Writings

  • Takeru Miyato, Shin-ichi Maeda, Masanori Koyama, Ken Nakae, Shin Ishii, Distributional Smoothing by Virtual Adversarial Examples. Submitted to arxiv, 2015
  • Sotetsu Koyamada, Masanori Koyama, Ken Nakae, Shin Ishii, Principal Sensitivity Analysis. The Pacific-Asia Conference on Knowledge Discovery and Data Mining (PAKDD), Ho Chi Minh City, Vietnam, 05/2015
    • David F.Anderson and Masanori Koyama, An asymptotic relationship between coupling methods for stochastically modeled population processes ,IMA Journal of Numerical Analysis, IMA Journal of Numerical Analysis 03/2014; DOI:10.1093/imanum/dru044
  • Gota Morota, Masanori Koyama, Guilherme J M Rosa, Kent A Weigel, Daniel Gianola Predicting complex traits using a diffusion kernel on genetic markers with an application to dairy cattle and wheat data,Genetics Selection Evolution 06/2013; 45(1):17. DOI:10.1186/1297-9686-45-17
  • David F. Anderson and Masanori Koyama, Weak error analysis of approximate simulation methods for multi-scale stochastic chemical kinetic systems , SIAM: Multiscale Modeling and Simulation, Vol. 10, No. 4, 1493 - 1524, 2012.
  • Masanori Koyama, Michael Orrison and David Neel, Irreducible graphs . Journal of Combi- natorial Mathematics and Combinatorial Computing 62 (2007), 35-43.

    Graduate Works:

  • Masanori Koyama, Fast Fourier Transform for Symmetric Group. (Bachelor Thesis)
  • Masanori Koyama, Analysis for stochastically modeled biochemcial processes with applications to numerical methods (Doctoral Thesis)

    • Others:

  • Efficient Monte Carlo Image Analysis for the Location Of Vascular Entity. Henrik Skibbe, Marco Reisert, Shin-Ichi Maeda, Masanori Koyama, Shigeyuki Oba, Kei Ito, Shin Ishii, IEEE Transactions on Medical Imaging 10/2014; 34(2). DOI:10.1109/TMI.2014.2364404
    • A Statistical Method of Identifying Interactions in Neuron–Glia Systems Based on Functional Multicell Ca2+ Imaging, PLoS Computational Biology 11/2014; 10(11):e1003949. DOI:10.1371/journal.pcbi.1003949
  • Deep learning of fMRI big data: a novel approach to subject-transfer decoding Sotetsu Koyamada, Yumi Shikauchi, Ken Nakae, Masanori Koyama, Shin Ishii, Submitted

    • Talks and conferences(Non peer reviewed):

  • Pacific Coast Undergraduate Mathematics Conference “Fast Fourier Transform for Symmetric Group,” 2007
  • Joint Mathematics Meeting in New Orleans, “Irreducible Graphs”, poster award, 2007
  • qBio Summer School in Los Alamos, “Weak Analysis of stochastic chemical kinetic systems”, 2011
  • Winter qBIO Conference, poster presentation “Inference of stochastic dynamics from snapshot data”, 2015 
  • Invited talk, Ritsumeikan University, “Weak analysis and MLMC for the system of interacting Poisson processes”, 2015
    • Work in Progress
  • Michael Hansen, Masanori Koyama, Michael Orrison, Doubly adapted tensor basis of the Symmetric Group Algebra
  • Masanori Koyama, Shin Ishii, Inference of stochastic models from snapshot data.

    • Interests

    Applied Probability Theory, Statistics, Applied Representation Theory.

