Linking the statistic and the machine learning literature, we provide new general results on the convergence of stochastic approximation schemes and inexact Newton methods. Building on these results, we put forward a new optimization scheme that we call generalized inexact Newton method (GINM)....

Linking the statistic and the machine learning literature, we provide new general results on the convergence of stochastic approximation schemes and inexact Newton methods. Building on these results, we put forward a new optimization scheme that we call generalized inexact Newton method (GINM)....

We develop two new methods for selecting the penalty parameter for the e1-penalized high-dimensional M-estimator, which we refer to as the analytic and bootstrap-after-cross-validation methods. For both methods, we derive nonasymptotic error bounds for the corresponding e1-penalized M-estimator...

We develop two new methods for selecting the penalty parameter for the e1-penalized high-dimensional M-estimator, which we refer to as the analytic and bootstrap-after-cross-validation methods. For both methods, we derive nonasymptotic error bounds for the corresponding e1-penalized M-estimator...