Related papers: Inference using shape-restricted regression spline…

We propose a novel nonparametric regression method that models complex input-output relationships as the sum of convex and concave components. The method-Identifiable Convex-Concave Nonparametric Least Squares (ICCNLS)-decomposes the target…

This paper develops theoretical results regarding noisy 1-bit compressed sensing and sparse binomial regression. We show that a single convex program gives an accurate estimate of the signal, or coefficient vector, for both of these models.…

A robust and sparse estimator for multinomial regression is proposed for high dimensional data. Robustness of the estimator is achieved by trimming the observations, and sparsity of the estimator is obtained by the elastic net penalty,…

A basis expansion with regularization methods is much appealing to the flexible or robust nonlinear regression models for data with complex structures. When the underlying function has inhomogeneous smoothness, it is well known that…

We extend the adaptive regression spline model by incorporating saturation, the natural requirement that a function extend as a constant outside a certain range. We fit saturating splines to data using a convex optimization problem over a…

We present SplineNets, a practical and novel approach for using conditioning in convolutional neural networks (CNNs). SplineNets are continuous generalizations of neural decision graphs, and they can dramatically reduce runtime complexity…

This paper introduces a novel framework for estimation and inference in penalized M-estimators applied to robust high-dimensional linear regression models. Traditional methods for high-dimensional statistical inference, which predominantly…

In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The…

Statisticians generally use ordinary least squares to minimize the random error in a subject response with respect to independent explanatory variable. However, Wooten shows illustrates how ordinary least squares can be used to minimize the…

We consider efficient estimation of flexible transformation models with interval-censored data. To reduce the dimension of semi-parametric models, the unknown monotone transformation function is approximated via monotone splines. A…

We consider the weighted least squares spline approximation of a noisy dataset. By interpreting the weights as a probability distribution, we maximize the associated entropy subject to the constraint that the mean squared error is…

We consider a variant of regression problem, where the correspondence between input and output data is not available. Such shuffled data is commonly observed in many real world problems. Taking flow cytometry as an example, the measuring…

We consider spline estimates which preserve prescribed piecewise convex properties of the unknown function. A robust version of the penalized likelihood is given and shown to correspond to a variable halfwidth kernel smoother where the…

Informed learning is an emerging field in machine learning that aims to compensate for insufficient data with prior knowledge. Shape knowledge covers many types of prior knowledge concerning the relationship of a function's output with…

$\ell_1$-penalized quantile regression is widely used for analyzing high-dimensional data with heterogeneity. It is now recognized that the $\ell_1$-penalty introduces non-negligible estimation bias, while a proper use of concave…

In this work we consider numerical efficiency and convergence rates for solvers of non-convex multi-penalty formulations when reconstructing sparse signals from noisy linear measurements. We extend an existing approach, based on reduction…

We propose a unified framework for likelihood-based regression modeling when the response variable has finite support. Our work is motivated by the fact that, in practice, observed data are discrete and bounded. The proposed methods assume…

Continuous signal representations are naturally suited for inverse problems, such as magnetic resonance imaging (MRI) and computed tomography, because the measurements depend on an underlying physically continuous signal. While classical…

Nonparametric regression problems with qualitative constraints such as monotonicity or convexity are ubiquitous in applications. For example, in predicting the yield of a factory in terms of the number of labor hours, the monotonicity of…

We consider estimating a compact set from finite data by approximating the support function of that set via sublinear regression. Support functions uniquely characterize a compact set up to closure of convexification, and are sublinear…