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Tree-based models are used in many high-stakes application domains such as finance and medicine, where robustness and interpretability are of utmost importance. Yet, methods for improving and certifying their robustness are severely…

Machine Learning · Computer Science 2022-11-16 Miklós Z. Horváth , Mark Niklas Müller , Marc Fischer , Martin Vechev

We introduce a new nonparametric density estimator inspired by Markov Chains, and generalizing the well-known Kernel Density Estimator (KDE). Our estimator presents several benefits with respect to the usual ones and can be used…

Methodology · Statistics 2020-09-15 Andrea De Simone , Alessandro Morandini

Kernel density estimation on a finite interval poses an outstanding challenge because of the well-recognized bias at the boundaries of the interval. Motivated by an application in cancer research, we consider a boundary constraint linking…

Statistics Theory · Mathematics 2020-12-01 Matthew J. Colbrook , Zdravko I. Botev , Karsten Kuritz , Shev MacNamara

Real-world large-scale datasets are heteroskedastic and imbalanced -- labels have varying levels of uncertainty and label distributions are long-tailed. Heteroskedasticity and imbalance challenge deep learning algorithms due to the…

Machine Learning · Computer Science 2021-03-19 Kaidi Cao , Yining Chen , Junwei Lu , Nikos Arechiga , Adrien Gaidon , Tengyu Ma

We propose statistical inferential procedures for panel data models with interactive fixed effects in a kernel ridge regression framework.Compared with traditional sieve methods, our method is automatic in the sense that it does not require…

Statistics Theory · Mathematics 2017-03-10 Shunan Zhao , Ruiqi Liu , Zuofeng Shang

In modern classification tasks, the number of labels is getting larger and larger, as is the size of the datasets encountered in practice. As the number of classes increases, class ambiguity and class imbalance become more and more…

Machine Learning · Statistics 2022-07-19 Camille Garcin , Maximilien Servajean , Alexis Joly , Joseph Salmon

Given a set of points $P\subset \mathbb{R}^{d}$ and a kernel $k$, the Kernel Density Estimate at a point $x\in\mathbb{R}^{d}$ is defined as $\mathrm{KDE}_{P}(x)=\frac{1}{|P|}\sum_{y\in P} k(x,y)$. We study the problem of designing a data…

Data Structures and Algorithms · Computer Science 2018-09-03 Moses Charikar , Paris Siminelakis

We present several generative and predictive algorithms based on the RKHS (reproducing kernel Hilbert spaces) methodology, which, most importantly, are scale up efficiently with large datasets or high-dimensional data. It is well recognized…

Numerical Analysis · Mathematics 2024-12-12 Philippe G. LeFloch , Jean-Marc Mercier , Shohruh Miryusupov

This paper studies the use of kernel density estimation (KDE) for linear algebraic tasks involving the kernel matrix of a collection of $n$ data points in $\mathbb R^d$. In particular, we improve upon existing algorithms for computing the…

Data Structures and Algorithms · Computer Science 2026-03-05 Rikhav Shah , Sandeep Silwal , Haike Xu

Ensemble learning has proven effective in improving predictive performance and estimating uncertainty in neural networks. However, conventional ensemble methods often suffer from redundant parameter usage and computational inefficiencies…

Machine Learning · Computer Science 2024-12-23 Arnav Kharbanda , Advait Chandorkar

We present a novel approach for the problem of frequency estimation in data streams that is based on optimization and machine learning. Contrary to state-of-the-art streaming frequency estimation algorithms, which heavily rely on random…

Data Structures and Algorithms · Computer Science 2022-07-19 Dimitris Bertsimas , Vassilis Digalakis

The paper considers nonparametric kernel density/regression estimation from a stochastic optimization point of view. The estimation problem is represented through a family of stochastic optimization problems. Recursive constrained…

Statistics Theory · Mathematics 2024-09-05 Vladimir Norkin , Vladimir Kirilyuk

In this paper, we develop a new sequential regression modeling approach for data streams. Data streams are commonly found around us, e.g in a retail enterprise sales data is continuously collected every day. A demand forecasting model is an…

Machine Learning · Statistics 2017-01-11 Chitta Ranjan , Samaneh Ebrahimi , Kamran Paynabar

In single-cell research, tracing and analyzing high-throughput single-cell differentiation trajectories is crucial for understanding biological processes. Key to this is the robust modeling of hierarchical structures that govern cellular…

Machine Learning · Computer Science 2026-05-19 Zelin Zang , WenZhe Li , Yongjie Xu , Chang Yu , Changxi Chi , Jingbo Zhou , Zhen Lei , Stan Z. Li

Tree-based ensemble methods, as Random Forests and Gradient Boosted Trees, have been successfully used for regression in many applications and research studies. Furthermore, these methods have been extended in order to deal with uncertainty…

Machine Learning · Computer Science 2018-11-20 Myriam Tami , Marianne Clausel , Emilie Devijver , Adrien Dulac , Eric Gaussier , Stefan Janaqi , Meriam Chebre

Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time.…

Machine Learning · Statistics 2021-11-05 Cristopher Salvi , Maud Lemercier , Chong Liu , Blanka Hovarth , Theodoros Damoulas , Terry Lyons

We extend the herding algorithm to continuous spaces by using the kernel trick. The resulting "kernel herding" algorithm is an infinite memory deterministic process that learns to approximate a PDF with a collection of samples. We show that…

Machine Learning · Computer Science 2012-03-19 Yutian Chen , Max Welling , Alex Smola

We consider a distributed learning approach in supervised learning for a large class of spectral regularization methods in an RKHS framework. The data set of size n is partitioned into $m=O(n^\alpha)$ disjoint subsets. On each subset, some…

Statistics Theory · Mathematics 2017-08-10 Gilles Blanchard , Nicole Mücke

We propose a flexible method for estimating luminosity functions (LFs) based on kernel density estimation (KDE), the most popular nonparametric density estimation approach developed in modern statistics, to overcome issues surrounding…

Methodology · Statistics 2020-05-01 Zunli Yuan , Matt J. Jarvis , Jiancheng Wang

This paper investigates the convergence properties of spectral algorithms -- a class of regularization methods originating from inverse problems -- under covariate shift. In this setting, the marginal distributions of inputs differ between…

Machine Learning · Statistics 2025-09-08 Ren-Rui Liu , Zheng-Chu Guo