Related papers: Approximation, characterization, and continuity of…

In many problems, a sensible estimator of a possibly multivariate monotone function may itself fail to be monotone. We study the correction of such an estimator obtained via projection onto the space of functions monotone over a finite grid…

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 study the problem of estimating a monotone function $f:\{0,1\}^d\to[0,1]$ from noisy observations at uniformly random vertices of the Boolean hypercube. As a measure of complexity for the target~$f$, we use the total $L^1$-influence…

These notes are about ridge functions. Recent years have witnessed a flurry of interest in these functions. Ridge functions appear in various fields and under various guises. They appear in fields as diverse as partial differential…

Suppose that we observe independent random pairs $(X_1,Y_1)$, $(X_2,Y_2)$, >..., $(X_n,Y_n)$. Our goal is to estimate regression functions such as the conditional mean or $\beta$--quantile of $Y$ given $X$, where $0<\beta <1$. In order to…

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 provide quantitative and abstract strong convergence results for sequences from a compact metric space satisfying a certain form of \emph{generalized Fej\'er monotonicity} where (1) the metric can be replaced by a much more general type…

We consider a misspecified optimization problem that requires minimizing a function f(x;q*) over a closed and convex set X where q* is an unknown vector of parameters that may be learnt by a parallel learning process. In this context, We…

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…

This paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions, also known as the quantile crossing problem. The method consists in sorting or monotone…

A partial least squares regression is proposed for estimating the function-on-function regression model where a functional response and multiple functional predictors consist of random curves with quadratic and interaction effects. The…

An important tool to quantify the likeness of two probability measures are f-divergences, which have seen widespread application in statistics and information theory. An example is the total variation, which plays an exceptional role among…

We consider the problem of adaptive inference on a regression function at a point under a multivariate nonparametric regression setting. The regression function belongs to a H\"older class and is assumed to be monotone with respect to some…

First we prove some kernel representations for the covariance of two functions taken on the same random variable and deduce kernel representations for some functionals of a continuous one-dimensional measure. Then we apply these formulas to…

We investigate conditions for logarithmic complete monotonicity of product ratios of gamma and q-gamma functions whose arguments are linear functions of the variable. We give necessary and sufficient conditions in terms of nonnegativity of…

The probabilistic satisfiability of a logical expression is a fundamental concept known as the partition function in statistical physics and field theory, an evaluation of a related graph's Tutte polynomial in mathematics, and the…

We consider the problem of deriving uniform confidence bands for the mean of a monotonic stochastic process, such as the cumulative distribution function (CDF) of a random variable, based on a sequence of i.i.d.~observations. Our approach…

We study the fundamental problem of fixed design {\em multidimensional segmented regression}: Given noisy samples from a function $f$, promised to be piecewise linear on an unknown set of $k$ rectangles, we want to recover $f$ up to a…

A simple method for numerical analytic continuation is developed. It is designed to analytically continue the imaginary time (Matsubara frequency) quantum Monte Carlo simulation results to the real time (real frequency) domain. Such a…

Isotonic regression provides a flexible, tuning-free approach to estimating monotonic functions without imposing global curvature constraints, yet the estimated regression function is inherently a step function. This paper addresses a key…