Related papers: Non-crossing convex quantile regression
We consider penalized regression models under a unified framework where the particular method is determined by the form of the penalty term. We propose a fully Bayesian approach that incorporates both sparse and dense settings and show how…
Cross-validation is the standard approach for tuning parameter selection in many non-parametric regression problems. However its use is less common in change-point regression, perhaps as its prediction error-based criterion may appear to…
Progression of chronic disease is often manifested by repeated occurrences of disease-related events over time. Delineating the heterogeneity in the risk of such recurrent events can provide valuable scientific insight for guiding…
Incorporating nonlinearity into quantum machine learning is essential for learning a complicated input-output mapping. We here propose quantum algorithms for nonlinear regression, where nonlinearity is introduced with feature maps when…
In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…
This paper considers a nonlinear quantile model with change-points. The quantile estimation method, which as a particular case includes median model, is more robust with respect to other traditional methods when model errors contain…
We develop a continuous-time penalized regression framework for the estimation of time-varying coefficients and variable selection when both the response and covariates are It\^o semimartingales with jumps. The coefficient paths are…
Complex-valued signals are used in the modeling of many systems in engineering and science, hence being of fundamental interest. Often, random complex-valued signals are considered to be proper. A proper complex random variable or process…
As a competitive alternative to least squares regression, quantile regression is popular in analyzing heterogenous data. For quantile regression model specified for one single quantile level $\tau$, major difficulties of semiparametric…
Much theoretical and applied work has been devoted to high-dimensional regression with clean data. However, we often face corrupted data in many applications where missing data and measurement errors cannot be ignored. Loh and Wainwright…
Quantile regression is a fundamental tool for distributional learning but poses significant optimization challenges for deep models due to the non-smoothness of the pinball loss. We propose ConquerNet, a class of…
The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…
The non-crossing rule for the energy levels of a parameter-dependent Hamiltonian is revisited and a flaw in a commonly accepted proof is revealed. Some aspects of avoided crossings are illustrated by means of simple models. One of them…
I argue that regularizing terms in standard regression methods not only help against overfitting finite data, but sometimes also yield better causal models in the infinite sample regime. I first consider a multi-dimensional variable…
Convolutional Neural Networks (CNNs) have recently emerged as the dominant model in computer vision. If provided with enough training data, they predict almost any visual quantity. In a discrete setting, such as classification, CNNs are not…
In this paper, for Lasso penalized linear regression models in high-dimensional settings, we propose a modified cross-validation method for selecting the penalty parameter. The methodology is extended to other penalties, such as Elastic…
We study the problem of modeling univariate distributions via their quantile functions. We introduce a flexible family of distributions whose quantile function is a linear combination of basis quantiles. Because the model is linear in its…
The paper considers a linear regression model in high-dimension for which the predictive variables can change the influence on the response variable at unknown times (called change-points). Moreover, the particular case of the heavy-tailed…
Conformalized Quantile Regression (CQR) is a recently proposed method for constructing prediction intervals for a response $Y$ given covariates $X$, without making distributional assumptions. However, existing constructions of CQR can be…
We present new large-scale algorithms for fitting a subgradient regularized multivariate convex regression function to $n$ samples in $d$ dimensions -- a key problem in shape constrained nonparametric regression with applications in…