Related papers: Robust Kernel Density Estimation with Median-of-Means principle

Robust Kernel Density Estimation with Median-of-Means principle

URL: http://arxiv.org/abs/2006.16590v1
Date: Tue, 30 Jun 2020 08:01:07 GMT
Title: Robust Kernel Density Estimation with Median-of-Means principle
Authors: Pierre Humbert (ENS Paris Saclay), Batiste Le Bars (ENS Paris Saclay), Ludovic Minvielle (ENS Paris Saclay), Nicolas Vayatis (ENS Paris Saclay)
Abstract summary: We introduce a robust nonparametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE) This estimator is shown to achieve robustness to any kind of anomalous data, even in the case of adversarial contamination.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: In this paper, we introduce a robust nonparametric density estimator combining the popular Kernel Density Estimation method and the Median-of-Means principle (MoM-KDE). This estimator is shown to achieve robustness to any kind of anomalous data, even in the case of adversarial contamination. In particular, while previous works only prove consistency results under known contamination model, this work provides finite-sample high-probability error-bounds without a priori knowledge on the outliers. Finally, when compared with other robust kernel estimators, we show that MoM-KDE achieves competitive results while having significant lower computational complexity.

Related papers

Robust Multi-Modal Density Estimation [14.643918024937758]
ROME (RObust Multi-modal Estimator) is a non-parametric approach for density estimation. We show that ROME can overcome the issues of over-fitting and over-smoothing exhibited by other estimators.
arXiv Detail & Related papers (2024-01-19T09:10:58Z)
Sobolev Space Regularised Pre Density Models [51.558848491038916]
We propose a new approach to non-parametric density estimation that is based on regularizing a Sobolev norm of the density. This method is statistically consistent, and makes the inductive validation model clear and consistent.
arXiv Detail & Related papers (2023-07-25T18:47:53Z)
Targeted Separation and Convergence with Kernel Discrepancies [61.973643031360254]
kernel-based discrepancy measures are required to (i) separate a target P from other probability measures or (ii) control weak convergence to P. In this article we derive new sufficient and necessary conditions to ensure (i) and (ii) For MMDs on separable metric spaces, we characterize those kernels that separate Bochner embeddable measures and introduce simple conditions for separating all measures with unbounded kernels.
arXiv Detail & Related papers (2022-09-26T16:41:16Z)
Evaluating the Adversarial Robustness for Fourier Neural Operators [78.36413169647408]
Fourier Neural Operator (FNO) was the first to simulate turbulent flow with zero-shot super-resolution. We generate adversarial examples for FNO based on norm-bounded data input perturbations. Our results show that the model's robustness degrades rapidly with increasing perturbation levels.
arXiv Detail & Related papers (2022-04-08T19:19:42Z)
TAKDE: Temporal Adaptive Kernel Density Estimator for Real-Time Dynamic Density Estimation [16.45003200150227]
We name the temporal adaptive kernel density estimator (TAKDE) TAKDE is theoretically optimal in terms of the worst-case AMISE. We provide numerical experiments using synthetic and real-world datasets, showing that TAKDE outperforms other state-of-the-art dynamic density estimators.
arXiv Detail & Related papers (2022-03-15T23:38:32Z)
Learning to Estimate Without Bias [57.82628598276623]
Gauss theorem states that the weighted least squares estimator is a linear minimum variance unbiased estimation (MVUE) in linear models. In this paper, we take a first step towards extending this result to non linear settings via deep learning with bias constraints. A second motivation to BCE is in applications where multiple estimates of the same unknown are averaged for improved performance.
arXiv Detail & Related papers (2021-10-24T10:23:51Z)
Kernel Mean Estimation by Marginalized Corrupted Distributions [96.9272743070371]
Estimating the kernel mean in a kernel Hilbert space is a critical component in many kernel learning algorithms. We present a new kernel mean estimator, called the marginalized kernel mean estimator, which estimates kernel mean under the corrupted distribution.
arXiv Detail & Related papers (2021-07-10T15:11:28Z)
Improved Estimation of Concentration Under $\ell_p$-Norm Distance Metrics Using Half Spaces [14.947511752748005]
Concentration of measure has been argued to be the fundamental cause of adversarial vulnerability. We propose a method to estimate the concentration of any empirical dataset under $ell_p$-norm distance metrics. Our proposed algorithm is more efficient than Mahloujifar et al.'s, and our experiments on synthetic datasets and image benchmarks demonstrate that it is able to find much tighter intrinsic robustness bounds.
arXiv Detail & Related papers (2021-03-24T01:16:28Z)
Nonparametric Density Estimation from Markov Chains [68.8204255655161]
We introduce a new nonparametric density estimator inspired by Markov Chains, and generalizing the well-known Kernel Density Estor. Our estimator presents several benefits with respect to the usual ones and can be used straightforwardly as a foundation in all density-based algorithms.
arXiv Detail & Related papers (2020-09-08T18:33:42Z)
Generalization Bounds in the Presence of Outliers: a Median-of-Means Study [8.905677748354364]
The Median-of-Means (MoM) is an estimator of the mean $theta$ of a square integrable r.v. $Z$. Thanks to the high confidence it achieves on heavy-tailed data, MoM has found various applications in machine learning. A new line of work is now trying to characterize and leverage MoM's ability to deal with corrupted data.
arXiv Detail & Related papers (2020-06-09T13:21:39Z)

This list is automatically generated from the titles and abstracts of the papers in this site.