Discrete Time Rescaling Theorem: Determining Goodness of Fit for Statistical Models of Neural Spiking
One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time-rescaling theorem provides a goodness-of-fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescal...
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| Format: | Article |
| Language: | en_US |
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MIT Press
2012
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| Online Access: | http://hdl.handle.net/1721.1/70963 https://orcid.org/0000-0003-2668-7819 |
| _version_ | 1811092295763623936 |
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| author | Haslinger, Robert Heinz Pipa, Gordon Brown, Emery N. |
| author2 | Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences |
| author_facet | Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences Haslinger, Robert Heinz Pipa, Gordon Brown, Emery N. |
| author_sort | Haslinger, Robert Heinz |
| collection | MIT |
| description | One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time-rescaling theorem provides a goodness-of-fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model's spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov-Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies on assumptions of continuously defined time and instantaneous events. However, spikes have finite width, and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time-rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time-rescaling theorem that analytically corrects for the effects of finite resolution. This allows us to define a rescaled time that is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting generalized linear models to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false-positive rate of the KS test and greatly increasing the reliability of model evaluation based on the time-rescaling theorem. |
| first_indexed | 2024-09-23T15:16:04Z |
| format | Article |
| id | mit-1721.1/70963 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T15:16:04Z |
| publishDate | 2012 |
| publisher | MIT Press |
| record_format | dspace |
| spelling | mit-1721.1/709632022-10-02T01:45:47Z Discrete Time Rescaling Theorem: Determining Goodness of Fit for Statistical Models of Neural Spiking Haslinger, Robert Heinz Pipa, Gordon Brown, Emery N. Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences Brown, Emery N. Haslinger, Robert Heinz Pipa, Gordon Brown, Emery N. One approach for understanding the encoding of information by spike trains is to fit statistical models and then test their goodness of fit. The time-rescaling theorem provides a goodness-of-fit test consistent with the point process nature of spike trains. The interspike intervals (ISIs) are rescaled (as a function of the model's spike probability) to be independent and exponentially distributed if the model is accurate. A Kolmogorov-Smirnov (KS) test between the rescaled ISIs and the exponential distribution is then used to check goodness of fit. This rescaling relies on assumptions of continuously defined time and instantaneous events. However, spikes have finite width, and statistical models of spike trains almost always discretize time into bins. Here we demonstrate that finite temporal resolution of discrete time models prevents their rescaled ISIs from being exponentially distributed. Poor goodness of fit may be erroneously indicated even if the model is exactly correct. We present two adaptations of the time-rescaling theorem to discrete time models. In the first we propose that instead of assuming the rescaled times to be exponential, the reference distribution be estimated through direct simulation by the fitted model. In the second, we prove a discrete time version of the time-rescaling theorem that analytically corrects for the effects of finite resolution. This allows us to define a rescaled time that is exponentially distributed, even at arbitrary temporal discretizations. We demonstrate the efficacy of both techniques by fitting generalized linear models to both simulated spike trains and spike trains recorded experimentally in monkey V1 cortex. Both techniques give nearly identical results, reducing the false-positive rate of the KS test and greatly increasing the reliability of model evaluation based on the time-rescaling theorem. National Institutes of Health (U.S.) (grant K25 NS052422-02) National Institutes of Health (U.S.) (grant DP1 OD003646-01) National Institutes of Health (U.S.) (grant MH59733-07) Hertie Foundation Max Planck Society for the Advancement of Science European Union (grant FP6-2005-NEST-Path-043309.) 2012-05-31T17:40:08Z 2012-05-31T17:40:08Z 2010-10 Article http://purl.org/eprint/type/JournalArticle 0899-7667 1530-888X http://hdl.handle.net/1721.1/70963 Haslinger, Robert, Gordon Pipa, and Emery Brown. “Discrete Time Rescaling Theorem: Determining Goodness of Fit for Discrete Time Statistical Models of Neural Spiking.” Neural Computation 22.10 (2010): 2477-2506. https://orcid.org/0000-0003-2668-7819 en_US http://dx.doi.org/10.1162/NECO_a_00015 Neural Computation Creative Commons Attribution-Noncommercial-Share Alike 3.0 http://creativecommons.org/licenses/by-nc-sa/3.0/ application/pdf MIT Press PubMed Central |
| spellingShingle | Haslinger, Robert Heinz Pipa, Gordon Brown, Emery N. Discrete Time Rescaling Theorem: Determining Goodness of Fit for Statistical Models of Neural Spiking |
| title | Discrete Time Rescaling Theorem: Determining Goodness of Fit for Statistical Models of Neural Spiking |
| title_full | Discrete Time Rescaling Theorem: Determining Goodness of Fit for Statistical Models of Neural Spiking |
| title_fullStr | Discrete Time Rescaling Theorem: Determining Goodness of Fit for Statistical Models of Neural Spiking |
| title_full_unstemmed | Discrete Time Rescaling Theorem: Determining Goodness of Fit for Statistical Models of Neural Spiking |
| title_short | Discrete Time Rescaling Theorem: Determining Goodness of Fit for Statistical Models of Neural Spiking |
| title_sort | discrete time rescaling theorem determining goodness of fit for statistical models of neural spiking |
| url | http://hdl.handle.net/1721.1/70963 https://orcid.org/0000-0003-2668-7819 |
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