Lasso and probabilistic inequalities for multivariate point processes

Understand

Due to its low computational cost, Lasso is an attractive regularization method for high-dimensional statistical settings.

• In this paper, we consider multivariate counting processes depending on an unknown function parameter to be estimated by linear combinations of a fixed dictionary.
• To select coefficients, we propose an adaptive $\ell_1$-penalization methodology, where data-driven weights of the penalty are derived from new Bernstein type inequalities for martingales.
• Oracle inequalities are established under assumptions on the Gram matrix of the dictionary.