Statistical concept / technique | Neuroscience application |
---|---|

Point processes; conditional intensity functions | Neural spike trains; photon-limited image data |

Time-rescaling theorem for point processes | Fast simulation of network models; goodness-of-fit tests for spiking models |

Bias, consistency, principal components | Spike-triggered averaging; spike-triggered covariance |

Generalized linear models | Neural encoding models including spike-history effects; inferring network connectivity |

Regularization; shrinkage estimation | Maximum a posteriori estimation of high-dimensional neural encoding models |

Laplace approximation; Fisher information | Model-based decoding and information estimation; adaptive design of optimal stimuli |

Mixture models; EM algorithm; Dirichlet processes | Spike-sorting / clustering |

Optimization and convexity techniques | Spike-train decoding; ML estimation of encoding models |

Markov chain Monte Carlo: Metropolis-Hastings and hit-and-run algorithms | Firing rate estimation and spike-train decoding |

State-space models; sequential Monte Carlo / particle filtering | Decoding spike trains; optimal voltage smoothing |

Fast high-dimensional Kalman filtering | Optimal smoothing of voltage and calcium signals on large dendritic trees |

Markov processes; first-passage times; Fokker-Planck equation | Integrate-and-fire-based neural models |

Hierarchical Bayesian models | Estimating multiple neural encoding models |

Amortized inference | Spike sorting; stimulus decoding |

A couple good older online courses in computational neuroscience: one directed by Raj Rao and Adrienne Fairhall, and another by Wulfram Gerstner.

Date | Topic | Reading | Notes |
---|---|---|---|

Sept 10-17 | Intro and overview | Paninski and Cunningham, `18; International Brain Lab, '17 | |

Sept 24 - Oct 1 | Signal acquisition: spike sorting | Lewicki '98; Pachitariu et al '16; Lee et al '20; Steinmetz et al '21; Calabrese and Paninski '11, Wang et al '19, Zanos et al '11 | EM notes; Blei et al review on variational inference. Guest lecture by Erdem Varol. |

Oct 8, 15 | Signal acquisition: single-cell-resolution functional imaging | Overview: Pnevmatikakis
and Paninski '18 Compression and denoising: Buchanan et al '18, Sun et al '19 Demixing: Pnevmatikakis et al '16; Zhou et al '18; Friedrich et al '17b; Lu et al '17; Giovanucci et al '17; Charles et al '19, Saxena et al '20 Deconvolution: Deneux et al '16; Picardo et al '16; Friedrich et al '17a; Berens et al '18, Rupprecht et al '21 Wei and Zhou et al '19 | HMM tutorial by Rabiner; HMM notes. Guest lecture by Ian Kinsella and Amol Pasarkar. |

Oct 22 | Optogenetic circuit mapping | Hu et al '09, Shababo et al '13, Hage et al '19 | Guest lecture by Marcus Triplett. |

Oct 29 | Behavioral video analysis | DeepLabCut, DeepGraphPose, MoSeq, PS-VAE, SLEAP, MONET, DAART | Guest lecture by Matt Whiteway. |

Nov 5 | Presentations of project ideas | Just two minutes each | |

Nov 12 | Network models. | Field et al '10, Soudry et al '15 | |

Nov 19 | Poisson regression models; hierarchical models for sharing information across cells; expected log-likelihood | Kass et al (2003), Wallstrom et al (2008), Batty et al (2017), Cadena et al (2017), Ramirez and Paninski, '14 | Generalized linear model notes |

Nov 26 | No class (University holiday) | Happy thanksgiving! | |

Dec 10-17 | Project presentations | E-mail me your report as a pdf by Dec 20. |

Thanks to the NSF for support.