Cellwise Outliers

• URL: http://arxiv.org/abs/2604.14182v1
• Date: Tue, 31 Mar 2026 10:36:09 GMT
• Title: Cellwise Outliers
• Abstract summary: In statistics and machine learning, the traditional meaning of the terms outlier' and anomaly' is a case in the dataset that behaves differently from the bulk of the data.<n>But nowadays increasing attention is being paid to so-called cellwise outliers.<n>It turns out that detecting cellwise outliers as well as constructing cellwise robust methods requires techniques that are quite different from the casewise setting.
• Score: 0.8029049649310211
• License: http://creativecommons.org/publicdomain/zero/1.0/
• Abstract: In statistics and machine learning, the traditional meaning of the terms `outlier' and `anomaly' is a case in the dataset that behaves differently from the bulk of the data. This raises suspicion that it may belong to a different population. But nowadays increasing attention is being paid to so-called cellwise outliers. These are individual values somewhere in the data matrix (or data tensor). Depending on the dimension, even a relatively small proportion of outlying cells can contaminate over half the cases, which is a problem for existing casewise methods. It turns out that detecting cellwise outliers as well as constructing cellwise robust methods requires techniques that are quite different from the casewise setting. For instance, one has to let go of some intuitive equivariance properties. The problem is difficult, but the past decade has seen substantial progress. For high-dimensional data the cellwise approach is becoming dominant, and typically can deal with missing values as well. We review developments in the estimation of location and covariance matrices as well as regression methods, principal component analysis, methods for tensor data, and various other settings.

Related papers

• Cellwise and Casewise Robust Covariance in High Dimensions [0.0]
  The cellRCov method simultaneously handles casewise outliers, cellwise outliers, and missing data.<n>A simulation study demonstrates the superior performance of cellRCov in contaminated and missing data scenarios.<n>We also construct and illustrate the cellRCCA method for robust and regularized canonical correlation analysis.
  arXiv  Detail & Related papers  (2025-05-26T12:46:44Z)
• Robust Multilinear Principal Component Analysis [0.0]
  Multilinear Principal Component Analysis (MPCA) is an important tool for analyzing tensor data.<n>Standard MPCA is sensitive to outliers.<n>This paper introduces a novel robust MPCA method that can handle both types of outliers simultaneously.
  arXiv  Detail & Related papers  (2025-03-10T13:41:03Z)
• Implicit Manifold Gaussian Process Regression [49.0787777751317]
  Gaussian process regression is widely used to provide well-calibrated uncertainty estimates. It struggles with high-dimensional data because of the implicit low-dimensional manifold upon which the data actually lies. In this paper we propose a technique capable of inferring implicit structure directly from data (labeled and unlabeled) in a fully differentiable way.
  arXiv  Detail & Related papers  (2023-10-30T09:52:48Z)
• The Cellwise Minimum Covariance Determinant Estimator [1.90365714903665]
  We propose a cellwise robust version of the MCD method, called cellMCD. It performs well in simulations with cellwise outliers, and has high finite-sample efficiency on clean data. It is illustrated with real data with visualizations of the results.
  arXiv  Detail & Related papers  (2022-07-27T12:33:51Z)
• On the Strong Correlation Between Model Invariance and Generalization [54.812786542023325]
  Generalization captures a model's ability to classify unseen data. Invariance measures consistency of model predictions on transformations of the data. From a dataset-centric view, we find a certain model's accuracy and invariance linearly correlated on different test sets.
  arXiv  Detail & Related papers  (2022-07-14T17:08:25Z)
• Equivariance Discovery by Learned Parameter-Sharing [153.41877129746223]
  We study how to discover interpretable equivariances from data. Specifically, we formulate this discovery process as an optimization problem over a model's parameter-sharing schemes. Also, we theoretically analyze the method for Gaussian data and provide a bound on the mean squared gap between the studied discovery scheme and the oracle scheme.
  arXiv  Detail & Related papers  (2022-04-07T17:59:19Z)
• Manifold Hypothesis in Data Analysis: Double Geometrically-Probabilistic Approach to Manifold Dimension Estimation [92.81218653234669]
  We present new approach to manifold hypothesis checking and underlying manifold dimension estimation. Our geometrical method is a modification for sparse data of a well-known box-counting algorithm for Minkowski dimension calculation. Experiments on real datasets show that the suggested approach based on two methods combination is powerful and effective.
  arXiv  Detail & Related papers  (2021-07-08T15:35:54Z)
• Scalable Marginal Likelihood Estimation for Model Selection in Deep Learning [78.83598532168256]
  Marginal-likelihood based model-selection is rarely used in deep learning due to estimation difficulties. Our work shows that marginal likelihoods can improve generalization and be useful when validation data is unavailable.
  arXiv  Detail & Related papers  (2021-04-11T09:50:24Z)
• Missing Value Imputation on Multidimensional Time Series [16.709162372224355]
  We present DeepMVI, a deep learning method for missing value imputation in multidimensional time-series datasets. DeepMVI combines fine-grained and coarse-grained patterns along a time series, and trends from related series across categorical dimensions. Experiments show that DeepMVI is significantly more accurate, reducing error by more than 50% in more than half the cases.
  arXiv  Detail & Related papers  (2021-03-02T09:55:05Z)
• What causes the test error? Going beyond bias-variance via ANOVA [21.359033212191218]
  Modern machine learning methods are often overparametrized, allowing adaptation to the data at a fine level. Recent work aimed to understand in greater depth why overparametrization is helpful for generalization. We propose using the analysis of variance (ANOVA) to decompose the variance in the test error in a symmetric way.
  arXiv  Detail & Related papers  (2020-10-11T05:21:13Z)
• Spectral Learning on Matrices and Tensors [74.88243719463053]
  We show that tensor decomposition can pick up latent effects that are missed by matrix methods. We also outline computational techniques to design efficient tensor decomposition methods.
  arXiv  Detail & Related papers  (2020-04-16T22:53:00Z)

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

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.