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 11 | Intro and overview | Paninski and Cunningham, `18; International Brain Lab, '17 | |

Sept 18-25 | Signal acquisition: spike sorting | Lewicki '98; Pachitariu et al '16; Lee et al '20; Calabrese and Paninski '11, Wang et al '19, Zanos et al '11 | EM notes; Blei et al review on variational inference |

Oct 2, 9 | 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, Wei and Zhou et al '19 | HMM tutorial by Rabiner; HMM notes |

Oct 16 | Reinforcement learning approaches | Overview: Botvinick et al '20. Further reading: Wang et al '18, Dabney et al '20 | Discussion led by Andrew Zimnik; slides here. |

Oct 23, Nov 13 | Behavioral video analysis | DeepLabCut, DeepGraphPose, MoSeq, Behavenet, SLEAP, MONET | |

Oct 30 | No class | Check out Neuromatch 3 | VOTE!!! |

Nov 6, 13 | Presentations of project ideas | Just two minutes each | |

Nov 20 | State space models | HMM tutorial by Rabiner; Kalman filter notes by Minka; Roweis and Ghahramani '99; Wu et al '05; Brown et al '98; Smith et al '04; Yu et al '05; Kulkarni and Paninski '08; Paninski et al '10, Vidne et al '12, Gao et al '16, Pandarinath et al '18, Linderman et al '19 | Discussion led by Keane Nguyen and Hyun Dong Lee; slides here. See also state-space notes (need updating) |

Nov 27 | No class | Happy Thanksgiving! | |

Dec 4 | Open office hours (optional) | Come talk about project questions if you'd like | |

Dec 11, 18 | Project presentations | E-mail me your report as a pdf by the end of this week. |

Thanks to the NSF for support.