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Mathematical Information Systems Lab
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A lab exploring the mathematics of extracting meaningful information from an uncertain world.
AboutAbout the lab
The mathematics of information amid uncertainty
The Mathematical Information Systems Lab aims to take a cross-disciplinary, mathematical view of the many problems of information processing in uncertain environments and to resolve them.
Much of today's information processing is expressed by large-scale probabilistic models, and making use of the laws that emerge from that large scale is the key to advanced information processing.
The lab's research spans many fields, including information theory, communication theory, probability theory, statistical science, statistical mechanics, and machine learning.
Key terms
- Compressed sensing
- A technique that exploits the property that most of the data are close to zero (sparse) to reconstruct the original signal from a small number of measurements
- Replica method
- A calculation technique that originated in statistical mechanics. It is also used to theoretically estimate the performance of machine learning and other methods
- Probabilistic model
- A mathematical model that uses probability to represent a phenomenon involving uncertainty
NewsLab news
A paper approximating the distribution of population sizes in growing cascade processes is published in Physical Review Research
A paper on neural collapse in deep models for ordinal regression is accepted at NeurIPS 2025
A paper predicting collision cross sections of peptides with a protein language model is published in Communications Chemistry
ResearchResearch themes
The lab takes a cross-disciplinary approach to theoretical problems in information statistical mechanics, which discusses the information mathematics of large-scale probabilistic models by analogy with statistical mechanics, as well as in statistical machine learning, deep learning, and data science.
*Illustrative imageMathematics and applications of compressed sensing
The lab examines the theoretical limits of compressed sensing, which focuses on the sparsity of data, using tools such as the replica method from statistical mechanics. It also studies applications to MRI, protein NMR analysis, and mass spectrometry jointly with researchers in medicine, pharmacy, and other fields.
*Illustrative imageInformation processing based on probabilistic models
To efficiently extract meaningful information from uncertain environments, the lab studies inference and learning based on probabilistic models. Topics include Gaussian process regression, game theory, the inverse Ising problem, and estimating asymptomatic carriers of infectious diseases.
*Illustrative imageWhy does deep learning work so well?
The lab takes a mathematical approach to open questions such as why deep learning works. This includes analysis of stochastic gradient descent, learning methods based on optimal transport theory, and evaluating the theoretical performance of graph neural networks.
MembersFaculty
The faculty of the Mathematical Information Systems Lab are Professor Toshiyuki Tanaka, Associate Professor Tomoyuki Obuchi, and Assistant Professor Koki Okajima.
- ProfessorToshiyuki Tanaka
- Associate ProfessorTomoyuki Obuchi
- Assistant ProfessorKoki Okajima
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Cosine Series Plus Noise” Fourier1789 / CC BY-SA 4.0 (cropped)
- Mathematics and applications of compressed sensing: “MRI Brain axial FLAIR sequence showing lentiform fork sign” author of article (Mansoor, S., De Klerk, L., Lineen, J. et al.) / CC BY 4.0 (cropped)
- Information processing based on probabilistic models: “Bayesian inference results” Gnathan87 / CC0 (cropped)
- Why does deep learning work so well?: “Artificial Neural Network Example” Jhedengren / CC BY-SA 4.0 (cropped)
- Related lab (集合知システム): “DataAppliedWeb” Marksenizer / CC BY-SA 3.0 (cropped)
- Related lab (離散数理): “Graph example (Graph theory)” Römert / CC BY-SA 3.0 (cropped)
- Related lab (統計知能): “Normal distribution function” Shishirdasika / CC BY-SA 3.0 (cropped)
- Related lab (コンピュータアルゴリズム): “BDD” The original uploader was IMeowbot at English Wikipedia. / CC BY-SA 3.0 (cropped)
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