Randomised linear algebra

See random matrices, vector random projections and many other related tricks Notes on doing linear algebra operations using randomised matrix projections. Useful for, e.g. randomised regression.


Obligatory Igor Carron mention: Random matrices are too damn large. Martinsson (2016) seems to be a fresh review of the action.

Random Fourier Features

See Random Fourier Features.

Randomisation in matrix factorization

See various matrix factorisation methods.

Random regression

See randomised regression

Hutchinson trace estimator

Shakir Mohamed mentions Hutchinson’s Trick, and was introduced to it, as I was, by Dr Maurizio Filippone. This trick also works with efficiently with the ensemble Kalman filter, where the randomised products are cheap.

Stochastic Lanczos Quadrature

Overview β€” imate Manual



Overview β€” imate

The main purpose of Δ±mate is to estimate the algebraic quantity \[ \operatorname{trace}(f(\mathbf{A})) \] where \(\mathbf{A}\) is a square matrix, \(f\) is a matrix function, and trace \((\cdot)\) is the trace operator. Imate can also compute variants of \((1)\), such as \[ \operatorname{trace}(\mathbf{B} f(\mathbf{A})) \] and \[ \operatorname{trace}(\mathbf{B} f(\mathbf{A}) \mathbf{C} f(\mathbf{A})) \] where \(\mathbf{B}\) and \(\mathbf{C}\) are matrices. Other variations include the cases where \(\mathbf{A}\) is replaced by \(\mathbf{A}^{\top} \mathbf{A}\) in the above expressions.



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