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 |

More recently, a couple good online courses in computational neuroscience have appeared: one directed by Raj Rao and Adrienne Fairhall, another by Wulfram Gerstner, and another by Idan Segev.

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

Sep 5 | No class due to graphical models workshop | ||

Sep 12,19 | Introduction; background on neuronal biophysics, regression, MCMC | Spikes introduction; Kass et al '05; Brown et al. '04 | Neuroscience review by Josh Merel. Regression notes |

Sep 26 | Estimating time-varying firing rates | Kass et al (2003), Wallstrom et al (2008) | Generalized linear model notes |

Oct 3 | Linear-nonlinear Poisson cascade models: spike-triggered averaging; Poisson regression | Simoncelli et al. '04; Chichilnisky '01; Paninski '03; Sharpee et al. '04; Paninski '04; Weisberg and Welsh '94; Williamson et al '13 | Try these practice problems, courtesy of Dayan and Abbott; any problem in chapter 1; also problems 2-3 in chapter 2. |

Oct 10 | Expected log-likelihood; quadratic models; spike-triggered covariance; sparsity-promoting and rank-penalizing priors; hierarchical models | Park and Pillow '11, Ramirez and Paninski, '13, Field, Gauthier, Sher et al '10, Ahrens et al '08 | |

Oct 17 | No class due to Grossman workshop | Hope to see you there. | |

Oct 24 | The expectation-maximization (EM) algorithm for maximum likelihood given indirect measurements / hidden data; mixture models; spike sorting | Neal and Hinton '98; Lewicki '98; Salakhutdinov et al '03; Shoham et al '03; Pouzat et al '04, Pillow et al `13, Carlson et al '13 | Guest lecture by David Carlson; EM notes |

Oct 31, Nov 7 | Experimental design. Point processes: Poisson process, renewal process, self-exciting process, Cox process; time-rescaling: goodness-of-fit, fast simulation of network models | Lewi et al '09; Shababo et al '13; Keshri et al '13; Brown et al. '01 | Uri Eden's point process notes; supplementary notes. Do inhomogenous Poisson problem set, available on courseworks. |

Nov 7 | Presentations of project ideas | ||

Nov 14 | No class | ||

Nov 21 | State space models; autoregressive models; Kalman filter; extended Kalman filter; fast tridiagonal methods. Applications in neural prosthetics, optimal smoothing of voltage/calcium traces, fitting common-input models for population spike train data, and analysis of nonstationary spike train data | Kalman filter notes by Minka; Roweis and Ghahramani '99; Huys et al '06; Paninski et al '04; Jolivet et al '04; Beeman's notes on conductance-based neural modeling; Wu et al '05; Brown et al '98; Smith et al '04; Yu et al '05; Kulkarni and Paninski '08; Calabrese and Paninski '11; Paninski et al '10, Vogelstein et al '10. Additional useful papers collected by Minka here. | notes. Do state-space problem set, on courseworks. |

Thanks to the NSF for support.