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Related papers: Brenier Isotonic Regression

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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…

Statistics Theory · Mathematics 2023-11-21 Soham Mallick , Siddhaarth Sarkar , Arun Kumar Kuchibhotla

This manuscript bridges nonparametric smoothness-based and shape-restricted estimation, which may appear as two disjoint paradigms in the field. The proposed approach is motivated by a conceptually simple observation: every Lipschitz…

Methodology · Statistics 2026-05-22 Kenta Takatsu , Tianyu Zhang , Arun Kumar Kuchibhotla

In this paper, we investigate a constrained formulation of neural networks where the output is a convex function of the input. We show that the convexity constraints can be enforced on both fully connected and convolutional layers, making…

Machine Learning · Computer Science 2021-07-13 Sarath Sivaprasad , Ankur Singh , Naresh Manwani , Vineet Gandhi

We present a computational and statistical approach for fitting isotonic models under convex differentiable loss functions. We offer a recursive partitioning algorithm which provably and efficiently solves isotonic regression under any such…

Methodology · Statistics 2012-10-09 Ronny Luss , Saharon Rosset

We study the non-parametric isotonic regression problem for bivariate elicitable functionals that are given as an elicitable univariate functional and its Bayes risk. Prominent examples for functionals of this type are (mean, variance) and…

Statistics Theory · Mathematics 2021-06-30 Anja Mühlemann , Johanna F. Ziegel

We consider the problem of constructing confidence intervals (CIs) for a linear functional of a regression function, such as its value at a point, the regression discontinuity parameter, or a regression coefficient in a linear or partly…

Statistics Theory · Mathematics 2018-04-03 Timothy B. Armstrong , Michal Kolesár

Given a directed acyclic graph $G,$ and a set of values $y$ on the vertices, the Isotonic Regression of $y$ is a vector $x$ that respects the partial order described by $G,$ and minimizes $||x-y||,$ for a specified norm. This paper gives…

Machine Learning · Computer Science 2015-11-12 Rasmus Kyng , Anup Rao , Sushant Sachdeva

This paper deals with estimation with functional covariates. More precisely, we aim at estimating the regression function $m$ of a continuous outcome $Y$ against a standard Wiener coprocess $W$. Following Cadre and Truquet (2015) and Cadre,…

Statistics Theory · Mathematics 2020-11-23 Karine Bertin , Nicolas Klutchnikoff

The ill-posedness of the inverse problem of recovering a regression function in a nonparametric instrumental variable model leads to estimators that may suffer from a very slow, logarithmic rate of convergence. In this paper, we show that…

Applications · Statistics 2017-09-27 Denis Chetverikov , Daniel Wilhelm

Learning accurate probabilistic models from data is crucial in many practical tasks in data mining. In this paper we present a new non-parametric calibration method called \textit{ensemble of near isotonic regression} (ENIR). The method can…

Machine Learning · Computer Science 2015-11-18 Mahdi Pakdaman Naeini , Gregory F. Cooper

The Conway-Maxwell-Poisson (CMP) or COM-Poison regression is a popular model for count data due to its ability to capture both under dispersion and over dispersion. However, CMP regression is limited when dealing with complex nonlinear…

Methodology · Statistics 2020-04-27 Suneel Babu Chatla , Galit Shmueli

In general, the solution to a regression problem is the minimizer of a given loss criterion, and depends on the specified loss function. The nonparametric isotonic regression problem is special, in that optimal solutions can be found by…

Statistics Theory · Mathematics 2020-05-06 Alexander I. Jordan , Anja Mühlemann , Johanna F. Ziegel

Real-world machine learning applications may require functions that are fast-to-evaluate and interpretable. In particular, guaranteed monotonicity of the learned function can be critical to user trust. We propose meeting these goals for…

We provide an inference procedure for the sharp regression discontinuity design (RDD) under monotonicity, with possibly multiple running variables. Specifically, we consider the case where the true regression function is monotone with…

Econometrics · Economics 2020-12-01 Koohyun Kwon , Soonwoo Kwon

We study the isotonic regression estimator over a general countable pre-ordered set. We obtain the limiting distribution of the estimator and study its properties. It is proved that, under some general assumptions, the limiting distribution…

Statistics Theory · Mathematics 2018-11-06 Dragi Anevski , Vladimir Pastukhov

We investigate the calibration of estimations to increase performance with an optimal monotone transform on the estimator outputs. We start by studying the traditional square error setting with its weighted variant and show that the optimal…

Machine Learning · Computer Science 2021-11-02 Kaan Gokcesu , Hakan Gokcesu

We study the problem of estimating piecewise monotone vectors. This problem can be seen as a generalization of the isotonic regression that allows a small number of order-violating changepoints. We focus mainly on the performance of the…

Statistics Theory · Mathematics 2020-03-10 Kentaro Minami

The gradients of convex functions are expressive models of non-trivial vector fields. For example, Brenier's theorem yields that the optimal transport map between any two measures on Euclidean space under the squared distance is realized as…

Machine Learning · Computer Science 2021-11-25 Jack Richter-Powell , Jonathan Lorraine , Brandon Amos

Regression analysis under the assumption of monotonicity is a well-studied statistical problem and has been used in a wide range of applications. However, there remains a lack of a broadly applicable methodology that permits information…

Methodology · Statistics 2023-05-30 Christian Rohrbeck , Deborah A Costain

Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…

Numerical Analysis · Mathematics 2025-06-24 Chai Wah Wu , Mark S. Squillante , Vasileios Kalantzis , Lior Horesh