Related papers: On the Consistency of Ordinal Regression Methods

SARAH and SPIDER are two recently developed stochastic variance-reduced algorithms, and SPIDER has been shown to achieve a near-optimal first-order oracle complexity in smooth nonconvex optimization. However, SPIDER uses an…

Gradient-free optimization methods, such as surrogate based optimization (SBO) methods, and genetic (GAs), or evolutionary (EAs) algorithms have gained popularity in the field of constrained optimization of expensive black-box functions.…

Surrogate risk minimization is an ubiquitous paradigm in supervised machine learning, wherein a target problem is solved by minimizing a surrogate loss on a dataset. Surrogate regret bounds, also called excess risk bounds, are a common tool…

In networked dynamical systems, inferring governing parameters is crucial for predicting nodal dynamics, such as gene expression levels, species abundance, or population density. While many parameter estimation techniques rely on…

Machine learning has demonstrated remarkable performance over finite datasets, yet whether the scores over the fixed benchmarks can sufficiently indicate the model's performance in the real world is still in discussion. In reality, an ideal…

In this article we investigate consistency of selection in regression models via the popular Lasso method. Here we depart from the traditional linear regression assumption and consider approximations of the regression function $f$ with…

This article introduces a subbagging (subsample aggregating) approach for variable selection in regression within the context of big data. The proposed subbagging approach not only ensures that variable selection is scalable given the…

Semi-supervised ordinal regression (S$^2$OR) problems are ubiquitous in real-world applications, where only a few ordered instances are labeled and massive instances remain unlabeled. Recent researches have shown that directly optimizing…

Fisher-consistent loss functions play a fundamental role in the construction of successful binary margin-based classifiers. In this paper we establish the Fisher-consistency condition for multicategory classification problems. Our approach…

It is often desired that ordinal regression models yield unimodal predictions. However, in many recent works this characteristic is either absent, or implemented using soft targets, which do not guarantee unimodal outputs at inference. In…

We consider the problem of fitting variational posterior approximations using stochastic optimization methods. The performance of these approximations depends on (1) how well the variational family matches the true posterior…

In empirical risk optimization, it has been observed that stochastic gradient implementations that rely on random reshuffling of the data achieve better performance than implementations that rely on sampling the data uniformly. Recent works…

Majorization-minimization algorithms consist of successively minimizing a sequence of upper bounds of the objective function. These upper bounds are tight at the current estimate, and each iteration monotonically drives the objective…

Functional linear regression is a widely used approach to model functional responses with respect to functional inputs. However, classical functional linear regression models can be severely affected by outliers. We therefore introduce a…

We give the first mathematically rigorous analysis of an emerging approach to finite element analysis (see, e.g., Bauer et al. [Appl. Numer. Math., 2017]), which we hereby refer to as the surrogate matrix methodology. This methodology is…

The problem of determining the achievable sensitivity with digitization exhibiting minimal complexity is addressed. In this case, measurements are exclusively available in hard-limited form. Assessing the achievable sensitivity via the…

While matrix variate regression models have been studied in many existing works, classical statistical and computational methods for the analysis of the regression coefficient estimation are highly affected by high dimensional and noisy…

We consider a distributionally robust formulation of stochastic optimization problems arising in statistical learning, where robustness is with respect to uncertainty in the underlying data distribution. Our formulation builds on…

The $F_\beta$ score is a commonly used measure of classification performance, which plays crucial roles in classification tasks with imbalanced data sets. However, the $F_\beta$ score cannot be used as a loss function by gradient-based…

Ordinal regression predicts the objects' labels that exhibit a natural ordering, which is important to many managerial problems such as credit scoring and clinical diagnosis. In these problems, the ability to explain how the attributes…