Shinsuke Koyama
Department of Physics, Graduate School of Science, Kyoto University
Department of Statistics and Center for the Neural Basis of Cognition,
Carnegie Mellon University
Research
- Interests
I am interested in the interface between physics, biology and computer science.
Currentlly I focus on several topics as follows:
- Stochastic processes and their statistical inference,
- Bayesian statistics and its relation to statistical physics,
- Mathematical neuroscience.
- Papers
- [1] "Storage capacity of two-dimensional neural networks."
Shinsuke Koyama.
Phys. Rev. E, 65, 016124 (2001).
(abstract)
We investigate the maximum number of embedded patterns in the
two-dimensional Hopfield model.
The grand state energies of two specific network states, namely,
the energies of the pure-ferromagnetic state and the state of
specific one stored pattern are calculated exactly in terms of
the correlation function of the ferromagnetic Ising model.
We also investigate the energy landscape around them
and the stability of the pure retrieval state.
Taking into account the qualitative features of the phase diagrams
obtained by Nishimori, Whyte and Sherrington
[Phys. Rev. E {\bf 51}, 3628 (1995)],
we conclude that the network cannot retrieve more than three patterns.
- [2] "Histogram bin width selection for time-dependent Poisson processes."
Shinsuke Koyama and Shigeru Shinomoto.
J. Phys. A (2004), 37, 7255-7265.
(abstract)
In constructing a time histogram of the event sequences derived from a non-stationary point process, we wish to determine the bin width such that the mean squared error of the histogram from the underlying rate of occurrence is minimized.
We find that the optimal bin widths obtained for a doubly stochastic Poisson process and a sinusoidally regulated Poisson process exhibit different scaling relations with respect to the number of sequences, time scale and amplitude of rate
modulation, but both diverge under similar parametric conditions.
This implies that under these conditions, no determination of the time dependent rate can be made.
We also apply the kernel method to these point processes, and find that the optimal kernels do not exhibit any critical phenomena, unlike the time histogram method.
- [3] "A measure of local variation of inter-spike intervals."
Shigeru Shinomoto, Keiji Miura and Shinsuke Koyama.
Biosystems (2005), 79, 67-72.
(abstract)
It has been revealed that in our recent study that cortical neurons are
categorized into distinct types, according to a new measure of the
local variation of inter-spike intervals, Lv. In this paper, we obtain
values of the local variation Lv and a conventional coefficient of
variation Cv for a variety of model point processes. While the value of
Cv undergoes large change by rate fluctuation of the point processes,
the value of Lv does not undergo large changes by rate fluctuation and
is principally determined by the form of intrinsic interval distribution
of the original model point process.
- [4] "Empirical Bayes interpretations of random point events."
Shinsuke Koyama and Shigeru Shinomoto.
J. Phys. A (2005), 38, L531-L537.
(abstract)
Given a sequence of apparently random point events, such as neuronal spikes, one may interpret them as being derived either irregularly in time from a constant rate or regularly from a fluctuating rate. To determine which interpretation is more plausible in any given case, we employ the empirical Bayes method. For a sequence of point events derived from a rate-fluctuating gamma process, the marginal likelihood function can possess two local maxima, and the system exhibits a first-order phase transition representing the switch of the most plausible interpretation from one to the other.
- [5] "Inference of intrinsic spiking irregularity based on the Kullback-Leibler information."
Shinsuke Koyama and Shigeru Shinomoto. (accepted)
(abstract)
We have recently established an empirical Bayes method that extracts both the intrinsic irregularity and the time-dependent rate from a spike sequence (J. Phys. A38: L531-L537, 2005). In the present paper, we examine an alternative method based on the more fundamental principle of minimizing the Kullback-Leibler information from the original distribution of spike sequences to a model distribution. Not only the empirical Bayes method but also the Kullback-Leibler information method exhibits a switch of the most plausible interpretation of the spikes between (I) being derived irregularly from a nearly constant rate, and (II) being derived rather regularly from a significantly fluctuating rate. The model distributions selected by both methods are similar for the same spike sequences derived from a given rate-fluctuating gamma process.
