Repository for the paper Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensions.
Left: logistic classification of three clusters with ridge regularisation for different values of the regularisation's strength λ. Center and right: test error and training error performing a ridge classification of a mixture of K=3 clusters with diagonal covariance in the high dimensional limit, with thoretical predictions compared with the results of numerical simulations.
In this repository we provide the code and some guided example to help the reader to reproduce the figures of the paper [1]. The repository is structured as follows.
| File | Description |
|---|---|
/K2mix |
Solver for the fixed point equations of the order parameters in the case of classification tasks on K=2 Gaussian clusters with nonhomogeneous diagonal covariances. The notebook how_to.ipynb provides a step-by-step explanation on how to use the package. This implementation has been used to produce the results in Section 3.1 of the paper. |
/multiK |
Solver for the fixed point equations of the order parameters in the case of classification tasks on K Gaussian clusters with diagonal covariances. The notebook how_to.ipynb provides a step-by-step explanation on how to use the package. This implementation has been used to produce the results in Section 3.2 of the paper. |
The notebooks are self-explanatory.
[1] Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensions, B Loureiro, G. Sicuro, C Gerbelot, A. Pacco, F Krzakala, L Zdeborová, arXiv: 2106.03791 [stat.ML]