Related papers: How Correlations Influence Lasso Prediction
Although the Lasso has been extensively studied, the relationship between its prediction performance and the correlations of the covariates is not fully understood. In this paper, we give new insights into this relationship in the context…
The choice of the tuning parameter in the Lasso is central to its statistical performance in high-dimensional linear regression. In this work, we study tuning regimes under which the Lasso exhibits suboptimal prediction performance, in the…
In spite of the wealth of literature on the theoretical properties of the Lasso, there is very little known when the value of the tuning parameter is chosen using the data, even though this is what actually happens in practice. We give a…
Convex estimators such as the Lasso, the matrix Lasso and the group Lasso have been studied extensively in the last two decades, demonstrating great success in both theory and practice. Two quantities are introduced, the noise barrier and…
High-dimensional predictive models, those with more measurements than observations, require regularization to be well defined, perform well empirically, and possess theoretical guarantees. The amount of regularization, often determined by…
This paper investigates the effect of the design matrix on the ability (or inability) to estimate a sparse parameter in linear regression. More specifically, we characterize the optimal rate of estimation when the smallest singular value of…
Penalized (or regularized) regression, as represented by Lasso and its variants, has become a standard technique for analyzing high-dimensional data when the number of variables substantially exceeds the sample size. The performance of…
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 computationally efficient regression regularization procedure that can produce sparse estimators when the number of predictors (p) is large. Oracle inequalities provide probability loss bounds for the Lasso estimator at a…
Correlation matrices contain a wide variety of spatio-temporal information about a dynamical system. Predicting correlation matrices from partial time series information of a few nodes characterizes the spatio-temporal dynamics of the…
We explore estimation and forecast accuracy for sparse linear models, focusing on scenarios where both predictors and errors carry serial correlations. We establish a clear link between predictor serial correlation and the performance of…
The effect of correlations between model parameters and nuisance parameters is discussed, in the context of fitting model parameters to data. Modifications to the usual $\chi^2$ method are required. Fake data studies, as used at present,…
We consider situations where a user feeds her attributes to a machine learning method that tries to predict her best option based on a random sample of other users. The predictor is incentive-compatible if the user has no incentive to…
The lasso and related sparsity inducing algorithms have been the target of substantial theoretical and applied research. Correspondingly, many results are known about their behavior for a fixed or optimally chosen tuning parameter specified…
It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…
In this paper we revisit the risk bounds of the lasso estimator in the context of transductive and semi-supervised learning. In other terms, the setting under consideration is that of regression with random design under partial labeling.…
We study high-dimensional linear models and the $\ell_1$-penalized least squares estimator, also known as the Lasso estimator. In literature, oracle inequalities have been derived under restricted eigenvalue or compatibility conditions. In…
Conformal prediction is a popular framework of uncertainty quantification that constructs prediction sets with coverage guarantees. To uphold the exchangeability assumption, many conformal prediction methods necessitate an additional…
We present upper and lower bounds for the prediction error of the Lasso. For the case of random Gaussian design, we show that under mild conditions the prediction error of the Lasso is up to smaller order terms dominated by the prediction…
In a multivariate linear regression model with $p>1$ covariates, implementation of penalization techniques often implies a preliminary univariate standardization step. Although this prevents scale effects on the covariates selection…