- [6] "A solution to the controversy between rate and temporal coding."
Shigeru Shinomoto and Shinsuke Koyama. (in press)
- [7] "Phase transitions in the estimation of event-rate: A path integral analysis."
Shinsuke Koyama, Takeaki Shimokawa and Shigeru Shinomoto.
J. Phys. A (2007), 40, E383-E390.
(abstract)
We try to capture the instantaneous rate of event occurrence as a function of time.
The smoothness of the rate function has been chosen arbitrarily, but it is nevertheless possible to select a plausible one according to the principle of maximum likelihood.
It may take place that the optimized smoothness diverges, indicating that the data are insufficient to uncover the time dependence of the underlying rate.
By evaluating the likelihood function through a marginalization path integral, we found not only first order but also second order phase transitions.
- Presentations
- 2001年9月18日 日本物理学会秋季大会(徳島文理大学)
「構造のあるパターンを埋め込んだ2次元ホップフィールド模型の記憶容量 解析」
- 2001年9月25日 FAN Symposium '01 in Sakai
「統計物理学的2次元ホップフィールド模型のパターン記憶容量解析」
- 2002年11月11日 ニューロコンピューティング研究会(九工大)
「シナプス背景ノイズの皮質神経細胞モデルの応答特性への影響」
- 2003年9月8日 日本神経回路学会第13回全国大会(法政大学)
「時間変動Poisson過程に対するヒストグラム時間幅の選択」
- 2003年9月21日 日本物理学会秋季大会(岡山大学)
「スパイク時系列に基づく発火確率の時間変動の推定」
- 2004年6月25日 ニューロコンピューティング研究会(琉球大学)
「点過程を観測モデルとする隠れマルコフモデルのパラメータ推定」
- 2004年9月13日 日本物理学会秋季大会(青森大学)
「点過程モデルによるスパイク時系列の解析」
- 2004年9月27日 日本神経回路学会第14回全国大会(京都大学)
「点過程モデルによるスパイク時系列の解析」（口頭発表）
- 2005年9月21日 日本神経回路学会第15回全国大会(鹿児島大学)
「経験ベイズ法に基づくスパイク時系列の解釈について」（口頭発表）
- 2005年11月10日 第8回情報論的学習理論ワークショップ(IBIS)
(早稲田大学)
「経験ベイズ法に基づくスパイク時系列の解釈」（口頭発表）
- 6th International Neural Coding Workshop,
August 27, 2005, Marburg, Germany.
"Inference of intrinsic spiking irregularity based on
the Kullback-Leibler information" (aural)
- The Annual Meeting of the Network of European Neuroscience
Institutes, November 21, 2005, Prague, Czech Republic.
"On interpretations of random spike sequences" (poster)
- Third Workshop Statistical Analysis of Neuronal Data,
May 12-23, 2006, Pittsburgh PA.
"A solution to the controversy between rate and temporal coding"(poster)
- NIPS 2006 Workshops, Dynamical Systems, Stochastic Processes and Bayesian Inference, 9 December, 2006, Whistler, Canada.
"The Empirical Bayes Estimation of an Instantaneous Spike Rate with a Gaussian Process Prior" (aural)
- 5th Workshop on Bayesian Inference in Stochastic Processes.
June 14-16, 2007, Valencia Spain.
"Laplace approximation of recursive Bayesian filter" (poster)
Education
1996-2001: Factory of Engineering, Hokkaido University
2001-2003: Graduate School of Engineering, Hokkaido University
2003-2006: Department of Physics, Graduate School of Science, Kyoto University
March, 2006: PhD in Physics
May, 2006-: Postdoc at Department of Statistics and CNBC, Carnegie Mellon University