Section: New Results
High-dimensional learning and complex data
Participant : Gérard Biau.
We describe four (not so related) contributions on the theme of high-dimensional learning and complex data.
In [17] we address the problem of supervised classification of Cox process trajectories, whose random intensity is driven by some exogenous random covariable. The classification task is achieved through a regularized convex empirical risk minimization procedure, and a nonasymptotic oracle inequality is derived. The results are obtained by taking advantage of martingale and stochastic calculus arguments, which are natural in this context and fully exploit the functional nature of the problem.
The cellular tree classifier model addresses a fundamental problem
in the design of classifiers for a parallel or distributed computing
world: Given a data set, is it sufficient to apply a majority rule
for classification, or shall one split the data into
two or more parts and send each part to a potentially different
computer (or cell) for further processing?
At first sight, it seems impossible to define with this paradigm a consistent classifier as no cell knows
the “original data size”,
A new method for combining several initial estimators of the
regression function is introduced. Instead of building a linear or
convex optimized combination over a collection of basic estimators
The impact of letting the dimension