This project investigates alternative model-free approaches, in which model parameters are not explicitly estimated. From a theoretical point of view, the prime advantage of the new paradigm is conceptual unification of existing data modeling and model based data processing methods. From a practical point of view, the proposed paradigm offers new methods for data processing.

The underlying computational tool in the proposed setting is low-rank approximation. A major deliverable of the project is a publicly available robust and efficient software package that makes the new paradigm available in practice. The methods developed in the project and implemented in the package effectively exploit the structure of the data matrices that appears in the applications.

Exploiting the structure leads to statistically optimal maximum likelihood estimators in the errors-in-variables measurement errors setup as well as to numerically fast computational methods.

## Publications of Vladimir Sergeichuk

Areas benefiting from the tools developed in this project are: system and control, signal processing, machine learning, and computer algebra. Different applications lead to structured low-rank approximation problems with different types of structure and constraints. Exploiting the matrix structure in solving the low-rank approximation problem is our expertise. It provides students with the necessary skills to produce effective research in bioinformatics and computational biology. The objective is to provide a short introduction on bioinformatics modelling and advanced tools for the analysis of sequence data.

The first part of the course focuses on application in molecular biology and evolution, including hierarchical clustering and the analysis of phylogenetic and population genetic data. The second part of the course focuses on machine learning for biological data, and includes change point detection in sequences and unsupervised clustering of massive genetic data.

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The course is evaluated with two lab-works, one for each part of the course. Prerequisite: fundamental knowledge on matrix analysis and optimisation corresponding to the Refresher course given at the beginning of the semester is required. Face up challenging real-world problems in machine learning, be involved in multidisciplinary teams of data scientists, computer scientists, mathematicians and expert students in signal processing, and contribute to leading your team to the top rank!

Try and compare different approaches, take benefit from the computational power of clusters and from advice of your supervisors. The data challenges stretch on several months, include some tutored sessions, if needed mini-courses, and of course your regular involvement over that period of time. The objective is to predict the stratigraphy of snow layer height, grain size, density, liquid water content, etc. From a technical point of view, the challenge is to process a large amount of data: radar satellite observations have a repetitiveness of 6 days in the same geographical area.

By focusing only on the Alps, we obtain about xx6 data points every 6 days. Physical models of snow evolution are available and are used to predict snow stratigraphy. An assimilation algorithm allows these stratigraphy to be constrained from SAR satellite data through machine learning and in-depth learning approaches. Target skills : Data management and knowledge extraction have become the core activities of most organizations.

The increasing speed at which systems and users generate data has led to many interesting challenges, both in the industry and in the research community. The data management infrastructure is growing fast, leading to the creation of large data centers and federations of data centers. These can no longer be handled exclusively with classic DBMS. It requires a variety of flexible data models relational, NoSQLâ€¦ , consistency semantics and algorithms issued by the database and distributed system communities.

In addition, large-scale systems are more prone to failures, and should implement appropriate fault tolerance mechanisms. Data is processed in continuous streams providing information related of users context, such as their movement patterns and their surroundings. This data can be used to improve the context awareness of mobile applications and directly target the needs of the users without requiring an explicit query. Combining large amounts of data from different sources offers many opportunities in the domains of data mining and knowledge discovery.

Heterogeneous data, once reconciled, can be used to produce new information to adapt to the behavior of users and their context, thus generating a richer and more diverse experience. As more data becomes available, innovative data analysis algorithms are conceived to provide new services, focusing on two key aspects: accuracy and scalability. Program summary : In this course, we will study the fundamentals and research trends of distributed data management, including distributed query evaluation, consistency models and data integration.

We will give an overview of large-scale data management systems, peer-to-peer approches, MapReduce frameworks and NoSQL systems. Ubiquitous data management and crowdsourcing will also be discussed. Our master programs now include a series of 6 or 7 seminars given by active researchers in the field of data processing methods and analysis. These seminars are intended to give students some insights on modern problems and solutions developed in a data science framework, with applications in a variety of fields.

In order to make these seminars a most valuable experience for all students, a scientific paper dealing with the topic of the seminar will be selected by the speaker and dispatched to all students about 2 weeks before the seminar.

## Toeplitz Matrices, Algorithms and Applications

Students are expected to read and study this paper, and to prepare questions, before attending the seminar. Presence at the seminars is compulsory for master students. At the end of the seminar series, some oral exam is organized. One of the topic presented during the seminars is randomly assigned to each student a few days in advance.

