Python implementation of the Falkon algorithm for large-scale, approximate kernel ridge regression.

The code is well optimized and can scale to problems with tens of millions of points. Full kernel matrices are never computed explicitly so that you will not run out of memory on large problems.

Preconditioned conjugate gradient optimization ensures that only few iterations are necessary to obtain good results.

The basic algorithm is a Nyström approximation to KRR, which needs only three hyperparameters:

1. The number of centers M - this controls the quality of the approximation: a higher number of centers will produce more accurate results at the expense of more computation time, and higher memory requirements.
2. The penalty term, which controls the amount of regularization.
3. The kernel function. A good default is always the Gaussian (or RBF) kernel (falkon.kernels.GaussianKernel).

For more information about the algorithm and the optimized solver, download our paper: Kernel methods through the roof: handling billions of points efficiently

The API is sklearn-like, so that Falkon should be easy to integrate in your existing code.

Extensive documentation is available at https://falkonml.github.io/falkon/. Several worked-through examples are also provided in the docs.

If you find a bug, please open a new issue on GitHub!

Prerequisites are PyTorch >= 1.4 (with the CUDA toolkit if GPU support is desired) and a patched version of KeOps (which is distributed as a git submodule of this repository), cmake, and a C++ compiler which can compile PyTorch extensions (i.e. capable of compiling with -std=c++11).

Once the prerequisites are met, you can pip install . from the root of this repository.

For more detailed installation instructions see the docs.

If you find this library useful for your work, please cite the following publication:

@misc{falkonlibrary2020,
    title={Kernel methods through the roof: handling billions of points efficiently},
    authors={Meanti, Giacomo and Carratino, Luigi and Rosasco, Lorenzo and Rudi, Alessandro},
    year = {2020},
    archivePrefix = {arXiv},
    eprint = {2006.10350}
}