Related papers: Piecewise Linear Regression via a Difference of Co…
In some applications, one is interested in reconstructing a function $f$ from its Fourier series coefficients. The problem is that the Fourier series is slowly convergent if the function is non-periodic, or is non-smooth. In this paper, we…
Convex regression is a method for estimating the convex function from a data set. This method has played an important role in operations research, economics, machine learning, and many other areas. However, it has been empirically observed…
This paper proposes a regularized pairwise difference approach for estimating the linear component coefficient in a partially linear model, with consistency and exact rates of convergence obtained in high dimensions under mild scaling…
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…
The functional linear model is an important extension of the classical regression model allowing for scalar responses to be modeled as functions of stochastic processes. Yet, despite the usefulness and popularity of the functional linear…
Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…
This paper proposes a method for solving multivariate regression and classification problems using piecewise linear predictors over a polyhedral partition of the feature space. The resulting algorithm that we call PARC (Piecewise Affine…
This paper presents a Gaussian process (GP) model for estimating piecewise continuous regression functions. In scientific and engineering applications of regression analysis, the underlying regression functions are piecewise continuous in…
We derive an exact and efficient Bayesian regression algorithm for piecewise constant functions of unknown segment number, boundary location, and levels. It works for any noise and segment level prior, e.g. Cauchy which can handle outliers.…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
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…
This paper studies a \textit{partial functional partially linear single-index model} that consists of a functional linear component as well as a linear single-index component. This model generalizes many well-known existing models and is…
A sequential piecewise linear programming method is presented where bounded domains of non-convex functions are successively contracted about the solution of a piecewise linear program at each iteration of the algorithm. Although…
We consider a difference-of-convex formulation where one of the terms is allowed to be hypoconvex (or weakly convex). We first examine the precise behavior of a single iteration of the Difference-of-Convex algorithm (DCA), giving a tight…
We consider the estimation of the slope function in functional linear regression, where scalar responses are modeled in dependence of random functions. Cardot and Johannes [J. Multivariate Anal. 101 (2010) 395-408] have shown that a…
Function plays an important role in mathematics and many science branches. As the fast development of computer technology, more and more study on computational function analysis, e.g., Fast Fourier Transform, Wavelet Transform, Curve…
The complex nature of lithium-ion battery degradation has led to many machine learning based approaches to health forecasting being proposed in literature. However, machine learning can be computationally intensive. Linear approaches are…
We propose an $L_{2}$-based penalization algorithm for functional linear regression models, where the coefficient function is shrunk towards a data-driven shape template $\gamma$, which is constrained to belong to a class of piecewise…
We analyze the meta-learning of the initialization and step-size of learning algorithms for piecewise-Lipschitz functions, a non-convex setting with applications to both machine learning and algorithms. Starting from recent regret bounds…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…