相关论文: Linear and convex aggregation of density estimator…

We consider a partially linear framework for modelling massive heterogeneous data. The major goal is to extract common features across all sub-populations while exploring heterogeneity of each sub-population. In particular, we propose an…

We provide a new estimator of integral operators with smooth kernels, obtained from a set of scattered and noisy impulse responses. The proposed approach relies on the formalism of smoothing in reproducing kernel Hilbert spaces and on the…

Kernel matrices, as well as weighted graphs represented by them, are ubiquitous objects in machine learning, statistics and other related fields. The main drawback of using kernel methods (learning and inference using kernel matrices) is…

Modal linear regression (MLR) is a method for obtaining a conditional mode predictor as a linear model. We study kernel selection for MLR from two perspectives: "which kernel achieves smaller error?" and "which kernel is computationally…

We introduce a convex approach for mixed linear regression over $d$ features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\mathbb{R}^{d}$ for each data point.…

We study Sparse Multiple Kernel Learning (SMKL), which is the problem of selecting a sparse convex combination of prespecified kernels for support vector binary classification. Unlike prevailing l1 regularized approaches that approximate a…

Subgradient algorithms for training support vector machines have been quite successful for solving large-scale and online learning problems. However, they have been restricted to linear kernels and strongly convex formulations. This paper…

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…

We introduce new global and local inexact oracle concepts for a wide class of convex functions in composite convex minimization. Such inexact oracles naturally come from primal-dual framework, barrier smoothing, inexact computations of…

In this paper, we introduce structured sparsity estimators in Generalized Linear Models. Structured sparsity estimators in the least squares loss are introduced by Stucky and van de Geer (2018) recently for fixed design and normal errors.…

In this paper we study nonparametric estimators of copulas and copula densities. We first focus our study on a density copula estimator based on a polynomial orthogonal projection of the joint density. A new copula estimator is then…

The paper describes an application of Aggregating Algorithm to the problem of regression. It generalizes earlier results concerned with plain linear regression to kernel techniques and presents an on-line algorithm which performs nearly as…

Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…

This paper presents minimax rates for density estimation when the data dimension $d$ is allowed to grow with the number of observations $n$ rather than remaining fixed as in previous analyses. We prove a non-asymptotic lower bound which…

We build penalized least-squares estimators using the slope heuristic and resampling penalties. We prove oracle inequalities for the selected estimator with leading constant asymptotically equal to 1. We compare the practical performances…

Let $F$ be a finite model of cardinality $M$ and denote by $\operatorname {conv}(F)$ 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 $\operatorname…

In many practical applications including remote sensing, multi-task learning, and multi-spectrum imaging, data are described as a set of matrices sharing a common column space. We consider the joint estimation of such matrices from their…

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of depen\-dence of design elements. The estimators are the…

Coresets have emerged as a powerful tool to summarize data by selecting a small subset of the original observations while retaining most of its information. This approach has led to significant computational speedups but the performance of…

In this paper, we investigate the matrix estimation problem in the multi-response regression model with measurement errors. A nonconvex error-corrected estimator based on a combination of the amended loss function and the nuclear norm…