lab-en

Mathematics of design optimization

Design optimization is the methodology that utilizes mathematical
optimization to improve the rationality and sophistication of design
processes in engineering. We mainly focus on developing mathematical
modelings and numerical algorithms for solving diverse optimal design
problems.

Statistical Modeling of Dependence

We develop statistical models and inference methods of dependence
structure hidden in various data.
The keywords are copula theory, directional statistics, optimal
transport and algebraic statistics.

Statistical Analysis of Stochastic Processes

We study statistical methods for stochastic processes, especially parameter estimation methods such as maximum likelihood and Bayesian methods, and their asymptotic theories.
We are also conducting applied research on high-frequency data for the Japanese and U.S. stock markets.

Information-theoretic learning theory/Statistical learning theory

“What are the possibility and limitation of machine learning?” We take
information-theoretic and statistical approaches to answer this
question. As for information-theoretic learning theory, we study a
unifying methodology for model selection, representation learning,
change detection, high-dimensional sparse learning, etc. on the basis
of the minimum description length principle. As for statistical
learning, we study new algorithm designs and theoretical analysis of
deep learning and kernel methods on the basis of statistical theory.
We also develop new optimization methods to run the machine learning
algorithms efficiently on the big data.

Data Science Foundation

We study methodologies for knowledge discovery from big data (anomaly
detection, network mining, embedding, etc.) Specifically we are
interested in discovering deep knowledge from latent spaces. We aim at
building a new field called “Symptomatics”, in which we detect signs
of latent changes in future from data streams.

Data Science Applications

We study effective data science methodologies by applying machine
learning and data mining technologies to real complex data. The
applications include economics, financial data analysis, medical data
analysis, marketing, SNS data analysis, failure detection, spatial
data mining, security, etc. We often collaborate with industrial
companies to solve real data science problems.

Theoretical Statistics

We establish the basis of statistical methods. A wide range of mathematical tools such as information geometry, algebraic methods and algorithms play an essential role as well as probability theory.

Statistical Modeling

Statistical methods are used in various fields such as brain science, geoscience, finance, medical science, quantum information and sports science. We are developing specific statistical models for analyzing complex phenomena in the real world.

Data Assimilation

Data assimilation integrates large-scale numerical simulation models and observational big data based on Bayesian statistics.
We develop algorithms of data assimilation towards applications to practical problems.

Understanding, Predicting and Controlling Dynamics

Dynamics are hidden in a lot of things in the real world such as weather, renewable energy, earthquakes, economics, brain, lives and diseases. We are studying time series analysis for understanding, predicting and/or controlling them.

Prediction and verification of decision by sense

We are interested in computational principles of brains from the viewpoint of decision by sense.
We use artificial neural networks as models of neuronal circuits.
In particular, by using state-of-the-art techniques of imaging and optical genetics for mouses,
we verify the prediction derived from the models by experiments.

 

Computational Neuroscience

We study the mechanism how brain circuits adapt to and learn from the environment.
By combining theoretical techniques from statistical physics and information theory and analysis of experimental data,
we understand how the information processing of brains changes by learning,
and find out the fundamental principle explaining the changes.

To understand natural, biological, and artificial systems, we perform mathematical modeling and analysis. Moreover, closely collaborating with experimentalists of various fields, we try to solve problems related to our lives. 

Modeling and development of general theories
By constructing simple models that describe complex dynamical phenomena, we try to understand, predict, and control such phenomena. Moreover, through the generalizing and abstraction of problems, we try to construct general theories. Examples of our subjects include biological rhythms, locomotion, hydrodynamic phenomena, power grids, transportation networks, traffic networks, pattern formation in biological and chemical systems, social systems, neural networks.

Collaboration with experimentalists
To solve problems closely related to our lives, we collaborate with researchers of various disciplines such as engineering and biology. Our roles are to provide theoretical ideas, to analyze and interpret experimental data, and to propose new experiments. 

Keywords
nonlinear phenomena, oscillations, synchronization, fluctuation, complex networks, control, optimization, biological rhythms, circadian rhythms, locomotion, biological physics

We explore the universal properties underlying large-scale social
systems through mathematical models derived by computing with big data
obtained from large-scale resources. Using these models, we explore
new ways of engineering to aid human social activities.

