### Abstract

Recent work on the statistical modeling of neural responses has focused on modulated renewal processes in which the spike rate is a function of the stimulus and recent spiking history. Typically, these models incorporate spike-history dependencies via either: (A) a conditionally-Poisson process with rate dependent on a linear projection of the spike train history (e.g., generalized linear model); or (B) a modulated non-Poisson renewal process (e.g., inhomogeneous gamma process). Here we show that the two approaches can be combined, resulting in a conditional renewal (CR) model for neural spike trains. This model captures both real-time and rescaled-time history effects, and can be fit by maximum likelihood using a simple application of the time-rescaling theorem [1]. We show that for any modulated renewal process model, the log-likelihood is concave in the linear filter parameters only under certain restrictive conditions on the renewal density (ruling out many popular choices, e.g. gamma with shape κ ≠ 1), suggesting that real-time history effects are easier to estimate than non-Poisson renewal properties. Moreover, we show that goodness-of-fit tests based on the time-rescaling theorem [1] quantify relative-time effects, but do not reliably assess accuracy in spike prediction or stimulus-response modeling. We illustrate the CR model with applications to both real and simulated neural data.

Original language | English (US) |
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Title of host publication | Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference |

Pages | 1473-1481 |

Number of pages | 9 |

State | Published - Dec 1 2009 |

Event | 23rd Annual Conference on Neural Information Processing Systems, NIPS 2009 - Vancouver, BC, Canada Duration: Dec 7 2009 → Dec 10 2009 |

### Publication series

Name | Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference |
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### Other

Other | 23rd Annual Conference on Neural Information Processing Systems, NIPS 2009 |
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Country | Canada |

City | Vancouver, BC |

Period | 12/7/09 → 12/10/09 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Information Systems

### Cite this

*Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference*(pp. 1473-1481). (Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference).

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*Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference.*Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference, pp. 1473-1481, 23rd Annual Conference on Neural Information Processing Systems, NIPS 2009, Vancouver, BC, Canada, 12/7/09.

**Time-rescaling methods for the estimation and assessment of non-Poisson neural encoding models.** / Pillow, Jonathan William.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Time-rescaling methods for the estimation and assessment of non-Poisson neural encoding models

AU - Pillow, Jonathan William

PY - 2009/12/1

Y1 - 2009/12/1

N2 - Recent work on the statistical modeling of neural responses has focused on modulated renewal processes in which the spike rate is a function of the stimulus and recent spiking history. Typically, these models incorporate spike-history dependencies via either: (A) a conditionally-Poisson process with rate dependent on a linear projection of the spike train history (e.g., generalized linear model); or (B) a modulated non-Poisson renewal process (e.g., inhomogeneous gamma process). Here we show that the two approaches can be combined, resulting in a conditional renewal (CR) model for neural spike trains. This model captures both real-time and rescaled-time history effects, and can be fit by maximum likelihood using a simple application of the time-rescaling theorem [1]. We show that for any modulated renewal process model, the log-likelihood is concave in the linear filter parameters only under certain restrictive conditions on the renewal density (ruling out many popular choices, e.g. gamma with shape κ ≠ 1), suggesting that real-time history effects are easier to estimate than non-Poisson renewal properties. Moreover, we show that goodness-of-fit tests based on the time-rescaling theorem [1] quantify relative-time effects, but do not reliably assess accuracy in spike prediction or stimulus-response modeling. We illustrate the CR model with applications to both real and simulated neural data.

AB - Recent work on the statistical modeling of neural responses has focused on modulated renewal processes in which the spike rate is a function of the stimulus and recent spiking history. Typically, these models incorporate spike-history dependencies via either: (A) a conditionally-Poisson process with rate dependent on a linear projection of the spike train history (e.g., generalized linear model); or (B) a modulated non-Poisson renewal process (e.g., inhomogeneous gamma process). Here we show that the two approaches can be combined, resulting in a conditional renewal (CR) model for neural spike trains. This model captures both real-time and rescaled-time history effects, and can be fit by maximum likelihood using a simple application of the time-rescaling theorem [1]. We show that for any modulated renewal process model, the log-likelihood is concave in the linear filter parameters only under certain restrictive conditions on the renewal density (ruling out many popular choices, e.g. gamma with shape κ ≠ 1), suggesting that real-time history effects are easier to estimate than non-Poisson renewal properties. Moreover, we show that goodness-of-fit tests based on the time-rescaling theorem [1] quantify relative-time effects, but do not reliably assess accuracy in spike prediction or stimulus-response modeling. We illustrate the CR model with applications to both real and simulated neural data.

UR - http://www.scopus.com/inward/record.url?scp=78650611326&partnerID=8YFLogxK

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M3 - Conference contribution

SN - 9781615679119

T3 - Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference

SP - 1473

EP - 1481

BT - Advances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference

ER -