Related papers: Selecting Penalty Parameters of High-Dimensional M…
We consider both $\ell _{0}$-penalized and $\ell _{0}$-constrained quantile regression estimators. For the $\ell _{0}$-penalized estimator, we derive an exponential inequality on the tail probability of excess quantile prediction risk and…
This paper considers a new bootstrap procedure to estimate the distribution of high-dimensional $\ell_p$-statistics, i.e. the $\ell_p$-norms of the sum of $n$ independent $d$-dimensional random vectors with $d \gg n$ and $p \in [1,…
Skew normal model suffers from inferential drawbacks, namely singular Fisher information in the vicinity of symmetry and diverging of maximum likelihood estimation. To address the above drawbacks, Azzalini and Arellano-Valle (2013)…
Beta regression is commonly employed when the outcome variable is a proportion. Since its conception, the approach has been widely used in applications spanning various scientific fields. A series of extensions have been proposed over time,…
Despite the extensive literature on training loss functions, the evaluation of generalization on the validation set remains underexplored. In this work, we conduct a systematic empirical and statistical study of how the validation criterion…
Bootstrapping can produce confidence levels for hypotheses about quadratic regression models - such as whether the U-shape is inverted, and the location of optima. The method has several advantages over conventional methods: it provides…
Penalized $M-$estimators for logistic regression models have been previously study for fixed dimension in order to obtain sparse statistical models and automatic variable selection. In this paper, we derive asymptotic results for penalized…
Cross-validation is a statistical tool that can be used to improve large covariance matrix estimation. Although its efficiency is observed in practical applications and a convergence result towards the error of the non linear shrinkage is…
The expectation-maximization (EM) algorithm and its variants are widely used in statistics. In high-dimensional mixture linear regression, the model is assumed to be a finite mixture of linear regression and the number of predictors is much…
The bootstrap is a widely used procedure for statistical inference because of its simplicity and attractive statistical properties. However, the vanilla version of bootstrap is no longer feasible computationally for many modern massive…
Hyper-parameters tuning is a crucial task to make a model perform at its best. However, despite the well-established methodologies, some aspects of the tuning remain unexplored. As an example, it may affect not just accuracy but also…
This paper describes a method for performing inference on models chosen by cross-validation. When the test error being minimized in cross-validation is a residual sum of squares it can be written as a quadratic form. This allows us to apply…
This paper is concerned with testing global null hypotheses about population mean vectors of high-dimensional data. Current tests require either strong mixing (independence) conditions on the individual components of the high-dimensional…
Model selection is a crucial issue in machine-learning and a wide variety of penalisation methods (with possibly data dependent complexity penalties) have recently been introduced for this purpose. However their empirical performance is…
We propose a robust variable selection procedure using a divergence based M-estimator combined with a penalty function. It produces robust estimates of the regression parameters and simultaneously selects the important explanatory…
We construct a block bootstrap max-test for detecting the presence of significant predictors in a high dimensional setting, allowing for weakly dependent and heterogeneous (possibly non-stationary) data. The number of covariates to be…
We propose an $\ell_1$-penalized estimation procedure for high-dimensional linear mixed-effects models. The models are useful whenever there is a grouping structure among high-dimensional observations, i.e. for clustered data. We prove a…
In this paper, we aim to give a theoretical approximation for the penalty level of $\ell_{1}$-regularization problems. This can save much time in practice compared with the traditional methods, such as cross-validation. To achieve this…
Upper Confidence Bound (UCB) method is arguably the most celebrated one used in online decision making with partial information feedback. Existing techniques for constructing confidence bounds are typically built upon various concentration…
We propose a nonparametric quantile regression method using deep neural networks with a rectified linear unit penalty function to avoid quantile crossing. This penalty function is computationally feasible for enforcing non-crossing…