sergios Theodoridis, Machine Learning A Bayesian and Optimization Perspective, Elsevier, 2015

**Lecturer 4 : Guido Montúfar, Max Planck Institute for Mathematics in the Sciences & UCLA**

Course title: **Wasserstein Information Geometry for Learning from Data***Abstract*: This lecture will provide an introduction to Wasserstein Information Geometry for learning from data. This is an active area that combines Information Geometry and Wasserstein Geometry in order to capture two important aspects of learning: the geometry of the learning model and the geometry of the data under consideration. First we introduce Information Geometry, which emphasises the geometry of the learning model, based on natural notions of invariance with respect to transformations of the hypotheses and their parametrisation. Then we introduce Wasserstein Geometry, which departs from the geometry of the data space. We discuss consequences, computation, applications, and topics of current research.**Lecturer 5: Duc Hoang LUU, Institute of Mathematics, VAST & Max Planck Institute for Mathematics in the Sciences**

Course Title:** Rough paths, signatures in data streams**

*Abstract*: In the recent years, the signature first studied by K.T. Chen has gained attention in the mathematical and statistical community due to its connection with T. Lyons' theory of rough paths. It also provide new tools for analysing and describing these data streams and extracting the vital information. This course aims to illustrate how effectively the information obtained from the signature of data can be used to classify the data, based on which useful predictions could be made.

The course presents first the fundamental application of signature in integration theory and rough differential equations. The second part shows examples in finance and machine learning, where the signature method transforms raw data into a set of features used in machine learning tasks, thus representing a non-parametric way for extraction of characteristic features from data.**Van Hau NGUYEN, Hung Yen University of Technology and Education, Vietnam**

Course title: **Introduction to Machine Learning with Python**

*Abstract*: This course provides the basics of machine learning using a well-known programming language Python. In particular, we will address three parts: First, you will be introducing about Machine Learning in general, i.e. where, why and when ML is used. Second, you will get an overview of Machine Learning topics such as supervised vs unsupervised learning, and Machine

Learning algorithms. Third, you will be providing some Python libraries (e.g. scikit-learn) for Machine Learning.

Throughout practice with real-life examples of Machine learning, the learners will be able to: use Python and its libraries to implement Machine learning algorithms, e.g. regression, classification, clustering; and apply machine learning algorithms to some domains, for example cancer detection, predicting economic trends, recommendation engines, etc.**Viet Hung PHAM, Institute of Mathematics, VAST, Vietnam**

Course title: **Preparation course on Statistics**

* Abstract*: This course aims to provide students with basic knowlegde in probability and statistics in order to have better understanding of their applications in the following courses on data science and machine learning. We will review important topics on: probability space, random variables, limit theorems, point estimation with Maximum Likelihood Estimation technique, regression, clustering and time series analysis.

**Registration**

- There are no registration fees
- If you are interested in participating in the school, please register online here
- We have some financial supports (travels, accommodation and living expenses) for participants from neighboring countries and from outside of Hanoi. To apply you need to submit your CV and one letter of recommendation to the address here misimh2020@math.ac.vn

- Max Planck Institute for Mathematics in the Sciences
- International Centre for Research and Postgraduate Training in Mathematics, Hanoi (ICRTM)
- The Simons Foundation Targeted Grant for the Institute of Mathematics, Hanoi

**Sketch timetable**

Time | Wednesday 4/3 | Thursday 5/3 | Friday 6/3 |

08:30-09:00 | REGISTRATION | ||

09:00-09:45 | Prep. course | Prep. course | Prep. course |

09:45-10:30 | Prep. course | Prep. course | Prep. course |

10:30-11:00 | Coffee break | Coffee break | Coffee break |

11:00-11:45 | Prep. course | Prep. course | Prep. course |

11:45-14:00 | Lunch | Lunch | Lunch |

14:00-14:45 | Python course | Python course | Python course |

14:45-15:30 | Python course | Python course | Python course |

15:30-16:00 | Coffee break | Coffee break | Coffee break |

16:00-16:45 | Python course | Python course | Python course |

Time | Monday 9/3 | Tuesday 10/3 | Wednesday 11/3 | Thursday 12/3 | Friday 13/3 |

08:30-09:00 | OPENING | ||||

09:00-09:45 | Mini-course 1 | Mini-course 3 | Mini-course 5 | Mini-course 2 | Mini-course 4 |

09:45-10:30 | Mini-course 1 | Mini-course 3 | Mini-course 5 | Mini-course 2 | Mini-course 4 |

10:30-11:00 | Coffee break | Coffee break | Coffee break | Coffee break | Coffee break |

11:00-11:45 | Mini-course 1 | Mini-course 3 | Mini-course 5 | Mini-course 2 | Mini-course 4 |

11:45-14:00 | Lunch | Lunch | Lunch | Lunch | Lunch |

14:00-14:45 | Mini-course 2 | Mini-course 4 | Mini-course 1 | Mini-course 3 | Mini-course 5 |

14:45-15:30 | Mini-course 2 | Mini-course 4 | Mini-course 1 | Mini-course 3 | Mini-course 5 |

15:30-16:00 | Coffee break | Coffee break | Coffee break | Coffee break | Coffee break |

16:00-16:45 | Mini-course 2 | Mini-course 4 | Mini-course 1 | Mini-course 3 | Mini-course 5 |

16:45-17:00 | CLOSING | ||||

19:00-21:30 | BANQUET |

**1. About Institute of Mathematics, Hanoi**

The Institute of Mathematics, Hanoi (IMH) is a leading research institute of Vietnam. Along its 50 year history, it is recognized by the Third World Academy of Science (TWAS) as a Center of Excellence in developing countries. The IMH has a long history of hosting many international workshops and conferences in many fields of mathematical research.

Website: http://www.math.ac.vn

**2. How to apply visa to Vietnam**

Visitors to Vietnam must have a valid passport. Firstly, one should find out if one needs a visa to enter Vietnam.

Visa exemptions are provided to citizens of many countries such as Asean countries, France, Germany, South Korea. Please check here for more detail.

For citizens of other countries, complete information on how to apply for a VISA to enter Vietnam can be found on the website of Vietnam embassies or consulates. Please visit this link for the list of them.

Attendees of a scientific conference should apply for a business visitor visa to Vietnam. We are very glad to assist you if you need a visa. In this case, please download this form and send your data to the email misimh2020@math.ac.vn before January 15^{st}, 2020.

**3. How to go from NoiBai International Airport to Hotels/guesthouse**

For lecturers and invited guests, we will arrange a pick-up service for you. In case of unexpected event that you cannot meet the pick-up person, you can take a taxi from Noi Bai airport to the hotel or any other places in the city center. The taxi costs you around 15-20 USD for one way trip.** **

Those who stay in the guesthouse should remember the address of the Institute of Mathematics: 18 Hoang Quoc Viet street, Cau Giay district, Hanoi.

We recommend you to visit the website http://www.vietnamtourism.vn/ for useful information about Hanoi and Vietnam with its charm and rich culture.