I like reading papers about statistical and methodological innovations for (cognitive neuro)science, but I often have difficulties grasping the mathematical details. Simulating and/or implementing the methods myself aided my understanding a lot, so I decided to keep track of these efforts in this repository with Jupyter notebooks. Feel free to use them in whatever way you like.
Concepts/papers/methods I want to check out in the future:
- Pattern component modelling from Diedrichsen et al. (2011).
- Modelling correlated noise in decoding analyses by van Bergen & Jehee (2017).
This repo contains notebooks on the following concepts/methods:
cv_MANOVA.ipynb
This extensively annotated notebook contains an implementation of the cross-validated MANOVA method for (searchlight-based) fMRI analysis based on the article by Allefeld & Haynes (2014).
haufe_activation_weights.ipynb
This notebook contains code that is used to invert the weights from linear backward ("decoding") models to forward ("encoding") models based on the article by Haufe et al. (2014). It contains almost no annotation, which is something I still want to do at one point.
inverted_encoding_models.ipynb
This notebook contains an implementation of "inverted encoding models", in which a forward model (features → brain) is inverted (brain ← features), which yields an estimation of the features from a (multivariate) brain pattern. This implementation is based on papers like Ester, Sprague, & Serences (2015) and on the code from Tommy Sprague's Github.
polynomial_regression.ipynb
Simple notebook with some snippets that implement polynomial regression for the purpose of demonstrating how overfitting works (used it once to create figures for a course I taught).
prevalence_inference.ipynb
I'm pretty proud of this notebook! It contains a fully annotated implementation of "prevalence inference" as described in the paper by Allefeld, Gorgen, & Haynes (2016) and the notebook additionally contains a complete replication of the results (and plots) from the original article. Note that I implemented this method in my own skbold package in a separate module.
prewhitening.ipynb
A notebook with a simple implementation of prewhitening because I was interested in the "multivariate noise normalization" described in the paper by Walther et al. (2016). I aim to extend this to show prewhitening on actual fMRI data and in the context of RSA.
simulation_variance_OLS_parameters.ipynb
I used this notebook to gain a better intuition what "variance" of statistical parameters actually means.
tikhonov_regression_with_non_sphrerical_prior.ipynb
I came across this interesting abstract titled "Improving predictive models using non-spherical Gaussian priors" from Nunez-Elizalde, Huth, & Gallant (2017), which uses a more general form of Ridge regression - called Tikhonov regression - in which you specify a prior on the distribution model's parameters. I tried to implement Tikhonov regression in this notebook, which seems to demonstrate that if you have a reasonable estimate of the distribution (mean & variance) of the parameters, your predictions get much better.
convert_ovo_to_ovr.ipynb
For multiclass classification, scikit-learn provides implementations for both "one-versus-one" ("ovo") and "one-versus-rest" ("ovr") classification schemes. This choice affects the structure of the coefficient matrix after fitting (i.e., which column corresponds to which pairwise classification?). I used this notebook to see how I should convert these "ovo" coefficients to the structure of "ovr" coefficients (for the purpose of implementing 'inverting backwards coefficients' from the Haufe et al. paper in my skbold package).
time_domain_decoding.ipynb
This (draft!) notebook implements the "decoding in the time domain" method by Loula, Varoquaux, & Thirion (2017).