B1868
Title: Super ensemble learning using the highly-adaptive-lasso
Authors: Zeyi Wang - UC Berkeley (United States) [presenting]
Wenxin Zhang - UC Berkeley (United States)
Mark van der Laan - University of California at Berkeley (United States)
Abstract: The estimation of a functional parameter of a realistically modelled data distribution is considered based on observing independent and identically distributed observations. Suppose that the true function is defined as the minimizer of the expectation of a specified loss function over its parameter space. It is assumed that estimators of the true function are provided, which can be viewed as a data-adaptive coordinate transformation for the true function. For any -dimensional real-valued cadlag function with finite sectional variation norm, a candidate ensemble estimator is defined as the mapping from the data into the composition of the cadlag function and the estimated functions. Using $k$-fold cross-validation, the cross-validated empirical risk of each cadlag function-specific ensemble estimator is defined. The meta highly adaptive lasso minimum loss estimator (M-HAL-MLE) is then defined as the cadlag function that minimizes this cross-validated empirical risk of the cadlag function specific ensemble over all cadlag functions with a uniform bound on the sectional variation norm (and respecting the parameter space of functional parameter). The true function can be estimated with the average of these estimated functions, which is called the M-HAL super-learner, and a pathwise differentiable target feature of the true function is estimated with the corresponding plug-in estimator, or with an average of the plug-in estimated functions.
