相关论文: Simultaneous adaptation to the margin and to compl…

We consider the problem of adaptation to the margin in binary classification. We suggest a penalized empirical risk minimization classifier that adaptively attains, up to a logarithmic factor, fast optimal rates of convergence for the…

A classical condition for fast learning rates is the margin condition, first introduced by Mammen and Tsybakov. We tackle in this paper the problem of adaptivity to this condition in the context of model selection, in a general learning…

Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…

We give a general result concerning the rates of convergence of penalized empirical risk minimizers (PERM) in the regression model. Then, we consider the problem of agnostic learning of the regression, and give in this context an oracle…

We propose a general theorem providing upper bounds for the risk of an empirical risk minimizer (ERM).We essentially focus on the binary classification framework. We extend Tsybakov's analysis of the risk of an ERM under margin type…

Algorithms for binary classification based on adaptive tree partitioning are formulated and analyzed for both their risk performance and their friendliness to numerical implementation. The algorithms can be viewed as generating a set…

This article deals with the adaptive and approximative computation of the Lam\'e equations. The equations of linear elasticity are considered as boundary integral equations and solved in the setting of the boundary element method (BEM).…

We consider the problem of statistical learning for the intensity of a counting process with covariates. In this context, we introduce an empirical risk, and prove risk bounds for the corresponding empirical risk minimizers. Then, we give…

A efficient incremental learning algorithm for classification tasks, called NetLines, well adapted for both binary and real-valued input patterns is presented. It generates small compact feedforward neural networks with one hidden layer of…

In this paper, we propose a data-adaptive non-parametric kernel learning framework in margin based kernel methods. In model formulation, given an initial kernel matrix, a data-adaptive matrix with two constraints is imposed in an entry-wise…

This paper studies statistical aggregation procedures in regression setting. A motivating factor is the existence of many different methods of estimation, leading to possibly competing estimators. We consider here three different types of…

In this paper, we study adaptive finite element approximations in a perturbation framework, which makes use of the existing adaptive finite element analysis of a linear symmetric elliptic problem. We prove the convergence and complexity of…

We study methods for aggregating pairwise comparison data in order to estimate outcome probabilities for future comparisons among a collection of n items. Working within a flexible framework that imposes only a form of strong stochastic…

In the same spirit as Tsybakov (2003), we define the optimality of an aggregation procedure in the problem of classification. Using an aggregate with exponential weights, we obtain an optimal rate of convex aggregation for the hinge risk…

When considering a model selection or, more generally, an aggregation approach for adaptive statistical inference, it is often necessary to compute estimators over a wide range of model complexities including unnecessarily large models even…

Despite the enormous success of machine learning models in various applications, most of these models lack resilience to (even small) perturbations in their input data. Hence, new methods to robustify machine learning models seem very…

We aim to design strategies for sequential decision making that adjust to the difficulty of the learning problem. We study this question both in the setting of prediction with expert advice, and for more general combinatorial decision…

We consider the problem of cost sensitive multiclass classification, where we would like to increase the sensitivity of an important class at the expense of a less important one. We adopt an {\em apportioned margin} framework to address…

Given a finite collection of estimators or classifiers, we study the problem of model selection type aggregation, that is, we construct a new estimator or classifier, called aggregate, which is nearly as good as the best among them with…

Let $\cF$ 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 $\cF$. This fastest rate is called optimal…