Related papers: Regularized Quantile Regression with Interactive F…
This article deals with the analysis of high dimensional data that come from multiple sources (experiments) and thus have different possibly correlated responses, but share the same set of predictors. The measurements of the predictors may…
Quantile regression is studied in combination with a penalty which promotes structured (or group) sparsity. A mixed $\ell_{1,\infty}$-norm on the parameter vector is used to impose structured sparsity on the traditional quantile regression…
In this paper we study methods for estimating causal effects in settings with panel data, where some units are exposed to a treatment during some periods and the goal is estimating counterfactual (untreated) outcomes for the treated…
We propose a novel iterative algorithm for estimating a deterministic but unknown parameter vector in the presence of model uncertainties. This iterative algorithm is based on a system model where an overall noise term describes both, the…
In this paper we study the kernel multiple ridge regression framework, which we refer to as multi-task regression, using penalization techniques. The theoretical analysis of this problem shows that the key element appearing for an optimal…
This paper proposes computationally efficient methods that can be used for instrumental variable quantile regressions (IVQR) and related methods with statistical guarantees. This is much needed when we investigate heterogenous treatment…
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 study extends the Bayesian nonparametric instrumental variable regression model to determine the structural effects of covariates on the conditional quantile of the response variable. The error distribution is nonparametrically…
This paper focuses on the problem of modeling and estimating interaction effects between covariates and a continuous treatment variable on an outcome, using a single-index regression approach. The primary motivation is to estimate an…
We propose a penalized method for the least squares estimator of a multivariate concave regression function. This estimator is formulated as a quadratic programming (QP) problem with $O(n^2)$ constraints, where n is the number of…
We link conditional generative modelling to quantile regression. We propose a suitable loss function and derive minimax convergence rates for the associated risk under smoothness assumptions imposed on the conditional distribution. To…
Network regression with additive node-level random effects can be problematic when the primary interest is estimating unconditional regression coefficients and some covariates are exactly or nearly in the vector space of node-level effects.…
This paper presents a weighted optimization framework that unifies the binary,multi-valued, continuous, as well as mixture of discrete and continuous treatment, under the unconfounded treatment assignment. With a general loss function, the…
This paper develops bootstrap methods for practical statistical inference in panel data quantile regression models with fixed effects. We consider random-weighted bootstrap resampling and formally establish its validity for asymptotic…
We study sparse linear regression over a network of agents, modeled as an undirected graph (with no centralized node). The estimation problem is formulated as the minimization of the sum of the local LASSO loss functions plus a quadratic…
In this note, we make some observations about the equivalences between regularized estimating equations, fixed-point problems and variational inequalities. A summary of our findings is given below: (a) A regularized estimating equation is…
In causal inference, interference occurs when the treatment of one unit may affect the outcomes of other units. The goal of this work is to serve as a guide to the use of linear outcome modeling for estimating causal effects in settings…
Uncertainty quantification is vital for decision-making and risk assessment in machine learning. Mean-variance regression models, which predict both a mean and residual noise for each data point, provide a simple approach to uncertainty…
Regularization methods allow one to handle a variety of inferential problems where there are more covariates than cases. This allows one to consider a potentially enormous number of covariates for a problem. We exploit the power of these…
This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator…