SparseKolesky.jl

SparseKolesky.jl is a Julia package for the sparse Cholesky factorization of dense kernel ("covariance") matrices.

Our method enjoys a number of advantageous properties including

• Near-linear computational time and space efficiency
• Specifically, $\epsilon$-accuracy in time complexity $\mathcal{O}(N \log^{2d} (N/\epsilon))$ using just $\mathcal{O}(N \log^{d} (N/\epsilon))$ nonzero entries (and kernel function evaluations) where $d$ is the intrinsic dimensionality of the data
• Embarrassingly parallel factorization and simple implementation
• Optimal Kullback–Leibler divergence for a fixed sparsity pattern
• Guaranteed positive definiteness of the resulting factor

This is a fork of KoLesky.jl tailored to applications in Gaussian process regression (e.g. EarthquakeGPs.jl).