What is DynStatCov?

DynStatCov is a Cython Library for fast dynamic statistical co-variance update. It is intended for usage in applications, where a statistical co-variance matrix has to be computed from observations and periodically updated. The naive approach would require to re-compute the matrix every time from all samples and to hold them in memory. By re-organizing the formula (see Mathematical formulation for details), the computation can be realized using intermediate sums and thus achieving a higher speed.

Complexity

The update is considerably cheaper than the computation of the complete sample co-variance matrix, not only when \(n>>m\):

• complete: \(\mathcal O(nm^2)\)
• update: \(\mathcal O(m^2)\)

Speed

Tested with %timeit using 10000 initial observations of 3 features each and then computing an update upon arrival of a new observation:

• complete re-computation with numpy.cov: 553us
• dynamic update implemented in Python: 66us
• DynStatCov dynamic update: 0.804us