Related papers: Quantile Additive Trend Filtering
We study quantile trend filtering, a recently proposed method for nonparametric quantile regression with the goal of generalizing existing risk bounds known for the usual trend filtering estimators which perform mean regression. We study…
We study additive models built with trend filtering, i.e., additive models whose components are each regularized by the (discrete) total variation of their $k$th (discrete) derivative, for a chosen integer $k \geq 0$. This results in $k$th…
We study trend filtering, a recently proposed tool of Kim et al. [SIAM Rev. 51 (2009) 339-360] for nonparametric regression. The trend filtering estimate is defined as the minimizer of a penalized least squares criterion, in which the…
This paper presents a fast and robust algorithm for trend filtering, a recently developed nonparametric regression tool. It has been shown that, for estimating functions whose derivatives are of bounded variation, trend filtering achieves…
We study trend filtering, a relatively recent method for univariate nonparametric regression. For a given positive integer $r$, the $r$-th order trend filtering estimator is defined as the minimizer of the sum of squared errors when we…
Along with the widespread adoption of high-dimensional data, traditional statistical methods face significant challenges in handling problems with high correlation of variables, heavy-tailed distribution, and coexistence of sparse and dense…
This paper introduces the method of composite quantile factor model for factor analysis in high-dimensional panel data. We propose to estimate the factors and factor loadings across multiple quantiles of the data, allowing the estimates to…
Despite increasing accessibility to function data, effective methods for flexibly estimating underlying functional trend are still scarce. We thereby develop functional version of trend filtering for estimating trend of functional data…
We consider a flexible semiparametric quantile regression model for analyzing high dimensional heterogeneous data. This model has several appealing features: (1) By considering different conditional quantiles, we may obtain a more complete…
For time series data observed at non-random and possibly non-equidistant time points, we estimate the trend function nonparametrically. Under the assumption of a bounded total variation of the function and low-order moment conditions on the…
In practical applications, one often does not know the "true" structure of the underlying conditional quantile function, especially in the ultra-high dimensional setting. To deal with ultra-high dimensionality, quantile-adaptive marginal…
Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost…
We introduce a family of adaptive estimators on graphs, based on penalizing the $\ell_1$ norm of discrete graph differences. This generalizes the idea of trend filtering [Kim et al. (2009), Tibshirani (2014)], used for univariate…
This paper extends quantile factor analysis to a probabilistic variant that incorporates regularization and computationally efficient variational approximations. We establish through synthetic and real data experiments that the proposed…
We address the problem of estimating smoothly varying baseline trends in time series data. This problem arises in a wide range of fields, including chemistry, macroeconomics, and medicine; however, our study is motivated by the analysis of…
Quantile Factor Models (QFM) represent a new class of factor models for high-dimensional panel data. Unlike Approximate Factor Models (AFM), where only location-shifting factors can be extracted, QFM also allow to recover unobserved factors…
In the context of kernel machines, polynomial and Fourier features are commonly used to provide a nonlinear extension to linear models by mapping the data to a higher-dimensional space. Unless one considers the dual formulation of the…
This paper considers the problem of nonparametric quantile regression under the assumption that the target conditional quantile function is a composition of a sequence of low-dimensional functions. We study the nonparametric quantile…
Statistical learning evolves quickly with more and more sophisticated models proposed to incorporate the complicated data structure from modern scientific and business problems. Varying index coefficient models extend varying coefficient…
Factor modeling is a powerful statistical technique that permits to capture the common dynamics in a large panel of data with a few latent variables, or factors, thus alleviating the curse of dimensionality. Despite its popularity and…