The oral exam consists in a 25 min summarized presentation of the scientific issues that were addressed, and a 15 min session of discussion and questions. A second different topic is chosen by the student, and he. Basic notions: vector space, affine space, metric, topology, symmetry groups, linear and affine hulls, interior and closure, boundary, relative interior.

Convex functions: level sets, support functions, sub-gradients, quasi-convex functions, self-concordant functions. Optimization problems: classification, convex programs, constraints, objective, feasibility, optimality, boundedness, duality. Algorithms: 1-dimensional minimization, Ellipsoid method, gradient descent methods, 2nd order methods. Conic programming: barriers, Hessian metric, duality, interior-point methods, universal barriers, homogeneous cones, symmetric cones, semi-definite programming.

Polynomial optimization: matrix-valued polynomials in one variable, Toeplitz and Hankel matrices, moments, SOS relaxations.

Evaluation : A two-hours written exam E1 in December. For those who do not pass there will be another two-hours exam E2 in session 2 in spring. This lecture introduces fundamental concepts and associated numerical methods in model-based clustering, classification and models with latent structure.

These approaches are particularly relevant to model random vectors, sequences or graphs, to account for data heterogeneity, and to present general principles in statistical modelling. The following topics are addressed:.

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In this course, we will introduce parallel programming paradigms to the students in the context of applied mathematics. The students will learn to identify the parallel pattern in numerical algorithm. The key components that the course will focus on are : efficiency, scalability, parallel pattern, comparison of parallel algorithms, operational intensity and emerging programming paradigm.

Trough different lab assignments, the students will apply the concepts of efficient parallel programming using Graphic Processing Unit.

In the final project, the students will have the possibility to parallelize one of their own numerical application developed in a previous course. Through different lab assignments, the students will apply the concepts of efficient parallel programming using distributed and shared memory programming language OpenMP, MPI. This course addresses advanced aspects of information access and retrieval, focusing on several points: models probabilistic, vector-space and logical , multimedia indexing, web information retrieval, and their links with machine learning.

These last parts provide opportunities to present the processing of large amount of partially structured data. Each part is illustrated on examples associated with different applications. Course 1: Information retrieval basics.

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Course 2: Classical models for information retrieval. Course 3: Natural language processing for information retrieval. Course 4: Theoretical models for information retrieval. Course 5: Web information retrieval and evaluation. Course 6: Social networks and information retrieval. Course 7: Personalized and mobile information retrieval. Course 8: Recommender systems. Course 9: Visual content representation and retrieval. Course Classical machine Learning for multimedia indexing. Course Deep learning for information retrieval. Course Deep learning for multimedia indexing and retrieval.

InfoVis is the study of interactive graphical representations of abstract data e. Graphical representations are a powerfull way to leverage the human perceptual capabilities to allow the user to explore and make sense of abstract data, and also to expose findings and convey ideas. But to be efficient, a visualization has to be designed using knowledge about the human visual perception, the characteristics of the data, the kind of task that will be performed on those data.

The aim of this course is to provide the keys, both theoretical and practical, to build usable and useful interactive visualizations. Methods for addressing such problems are described in this course. These methods are based either on optimal control theory or on statistical estimation theory.

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Interpolation algorithms based on physical knowledge of images content will be studied. Theoretical as well as practical implementation aspects will be considered. Mathematics is necessary for these medical imaging systems to deliver images. We present mathematical problems arising from these medical imaging systems. We show how to reconstruct images from projections of the attenuation function in radiology or respectively of the activity in nuclear imaging.

We present recent advances in 2D and 3D reconstruction problems. Many industrial applications invole expensive computational codes which can take weeks or months to run. It is typical for weather prediction, in aerospace sector or in the civil engineering field. There is here an important economic challenge to reduce the computational cost by constructing a surrogate for the input-to-output relationship. This lecture focuses on some of the most recent advances in that direction. Target skills: The goal of this lecture is to address the difficult problem of approximating high-dimensional functions, meaning functions of a large number of parameters.

The first part of the lecture is devoted to interpolation techniques via polynomial functions or via Gaussian processes. In the second part, we present two methods for reducing the dimension of the input parameters space, namely the Sliced Inverse Regression and the Ridge Function Recovery. When estimating parameters in a statistical model, sharp calibration is important to get optimal performances. In this course, we will focus on the selection of estimators with respect to the data. Particularly, we will consider calibration of parameters e. We will focus on the penalized empirical risk, where the penalty may be deterministic as BIC or ICL or estimated with data as the slope heuristic.

References T. Hastie, R.