ndarray-glm
Rust library for solving linear, logistic, and generalized linear models through
iteratively reweighted least squares, using the ndarray-linalg module.
Status
This package is in early alpha and the interface is likely to undergo many changes.
Prerequisites
fortran and BLAS must be installed:
sudo apt update && sudo apt install gfortran libblas-dev
To use the OpenBLAS backend, install also libopenblas-dev and use this crate with the "openblas-src" feature.
Example
``` rust
use ndarray::array;
use ndarray_glm::{linear::Linear, model::ModelBuilder, standardize::standardize};
// define some test data
let datay = array![0.3, 1.3, 0.7];
let datax = array![[0.1, 0.2], [-0.4, 0.1], [0.2, 0.4]];
// The design matrix can optionally be standardized, where the mean of each independent
// variable is subtracted and each is then divided by the standard deviation of that variable.
let datax = standardize(datax);
// The model is general over floating point type.
// If the second argument is left "", it will be inferred if possible.
// L2 regularization can be applied with l2reg().
let model = ModelBuilder::::new(&datay, &datax).l2_reg(1e-5).build()?;
let fit = model.fit()?;
println!("Fit result: {}", fit.result);
```
Features
- [X] Linear regression
- [X] Logistic regression
- [X] Generalized linear model IRLS
- [X] Linear offsets
- [X] Allow non-float domain types
- [X] L2 (ridge) Regularization
- [ ] L1 (lasso) Regularization
- [X] Generic over floating point type
- [X] Poisson
- [ ] Exponential
- [ ] Gamma (which effectively reduces to exponential with an arbitrary
dispersion parameter)
- [ ] Inverse Gaussian
- [ ] Other exponential family distributions
- [ ] Option for data standardization/normalization
- [ ] Weighted regressions
- [ ] Weight the covariance matrix with point-by-point error bars
- [ ] Allow for off-diagonal correlations between points
- [ ] Fix likelihood functions
- [ ] Check the tolerance conditions for termination
- [ ] Non-canonical link functions
- [ ] Goodness-of-fit tests
- [ ] Log-likelihood difference from saturated model
- [ ] Aikaike and Bayesian information criteria
- [ ] generalized R^2?
TODO
- [ ] Generalize GLM interface to allow multi-parameter fits like a gamma
distribution.
- [ ] Exact Z-scores by re-minimizing after fixing each parameter to zero (?)
- [ ] Unit tests for correct convergence with linear offsets
- [ ] Calculate/estimate dispersion parameter from the data
References