Related papers: Lasso, knockoff and Gaussian covariates: a compari…
The Lasso regression is a popular regularization method for feature selection in statistics. Prior to computing the Lasso estimator in both linear and generalized linear models, it is common to conduct a preliminary rescaling of the feature…
We consider the problem of estimating and inferring treatment effects in randomized experiments. In practice, stratified randomization, or more generally, covariate-adaptive randomization, is routinely used in the design stage to balance…
This paper considers the objective comparison of stochastic models to solve inverse problems, more specifically image restoration. Most often, model comparison is addressed in a supervised manner, that can be time-consuming and partly…
We study the task of noiseless linear regression under Gaussian covariates in the presence of additive oblivious contamination. Specifically, we are given i.i.d.\ samples from a distribution $(x, y)$ on $\mathbb{R}^d \times \mathbb{R}$ with…
Locally weighted regression was created as a nonparametric learning method that is computationally efficient, can learn from very large amounts of data and add data incrementally. An interesting feature of locally weighted regression is…
We develop a novel Bayesian method to select important predictors in regression models with multiple responses of diverse types. A sparse Gaussian copula regression model is used to account for the multivariate dependencies between any…
We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…
In Gaussian graphical models, the likelihood equations must typically be solved iteratively. We investigate two algorithms: A version of iterative proportional scaling which avoids inversion of large matrices, and an algorithm based on…
We propose a new method to learn the structure of a Gaussian graphical model with finite sample false discovery rate control. Our method builds on the knockoff framework of Barber and Cand\`{e}s for linear models. We extend their approach…
We introduce a pliable lasso method for estimation of interaction effects in the Cox proportional hazards model framework. The pliable lasso is a linear model that includes interactions between covariates X and a set of modifying variables…
Gaussian process is a very promising novel technology that has been applied to both the regression problem and the classification problem. While for the regression problem it yields simple exact solutions, this is not the case for the…
A central error measure in Gaussian DDPMs is the path-space KL divergence between the exact reverse chain and the learned Gaussian reverse process. This quantity is especially relevant for procedures such as classifier guidance, which…
We present a novel method for controlling the $k$-familywise error rate ($k$-FWER) in the linear regression setting using the knockoffs framework first introduced by Barber and Cand\`es. Our procedure, which we also refer to as knockoffs,…
Choosing relevant predictors is central to the analysis of biomedical time-to-event data. Classical frequentist inference, however, presumes that the set of covariates is fixed in advance and does not account for data-driven variable…
We develop a fully automatic Bayesian Lasso via variational inference. This is a scalable procedure for approximating the posterior distribution. Special attention is driven to the knot selection in regression spline. In order to carry…
Model-X knockoffs allows analysts to perform feature selection using almost any machine learning algorithm while still provably controlling the expected proportion of false discoveries. To apply model-X knockoffs, one must construct…
Gaussian graphical model is one of the powerful tools to analyze conditional independence between two variables for multivariate Gaussian-distributed observations. When the dimension of data is moderate or high, penalized likelihood methods…
A Bayes factor is proposed for testing whether the effect of a key predictor variable on the dependent variable is linear or nonlinear, possibly while controlling for certain covariates. The test can be used (i) when one is interested in…
Many probabilistic models introduce strong dependencies between variables using a latent multivariate Gaussian distribution or a Gaussian process. We present a new Markov chain Monte Carlo algorithm for performing inference in models with…
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…