Performance of empirical risk minimization in linear aggregation
نویسندگان
چکیده
منابع مشابه
Performance of empirical risk minimization in linear aggregation
Let (X ,μ) be a probability space, set X to be distributed according to μ and put Y to be an unknown target random variable. In the usual setup in learning theory, one observes N independent couples (Xi, Yi)Ni=1 in X × R, distributed according to the joint distribution of X and Y . The goal is to construct a real-valued function f which is a good guess/prediction of Y . A standard way of measur...
متن کاملAggregation via Empirical Risk Minimization
Given a finite set F of estimators, the problem of aggregation is to construct a new estimator whose risk is as close as possible to the risk of the best estimator in F . It was conjectured that empirical minimization performed in the convex hull of F is an optimal aggregation method, but we show that this conjecture is false. Despite that, we prove that empirical minimization in the convex hul...
متن کاملAggregation versus Empirical Risk Minimization
Abstract Given a finite set F of estimators, the problem of aggregation is to construct a new estimator that has a risk as close as possible to the risk of the best estimator in F . It was conjectured that empirical minimization performed in the convex hull of F is an optimal aggregation method, but we show that this conjecture is false. Despite that, we prove that empirical minimization in the...
متن کاملEmpirical risk minimization is optimal for the convex aggregation problem
Let F be a finite model of cardinality M and denote by conv(F ) its convex hull. The problem of convex aggregation is to construct a procedure having a risk as close as possible to the minimal risk over conv(F ). Consider the bounded regression model with respect to the squared risk denoted by R(·). If f̂ ERM-C n denotes the empirical risk minimization procedure over conv(F ), then we prove that...
متن کاملAsymptotics in Empirical Risk Minimization
In this paper, we study a two-category classification problem. We indicate the categories by labels Y = 1 and Y = −1. We observe a covariate, or feature, X ∈ X ⊂ R. Consider a collection {ha} of classifiers indexed by a finite-dimensional parameter a, and the classifier ha∗ that minimizes the prediction error over this class. The parameter a∗ is estimated by the empirical risk minimizer ân over...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bernoulli
سال: 2016
ISSN: 1350-7265
DOI: 10.3150/15-bej701