Empirical risk minimization is optimal for the convex aggregation problem

نویسنده

  • GUILLAUME LECUÉ
چکیده

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 for any x > 0, with probability greater than 1 − 4 exp(−x),

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Aggregation 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 کامل

Aggregation 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 کامل

[hal-00736203, v1] Empirical 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 n denotes the empirical risk minimization procedure over conv(F ) then we prove that for an...

متن کامل

Suboptimality of Penalized Empirical Risk Minimization in Classification

Let F be a set of M classification procedures with values in [−1, 1]. Given a loss function, we want to construct a procedure which mimics at the best possible rate the best procedure in F . This fastest rate is called optimal rate of aggregation. Considering a continuous scale of loss functions with various types of convexity, we prove that optimal rates of aggregation can be either ((logM)/n)...

متن کامل

On the optimality of the empirical risk minimization procedure for the Convex Aggregation problem

We study the performance of empirical risk minimization (ERM), with respect to the quadratic risk, in the context of convex aggregation, in which one wants to construct a procedure whose risk is as close as possible to the best function in the convex hull of an arbitrary finite class F . We show that ERM performed in the convex hull of F is an optimal aggregation procedure for the convex aggreg...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2012