1. COE 出張報告 ２００６年１２月１ ４日 Tutorials – December 4, 2006 Conference Sessions – December 4-7, 2006 Hyatt Regency, Vancouver, B.C., Canada Workshops – December 8-9, 2006 Westin and Hilton, Whistler, B.C., Canada Neural Information Processing Systems 2006 物理学第一教室 非線形動力学研究室 島崎 秀昭

2. 参加者数約１０００人 発表件数２０４件 論文投稿 ８３３件 Peer Review (Double blind) 2~4 人の レビューアーによる採点 １０点満点 ４人による採点 合否 ２０４件が受理 ポスター発表 ６３件が口頭発表（講演 20 分 / スポットライト２分）

3. NIPS*06

4. Histogram The duration for eruptions of the Old Faithful geyser in Yellowstone National Park (in minutes) Bin width

5. HistogramUnderlying Rate Optimizing a time-histogram Unknown

6. Methods Calculate the mean and variance of the number of spikes. Compute the cost function Repeat i through iii while changing the bin size Δ. Find Δ* that minimize the cost function. Divide spike sequences with length T [s] into N bins of width Δ. Method: Selection of the Bin Size (i) (ii) (iii) (iv)

7. Data : Britten et al. (2004) neural signal archive Rate modulation of an MT neuron Extrapolation Too few to make a Histogram ! Estimation: At least 12 trials are required. Optimized Histogram

8. How many trials are required to make a Histogram? Required # of sequences (Estimation) Extrapolated: Finite optimal bin size Original: Optimal bin size diverges Optimal bin size v.s. m # of sequences used Required # of trials

9. (i) Expansion of the cost function by  : (ii) Expansion of the cost function by 1/  Critical number of trials: The second order phase transition. Scaling of the optimal bin size: Theoretical cost function: The mean and correlation function of the underlying rate is known. See also Koyama, S. and Shinomoto, S. J. Phys. A, 37(29):7255–7265. 2004

10. Reference A Method for Selecting the Bin Size of a Time Histogram Hideaki Shimazaki and Shigeru Shinomoto Neural Computation in Press 島崎秀昭 学位論文 ＠ ４階図書室 http://www.ton.scphys.kyoto-u.ac.jp/~hideaki/http://www.ton.scphys.kyoto-u.ac.jp/~hideaki/

11. Time-Varying Rate Spike Sequences Time Histogram The spike count in the bin obeys the Poisson distribution* : A histogram bar-height is an estimator of  : The mean underlying rate in an interval [0,  ]: *When the spikes are obtained by repeating an independent trial, the accumulated data obeys the Poisson point process due to a general limit theorem. Theory

12. Expectation by the Poisson statistics, given the rate. Variance of the rate Variance of an ideal histogram Decomposition of the Systematic Error Systematic Error Sampling Error Average over segmented bins. Independent of  Method I. Selection of the Bin Size

13. Variance of a Histogram Introduction of the cost function: The variance decomposition: Mean of a Histogram The Poisson statistics obeys: Unknown: Variance of ideal histogram Sampling error Variance of a histogramSampling error