Related papers: Lasso-type recovery of sparse representations for …
The Lasso has become a benchmark data analysis procedure, and numerous variants have been proposed in the literature. Although the Lasso formulations are stated so that overall prediction error is optimized, no full control over the…
Nowadays an increasing amount of data is available and we have to deal with models in high dimension (number of covariates much larger than the sample size). Under sparsity assumption it is reasonable to hope that we can make a good…
Sparse regularization such as $\ell_1$ regularization is a quite powerful and widely used strategy for high dimensional learning problems. The effectiveness of sparse regularization has been supported practically and theoretically by…
The Lasso is a prominent algorithm for variable selection. However, its instability in the presence of correlated variables in the high-dimensional setting is well-documented. Although previous research has attempted to address this issue…
The Lasso is a popular regression method for high-dimensional problems in which the number of parameters $\theta_1,\dots,\theta_N$, is larger than the number $n$ of samples: $N>n$. A useful heuristics relates the statistical properties of…
We study the problem of variable selection in convex nonparametric least squares (CNLS). Whereas the least absolute shrinkage and selection operator (Lasso) is a popular technique for least squares, its variable selection performance is…
Sparse modelling or model selection with categorical data is challenging even for a moderate number of variables, because one parameter is roughly needed to encode one category or level. The Group Lasso is a well known efficient algorithm…
Recent research has studied the role of sparsity in high dimensional regression and signal reconstruction, establishing theoretical limits for recovering sparse models from sparse data. This line of work shows that $\ell_1$-regularized…
Variance estimation in the linear model when $p > n$ is a difficult problem. Standard least squares estimation techniques do not apply. Several variance estimators have been proposed in the literature, all with accompanying asymptotic…
The LASSO estimator is an $\ell_1$-norm penalized least-squares estimator, which was introduced for variable selection in the linear model. When the design matrix satisfies, e.g. the Restricted Isometry Property, or has a small coherence…
The LASSO is a recent technique for variable selection in the regression model \bean y & = & X\beta + z, \eean where $X\in \R^{n\times p}$ and $z$ is a centered gaussian i.i.d. noise vector $\mathcal N(0,\sigma^2I)$. The LASSO has been…
Statistical inference for stochastic processes has advanced significantly due to applications in diverse fields, but challenges remain in high-dimensional settings where parameters are allowed to grow with the sample size. This paper…
It is more and more frequently the case in applications that the data we observe come from one or more random variables taking values in an infinite dimensional space, e.g. curves. The need to have tools adapted to the nature of these data…
Penalized regression models such as the Lasso have proved useful for variable selection in many fields - especially for situations with high-dimensional data where the numbers of predictors far exceeds the number of observations. These…
The high-dimensional linear model $y = X \beta^0 + \epsilon$ is considered and the focus is put on the problem of recovering the support $S^0$ of the sparse vector $\beta^0.$ We introduce Lasso-Zero, a new $\ell_1$-based estimator whose…
In high dimensional sparse regression, pivotal estimators are estimators for which the optimal regularization parameter is independent of the noise level. The canonical pivotal estimator is the square-root Lasso, formulated along with its…
In this paper, we review state-of-the-art methods for feature selection in statistics with an application-oriented eye. Indeed, sparsity is a valuable property and the profusion of research on the topic might have provided little guidance…
Recent work has focused on the problem of conducting linear regression when the number of covariates is very large, potentially greater than the sample size. To facilitate this, one useful tool is to assume that the model can be well…
Popular regularizers with non-differentiable penalties, such as Lasso, Elastic Net, Generalized Lasso, or SLOPE, reduce the dimension of the parameter space by inducing sparsity or clustering in the estimators' coordinates. In this paper,…
Large-scale empirical data, the sample size and the dimension are high, often exhibit various characteristics. For example, the noise term follows unknown distributions or the model is very sparse that the number of critical variables is…