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Motivated by models for multiway comparison data, we consider the problem of estimating a coordinate-wise isotonic function on the domain $[0, 1]^d$ from noisy observations collected on a uniform lattice, but where the design points have…
Variance parameter estimation in linear mixed models is a challenge for many classical nonlinear optimization algorithms due to the positive-definiteness constraint of the random effects covariance matrix. We take a completely novel view on…
Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…
Generalized alternating projections is an algorithm that alternates relaxed projections onto a finite number of sets to find a point in their intersection. We consider the special case of two linear subspaces, for which the algorithm…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
We present an alternative way to determine the unknown parameter associated to a gaussian approximation in a generic two-dimensional model. Instead of the standard variational approach, we propose a procedure based on a quantitative…
Many applications, including rank aggregation, crowd-labeling, and graphon estimation, can be modeled in terms of a bivariate isotonic matrix with unknown permutations acting on its rows and/or columns. We consider the problem of estimating…
Linear regression without correspondences is the problem of performing a linear regression fit to a dataset for which the correspondences between the independent samples and the observations are unknown. Such a problem naturally arises in…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
This work focuses on developing and motivating a stochastic version of a wellknown inverse problem methodology. Specifically, we consider the iteratively regularized Gauss-Newton method, originally proposed by Bakushinskii for…
In this paper, we examine a geometrical projection algorithm for statistical inference. The algorithm is based on Pythagorean relation and it is derivative-free as well as representation-free that is useful in nonparametric cases. We derive…
The generalized least square (GLS) is one of the most basic tools in regression analyses. A major issue in implementing the GLS is estimation of the conditional variance function of the error term, which typically requires a restrictive…
This paper studies how to capture dependency graph structures from real data which may not be Gaussian. Starting from marginal loss functions not necessarily derived from probability distributions, we utilize an additive…
This paper presents a novel online identification algorithm for nonlinear regression models. The online identification problem is challenging due to the presence of nonlinear structure in the models. Previous works usually ignore the…
Modern statistical applications often involve minimizing an objective function that may be nonsmooth and/or nonconvex. This paper focuses on a broad Bregman-surrogate algorithm framework including the local linear approximation, mirror…
Logistic regression is a well-known statistical model which is commonly used in the situation where the output is a binary random variable. It has a wide range of applications including machine learning, public health, social sciences,…
Rank regression offers robustness to outliers and heavy-tailed response distributions, invariance to monotonic transformations, and improved efficiency under non-Gaussian errors, making it a versatile tool for analyzing complex data. This…
Regression models with both high-dimensional responses and covariates have attracted growing attention. Standard multivariate regression models become inadequate when the response variables depend not only on observed covariates but also on…
The paper introduces a new estimation method for the standard linear regression model. The procedure is not driven by the optimisation of any objective function rather, it is a simple weighted average of slopes from observation pairs. The…