    I am particularly interested in the fields of mathematics that are on the boundary of different theories. I love to see the Mathematics(in particular, discrete Math) playing the role of bridge connecting various people from diverse fields. I am currently interested in;

  • Machine Learning and Stochastic Process. Mathematics is a subject that studies the behavior of "models", or the systems that follow very specific rules. By its nature, if we want to apply math to the real world one must find "good model" that describes the phenomena in the real world "well", and that is "a" purpose of statistics. I believe that there are two categories for the models, in general. One falls into the category that I call "White box" models. These are the models that loyally and intuitively describes the philosophy of the natural sciences that scientists developped over eons. The examples include PDE with explicit solutions and the models that can be described with Algebra, like the ones on the lists of my researches below. The other category is what I call "Black box" models. These models describes the data very well, but works in extremely covoluted and unintuitivate ways. People also talk about predictability. Even if the model describes the given data very well, it does not mean that it can describe the data that is yet to be observed. High order polynomials can mimic the observed data perfectly, but we all know that they are hardly the model that reflects the human philosophy, nor the model with high predictability. The family of models called neural network is a model known for high predictability, but it is also a black box model that cannot tell us "what's really going on". The good model is a model with good balance of "intuitiveness" and "predictability". This cannot be done with blackbox model alone, which are too simple, nor with whitebox model alone, which are too complicated. One can, however, aim to mix black box model and white box model, taking advantages from both. This is the very goal of my research. I am studying Machine learning to search for the right key.
  • Discrete Stochastic Process. The most major stochastic process used in applications is Wiener Process. However, when the dynamics is discrete, Poisson process plays the role. In particular, when the number of particles in the system is small, continuous approximation may not even "approximate" the dynamics correctly. The purpose of this research is to develop an efficient and fast algorithms to simulate/analyze a system of intertwining Poisson processes, with rates continuously dependent on the state of the system. One example of such system is a Chemical Reaction network. I am under the supervision of David Anderson. Our team is especially interested in Variance Reduction method including Multilevel Monte Carlo method and Euler type approximation algorithms. Many of the algorithms originally rose from applications, such as physics and biophysics; there are much rooms left for mathematical analysis to make improvements.

  • Stochastic System with Delay. In the usual Mass Action Kinetics model, Chemical reactions happens in an instant. When the model in concern in fact works this way, this simplification of the model might not cause any problem. However, some research (i.e Schwanhausser et al, Nature 473, 337-342, 19 May 2011) reports that a transcription speed can be as slow as two mRNA molecules per an hour. The transcription can also be a subject to premature cancellation. Ignoring the delay in such situation is absurd. I am interested in the Delayed Differential Equation that arises as the law of large numbers limit of the the stochastic delay system.


  • Fast Fourier Transform on Groups.

    Discrete Fourier Transform on finite group is a change of basis realized by the Wedderburn's isomorphism from the group ring CG to the block diagonal matrix ring. When the associated group is the cyclic group Cn, this becomes the familier DFT that is implemented in the Matlab. Fast Fouier Transform(FFT) is an efficient implementation of the DFT.

    Today, a very fast and easy implmentation of the DFT on commutative group ring is avaible. However, this has not been the case for non-commutative ring. It is a shame to leave this problem untouched, as the FFT for noncommutative group ring has applications in numerous interesting fields, such as in phylogenetics and in voting theory.Together with Micheal Orrison and Mike Hansen in the Applied representation theory group at Harvey Mudd College, I study the FFT on the Symmetric Group Sn. This FFT has applications in interesting fields like Voting theory and Genetics.

    The study of the FFT originally began as the study of "operators." The culmination of the FFT research in this direction is the FFT developped by David Maslen, which has a very fast asymptotic runtime O(n^2 n!). This algorithm, however, is extremely complicated, and requires very convoluted indexing scheme to implement.

    We suggest a change in paradigm here. By shifting our focus to the construction of the intermediate basis used in the algorithm, we can further exploit the hidden symmetries in the algebraic structures. In fact, using these symmetries, we can easily construct the sequence of orthogonal intermediate basis that yields a very efficient FFT (Simulation indicates that it is the fastest available today). Furthermore, our method might be applicable to the group algebra of general Weyl group.



  • Genomic Prediction. Making a prediction about a quantitative traits from Genome is equivalent to constructing an appropriate function from Genome to traits. Indeed, function can, and shall be be random, since we are bound to see errors and random effects from miscellaneous sources. The standard of the wellness of the prediciton is often an expected distance between the prediction and the actual data. Therefore it is essential to pick a right topology. For our most recent research, we constructed a RKHS in the space of function on SNPs(Single Nucleotide Polymorphism)s.

    I am also interested in any statistical methods used around Stochastic Process. I am especially interested, for example, in Bayesian parameter inference techniques for Chemical Reaction Networks.