Related papers: Optimization techniques for multivariate least tri…
We consider a fundamental problem in unsupervised learning called \emph{subspace recovery}: given a collection of $m$ points in $\mathbb{R}^n$, if many but not necessarily all of these points are contained in a $d$-dimensional subspace $T$…
We propose a robust approach for the registration of two sets of 3D points in the presence of a large amount of outliers. Our first contribution is to reformulate the registration problem using a Truncated Least Squares (TLS) cost that…
Anomaly detection in medical imaging is a challenging task in contexts where abnormalities are not annotated. This problem can be addressed through unsupervised anomaly detection (UAD) methods, which identify features that do not match with…
Given an unsupervised outlier detection (OD) algorithm, how can we optimize its hyperparameter(s) (HP) on a new dataset, without any labels? In this work, we address this challenging hyperparameter optimization for unsupervised OD problem,…
In this paper, we propose a novel solution for non-convex problems of multiple variables, especially for those typically solved by an alternating minimization (AM) strategy that splits the original optimization problem into a set of…
Robust training of machine learning models in the presence of outliers has garnered attention across various domains. The use of robust losses is a popular approach and is known to mitigate the impact of outliers. We bring to light two…
A classic problem in unsupervised learning and data analysis is to find simpler and easy-to-visualize representations of the data that preserve its essential properties. A widely-used method to preserve the underlying hierarchical structure…
Outlier detection has gained increasing interest in recent years, due to newly emerging technologies and the huge amount of high-dimensional data that are now available. Outlier detection can help practitioners to identify unwanted noise…
We study the problem of detecting outlier pairs of strongly correlated variables among a collection of $n$ variables with otherwise weak pairwise correlations. After normalization, this task amounts to the geometric task where we are given…
Data subject to heavy-tailed errors are commonly encountered in various scientific fields, especially in the modern era with explosion of massive data. To address this problem, procedures based on quantile regression and Least Absolute…
Robust estimation of a mean vector, a topic regarded as obsolete in the traditional robust statistics community, has recently surged in machine learning literature in the last decade. The latest focus is on the sub-Gaussian performance and…
We benchmark the robustness of maximum likelihood based uncertainty estimation methods to outliers in training data for regression tasks. Outliers or noisy labels in training data results in degraded performances as well as incorrect…
Robust regression models in the presence of outliers have significant practical relevance in areas such as signal processing, financial econometrics, and energy management. Many existing robust regression methods, either grounded in…
This paper delivers improved theoretical guarantees for the convex programming approach in low-rank matrix estimation, in the presence of (1) random noise, (2) gross sparse outliers, and (3) missing data. This problem, often dubbed as…
An efficient monotone data augmentation (MDA) algorithm is proposed for missing data imputation for incomplete multivariate nonnormal data that may contain variables of different types, and are modeled by a sequence of regression models…
Downsampling or under-sampling is a technique that is utilized in the context of large and highly imbalanced classification models. We study optimal downsampling for imbalanced classification using generalized linear models (GLMs). We…
The inflated beta regression model is widely used for modeling continuous proportions with values at the boundaries. Maximum likelihood estimation for these models is well-known for its sensitivity to outliers, which can severely distort…
Unsupervised anomaly detection (UAD) alleviates large labeling efforts by training exclusively on unlabeled in-distribution data and detecting outliers as anomalies. Generally, the assumption prevails that large training datasets allow the…
Ellipsoid fitting is of general interest in machine vision, such as object detection and shape approximation. Most existing approaches rely on the least-squares fitting of quadrics, minimizing the algebraic or geometric distances, with…
We revisit the problem of estimating the mean of a high-dimensional distribution in the presence of an $\varepsilon$-fraction of adversarial outliers. When $\varepsilon$ is at most some sufficiently small constant, previous works can…