Related papers: Adaptive post-Dantzig estimation and prediction fo…
To successfully work on variable selection, sparse model structure has become a basic assumption for all existing methods. However, this assumption is questionable as it is hard to hold in most of cases and none of existing methods may…
Transductive methods are useful in prediction problems when the training dataset is composed of a large number of unlabeled observations and a smaller number of labeled observations. In this paper, we propose an approach for developing…
In many important statistical applications, the number of variables or parameters $p$ is much larger than the number of observations $n$. Suppose then that we have observations $y=X\beta+z$, where $\beta\in\mathbf{R}^p$ is a parameter…
We consider the linear regression problem, where the number $p$ of covariates is possibly larger than the number $n$ of observations $(x_{i},y_{i})_{i\leq i \leq n}$, under sparsity assumptions. On the one hand, several methods have been…
Inference and prediction under the sparsity assumption have been a hot research topic in recent years. However, in practice, the sparsity assumption is difficult to test, and more importantly can usually be violated. In this paper, to study…
In modern data analysis, sparse model selection becomes inevitable once the number of predictors variables is very high. It is well-known that model selection procedures like the Lasso or Boosting tend to overfit on real data. The…
The Dantzig selector has received popularity for many applications such as compressed sensing and sparse modeling, thanks to its computational efficiency as a linear programming problem and its nice sampling properties. Existing results…
We propose a generalized version of the Dantzig selector. We show that it satisfies sparsity oracle inequalities in prediction and estimation. We consider then the particular case of high-dimensional linear regression model selection with…
We consider the sparse estimation for stochastic processes with possibly infinite-dimensional nuisance parameters, by using the Dantzig selector which is a sparse estimation method similar to $Z$-estimation. When a consistent estimator for…
We consider learning high-dimensional multi-response linear models with structured parameters. By exploiting the noise correlations among responses, we propose an alternating estimation (AltEst) procedure to estimate the model parameters…
In this paper, we consider the classic measurement error regression scenario in which our independent, or design, variables are observed with several sources of additive noise. We will show that our motivating example's replicated…
Lasso and Dantzig selector are standard procedures able to perform variable selection and estimation simultaneously. This paper is concerned with extending these procedures to spatial point process intensity estimation. We propose adaptive…
The scalar-on-image regression model examines the association between a scalar response and a bivariate function (e.g., images) through the estimation of a bivariate coefficient function. Existing approaches often impose smoothness…
The Dantzig selector (Candes and Tao, 2007) is a popular l1-regularization method for variable selection and estimation in linear regression. We present a very weak geometric condition on the observed predictors which is related to…
Causal inference is known to be very challenging when only observational data are available. Randomized experiments are often costly and impractical and in instrumental variable regression the number of instruments has to exceed the number…
This paper considers the problem of robust adaptive efficient estimating of a periodic function in a continuous time regression model with the dependent noises given by a general square integrable semimartingale with a conditionally…
This paper deals with the problem of density estimation. We aim at building an estimate of an unknown density as a linear combination of functions of a dictionary. Inspired by Cand\`es and Tao's approach, we propose an $\ell_1$-minimization…
The Lasso is an attractive technique for regularization and variable selection for high-dimensional data, where the number of predictor variables $p_n$ is potentially much larger than the number of samples $n$. However, it was recently…
Bayesian nonparametric regression under a rescaled Gaussian process prior offers smoothness-adaptive function estimation with near minimax-optimal error rates. Hierarchical extensions of this approach, equipped with stochastic variable…
This paper proposes a multi-stage projection-based Lasso procedure for the semiparametric sample selection model in high-dimensional settings under a weak nonparametric restriction on the selection correction. In particular, the number of…