Related papers: Monotonicity preservation properties of kernel reg…
This paper considers extensions of minimum-disparity estimators to the problem of estimating parameters in a regression model that is conditionally specified; that is where a parametric model describes the distribution of a response $y$…
Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to…
Several variations of the Watterson estimator of variability for Next Generation Sequencing (NGS) data have been proposed in the literature. We present a unified framework for generalized Watterson estimators based on Maximum Composite…
The aim of the present work is a comparative study of different persistence kernels applied to various classification problems. After some necessary preliminaries on homology and persistence diagrams, we introduce five different kernels…
In the regression model $Y = b(X) +\sigma(X)\varepsilon$, where $X$ has a density $f$, this paper deals with an oracle inequality for an estimator of $bf$, involving a kernel in the sense of Lerasle et al. (2016), selected via the PCO…
Topological data analysis is an emerging mathematical concept for characterizing shapes in multi-scale data. In this field, persistence diagrams are widely used as a descriptor of the input data, and can distinguish robust and noisy…
This paper studies the consistency of the kernel-based neural ranking model K-NRM, a recent state-of-the-art neural IR model, which is important for reproducible research and deployment in the industry. We find that K-NRM has low variance…
The property of learning-curve monotonicity, highlighted in a recent series of work by Loog, Mey and Viering, describes algorithms which only improve in average performance given more data, for any underlying data distribution within a…
In regression problems where covariates are naturally organized in a hierarchical tree structure, a central challenge is to select the resolution at which covariates enter the model. Determining this level of feature aggregation is of…
Three important properties of a classification machinery are: (i) the system preserves the core information of the input data; (ii) the training examples convey information about unseen data; and (iii) the system is able to treat…
In this article, basing on NQD samples, we investigate the fixed design nonparametric regression model, where the errors are pairwise NQD random errors, with fixed design points, and an unknown function. Nonparametric weighted estimator…
Topological data analysis (TDA) is an emerging mathematical concept for characterizing shapes in complex data. In TDA, persistence diagrams are widely recognized as a useful descriptor of data, and can distinguish robust and noisy…
Given an i.i.d sample $(Y_i,Z_i)$, taking values in $\RRR^{d'}\times \RRR^d$, we consider a collection Nadarya-Watson kernel estimators of the conditional expectations $\EEE(<c_g(z),g(Y)>+d_g(z)\mid Z=z)$, where $z$ belongs to a compact set…
Monotone operator equilibrium networks are implicit-layer models whose output is the unique equilibrium of a monotone operator, guaranteeing existence, uniqueness, and convergence. When deployed on low-precision hardware, weights are…
Quantum one-class support vector machines leverage the advantage of quantum kernel methods for semi-supervised anomaly detection. However, their quadratic time complexity with respect to data size poses challenges when dealing with large…
We adress the problem of consistency of the $k$-nearest neighbors kernel estimators of the density and the regression function in the multivariate case. We get the rates of strong uniform consistency on the whole space $\mathbb{R}^p$ for…
The Kaplan--Meier (KM) estimator, which provides a nonparametric estimate of a survival function for time-to-event data, has wide application in clinical studies, engineering, economics and other fields. The theoretical properties of the KM…
We develop an adaptive monotone shrinkage estimator for regression models with the following characteristics: i) dense coefficients with small but important effects; ii) a priori ordering that indicates the probable predictive importance of…
We study nonparametric regression and classification for path-valued data. We introduce a functional Nadaraya-Watson estimator that combines the signature transform from rough path theory with local kernel regression. The signature…
There has been a surge of interest in developing robust estimators for models with heavy-tailed and bounded variance data in statistics and machine learning, while few works impose unbounded variance. This paper proposes two type of robust…