1,082 research outputs found
-Penalization in Functional Linear Regression with Subgaussian Design
We study functional regression with random subgaussian design and real-valued
response. The focus is on the problems in which the regression function can be
well approximated by a functional linear model with the slope function being
"sparse" in the sense that it can be represented as a sum of a small number of
well separated "spikes". This can be viewed as an extension of now classical
sparse estimation problems to the case of infinite dictionaries. We study an
estimator of the regression function based on penalized empirical risk
minimization with quadratic loss and the complexity penalty defined in terms of
-norm (a continuous version of LASSO). The main goal is to introduce
several important parameters characterizing sparsity in this class of problems
and to prove sharp oracle inequalities showing how the -error of the
continuous LASSO estimator depends on the underlying sparsity of the problem
Active Clinical Trials for Personalized Medicine
Individualized treatment rules (ITRs) tailor treatments according to
individual patient characteristics. They can significantly improve patient care
and are thus becoming increasingly popular. The data collected during
randomized clinical trials are often used to estimate the optimal ITRs.
However, these trials are generally expensive to run, and, moreover, they are
not designed to efficiently estimate ITRs. In this paper, we propose a
cost-effective estimation method from an active learning perspective. In
particular, our method recruits only the "most informative" patients (in terms
of learning the optimal ITRs) from an ongoing clinical trial. Simulation
studies and real-data examples show that our active clinical trial method
significantly improves on competing methods. We derive risk bounds and show
that they support these observed empirical advantages.Comment: 48 Page, 9 Figures. To Appear in JASA--T&
Efficient median of means estimator
The goal of this note is to present a modification of the popular median of
means estimator that achieves sub-Gaussian deviation bounds with nearly optimal
constants under minimal assumptions on the underlying distribution. We build on
a recent work on the topic by the author, and prove that desired guarantees can
be attained under weaker requirements
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