1. Analysis of large-scale social systems by applying complex systems theory

Common scaling properties are known to hold across various large-scale social systems. Using real, large-scale data, we study the nature of these properties, from viewpoints such as complexity, degree of fluctuation, and self-similarity, and construct a mathematical model that explains them.

 

2. Deep/Machine learning methods for complex systems

We discuss the potential and limitations of deep learning and other machine learning techniques with respect to the nature of complex systems, and we study directions for improvement. Moreover, we explore unsupervised and semi-supervised methods for state-of-the-art learning techniques.

 

3. Mathematical informatics across language, financial markets, and communication

We explore common universal properties underlying language, finance, and communication, through computing with various kinds of large-scale data, and we apply our understanding of those properties to engineering across domains. For example, we study financial market analysis by using blogs and other information sources, and we simulate information spread on a large-scale communication network.

Operations Research（OR）

It is a scientific technique that builds mathematical models and finds their solutions by using computers for solving real problems. In particular, we focus on modeling as a mathematical optimization problem and developing algorithms to solve the problem. The scope of application of OR is diverse and we are conducting research to solve real-world problems in the fields of structure design, energy system, financial engineering, machine learning.

Efficient algorithms for continuous optimization and thier applications to real-world problems

Problems in real world often result in large scale, nonlinear, nonconvex continuous optimization problem. Also, in a situation where robustness against uncertainty (variation) of data is required, a model called a robust optimization problem may be useful. We aim to efficiently solve such optimization problems and contribute to real world problem solving.

Fundamental and Application Studies on Mathematical Modelling of Complex Systems

We perform theoretical studies for mathematical modelling and analysis of complex systems and application studies for real-world phenomena including artificial intelligence and power grids.

Complex Dynamics Analysis

Complex dynamical behavior is ubiquitous in a variety of phenomena, ranging from microscopic activities in cells and genes to macroscopic activities in earth and cosmos.  Towards understanding complex dynamical behavior and solving practical issues through mathematical modeling and analyses, we aim at developing a method for predicting, controlling, and optimizing complex dynamical phenomena. The subjects of this research include biology, medicine, public health, engineering, economics, and social problems. 

Augmented sound communication systems based on unsupervised optimization theory

In many cases, acoustic signal processing deals with data that can be observed only just one time. This is because propagation of acoustic waves strongly depends on a sound field and spectral structures of the sound source. Thus, it is required to establish a framework that treats not “big data” but “small data.” For this reason, we are addressing blind (unsupervised) theories, e.g., independent low-rank matrix analysis and, sparse tensor decomposition. Also, we aim to build some applications of acoustic signal processing including a human-robot interface and universal communication-supporting systems.

Mathematical analysis and sensibility quantification for non-linear signal processing

Non-linear audio signal processing is applied to many tasks nowadays. In recent years, it is revealed that lower- and higher-order statistical space have a hysteresis property, which provides the fixed point of a human auditory impression. On the basis of this finding, we are pursuing the meaningful statistical estimation for humans and produce a new beneficial framework of signal processing.

User-oriented and music signal processing

We aim for developing high-quality music signal processing by applying machine learning theories to various multidimensional music data. Also, user-oriented systems for music signal analysis are addressed to contribute to built a new artistic production from the engineering view.

Inverse problems for acoustic field

We tackle with inverse problems for acoustic field, such as sound field imaging, analysis, source localization, and estimation of room acoustic parameters. We pursuit new methodologies with various approaches (optimization, machine learning, etc.) and develop systems to achieve these purposes.

Signal processing for sound field recording, transmission, and reproduction

We deal with a broad range of problems for sound field recording, transmission, and reproduction. By using these methodologies, we develop new systems for telecommunication, virtual reality, and so on.

Augmented speech communication using speech synthesis and conversion

Utilizing machine-learning-based speech synthesis and conversion, we realize augmented speech communication beyond differences among AI and human beings.

Brain function recording

For instance, I investigate whether or not humans still possess subconscious geomagnetic reception by EEG recording and behavioral experiments.

Brain function control

I try to control brain functions by attaching a negative impedance circuit on the scalp, so that it modulates the volume conduction of dendritic currents.