Research Center for Statistical Machine Learning
The Institute of Statistical Mathematics, Tokyo, Japan
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Biography:I am interested in thoery and practice of learning with complex and structured data, and working from the viewpoints of statistics, mathematics and machine learning. More specific research projects include the following topics:
- Topological Data Analysis (TDA): A new methodoogy of data anlalysis for complex geometrical objects. TDA uses persistence homology, which expresses topological and geometrical information of data in an algebraic form.
- Kernel method (data analysis with positive definite kernels): Nonparametric data analysis with positive definite kernels and reproducing kernel Hilbert spaces. Expressing probabilistic knowledge using embedding of data in reproducing kernel Hilbert spaces, and its applications to extracting dependence, conditional dependence structure among variables. Inference of causal networks with these methods.
- Geometry of algorithms on graphs: Analysis of algorithms on graphs, such as belief propagation, with graph geometry, graph polynomial and so on.
- Singular statistical models: Statistical inference with parametric models with singularities. Nonstandard asymptotic behavior of the estimator around sigularities.
Abstract:Topological data analysis (TDA) is a recent methodology for extracting topological and geometrical features from complex geometric data structures. The key technology is a mathematical notion called "persistent homology", which was recently proposed by Edelsbrunner (2002). Persistence homology provides a multiscale descriptor for the topology of data, and has been recently applied to a variety of data analysis. In this tutorial I will give a basic and intuitive explanation on the framework of TDA and persistence homology. In TDA with persistence homology, the topological and geometrical properties of data are often expressed by a persistence diagram, which is a plot of the birth and death of all generators of the persistence homology. Application of standard data analysis methods to persistence diagrams, however, is not trivial due to its non-vector nature. I will introduce a method of kernel embedding of the persistence diagrams to obtain their vector representation, which enables one to apply a variety of data analysis to persistence diagrams. I will also show some examples of data analysis, including applications to material sciences, to demonstrate usefulness of the methodology.
Department of Computer Science and Electrical Engineering
University of Maryland Baltimore County, USA
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Biography:Tülay Adali received the Ph.D. degree in Electrical Engineering from North Carolina State University, Raleigh, NC, USA, in 1992 and joined the faculty at the University of Maryland Baltimore County (UMBC), Baltimore, MD, the same year. She is currently a Distinguished University Professor in the Department of Computer Science and Electrical Engineering at UMBC.
She has been very active in conference and workshop organizations. She was the general or technical co-chair of the IEEE Machine Learning for Signal Processing (MLSP) and Neural Networks for Signal Processing Workshops 2001-2008, and helped organize a number of conferences including the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP). She has served or currently serving on numerous editorial boards and technical committees of the IEEE Signal Processing Society. She was the chair of the IEEE Signal Processing Society Technical Committee on MLSP, 2003-2005 and 2011-2013, and the Technical Program Chair for ICASSP 2017. She is the Special Sessions Chair for ICASSP 2018.
Prof. Adali is a Fellow of the IEEE and the AIMBE, a Fulbright Scholar, and an IEEE Signal Processing Society Distinguished Lecturer. She is the recipient of a 2013 University System of Maryland Regents' Award for Research, an NSF CAREER Award, and a number of paper awards including the 2010 IEEE Signal Processing Society Best Paper Award.
Her current research interests are in the areas of statistical signal processing, machine learning, and applications in medical image analysis and fusion.
Abstract:Successful fusion of information from multiple sets of data is key to many problems in engineering and computer science. In data fusion, since most often, very little is known about the relationship of the underlying processes that give rise to such data, it is desirable to minimize the modeling assumptions, and at the same time, to maximally exploit the interactions within and across the multiple sets of data. This has been the main reason for the growing importance of data-driven methods, and in particular those based on matrix and tensor factorizations. A key concept in such decompositions is that of “diversity”. Diversity refers to any structural, numerical, or statistical inherent property or assumption on the data that contributes to the identifiability of the model. In the presence of multiple datasets, diversity establishes the link among them and is thus the key and enabling factor to data fusion.
In this tutorial, the main theoretical concepts for data fusion using matrix and tensor decompositions are reviewed starting with the concept of diversity, which enables identifiability. A number of models based on independent component analysis (ICA) and its recent extension to multiple datasets independent vector analysis (IVA) are discussed along with those based on basic tensor decompositions. Finally, the link between the theoretical results and practice is established by addressing interpretability and key implementation issues. A number of examples from multiple domains are presented to illustrate the concepts.