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COE 出張報告　２００６年１２月１４日

COE 出張報告　２００６年１２月１４日. Neural Information Processing Systems 2006. 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. 物理学第一教室　非線形動力学研究室　島崎 秀昭. 参加者数 約１０００人

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COE 出張報告　２００６年１２月１４日

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  1. COE出張報告　２００６年１２月１４日 Neural Information Processing Systems 2006 Tutorials – December 4, 2006Conference Sessions – December 4-7, 2006 Hyatt Regency, Vancouver, B.C., Canada Workshops – December 8-9, 2006Westin and Hilton, Whistler, B.C., Canada 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 Bin width The duration for eruptions of the Old Faithful geyser in Yellowstone National Park (in minutes)

  5. Optimizing a time-histogram Unknown Underlying Rate Histogram

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

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

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

  9. Theoretical cost function: The mean and correlation function of the underlying rate is known. (i) Expansion of the cost function by D: Scaling of the optimal bin size: (ii) Expansion of the cost function by 1/D: Critical number of trials: The second order phase transition. 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/

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

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

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

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