Related papers: Optimization techniques for multivariate least tri…
In this work, we propose a novel method for robust single rotation averaging that can efficiently handle an extremely large fraction of outliers. Our approach is to minimize the total truncated least unsquared deviations (TLUD) cost of…
We propose a robust and scalable procedure for general optimization and inference problems on manifolds leveraging the classical idea of `median-of-means' estimation. This is motivated by ubiquitous examples and applications in modern data…
This paper discusses regularized estimators in the multivariate statistical model as tools naturally arising within a Bayesian framework. First, a link is established between Bayesian estimation and inference under parameter rounding…
This paper is concerned with the ordered statistic decoding with local constraints (LC-OSD) of binary linear block codes, which is a near maximum-likelihood decoding algorithm. Compared with the conventional OSD, the LC-OSD significantly…
Principal component analysis (PCA) is widely used for dimensionality reduction, with well-documented merits in various applications involving high-dimensional data, including computer vision, preference measurement, and bioinformatics. In…
The Minimum Covariance Determinant (MCD) method is a highly robust estimator of multivariate location and scatter, for which a fast algorithm is available. Since estimating the covariance matrix is the cornerstone of many multivariate…
Reliable outlier detection in high-dimensional data is crucial in modern science, yet it remains a challenging task. Traditional methods often break down in these settings due to their reliance on asymptotic behaviors with respect to sample…
The presence of groups containing high leverage outliers makes linear regression a difficult problem due to the masking effect. The available high breakdown estimators based on Least Trimmed Squares often do not succeed in detecting masked…
Linear discriminant analysis (LDA) is a popular technique to learn the most discriminative features for multi-class classification. A vast majority of existing LDA algorithms are prone to be dominated by the class with very large deviation…
This work addresses the outlier removal problem in large-scale global structure-from-motion. In such applications, global outlier removal is very useful to mitigate the deterioration caused by mismatches in the feature point matching step.…
In this paper, we propose a novel linear discriminant analysis criterion via the Bhattacharyya error bound estimation based on a novel L1-norm (L1BLDA) and L2-norm (L2BLDA). Both L1BLDA and L2BLDA maximize the between-class scatters which…
In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…
Linear Discriminant Analysis (LDA) is a widely-used supervised dimensionality reduction method in computer vision and pattern recognition. In null space based LDA (NLDA), a well-known LDA extension, between-class distance is maximized in…
An outlier is an observation or a data point that is far from rest of the data points in a given dataset or we can be said that an outlier is away from the center of mass of observations. Presence of outliers can skew statistical measures…
We propose a deep neural network (DNN) based least distance (LD) estimator (DNN-LD) for a multivariate regression problem, addressing the limitations of the conventional methods. Due to the flexibility of a DNN structure, both linear and…
Aggregating data from multiple sources can be formalized as an Optimal Transport (OT) barycenter problem, which seeks to compute the average of probability distributions with respect to OT discrepancies. However, in real-world scenarios,…
Data-driven anomaly detection methods suffer from the drawback of detecting all instances that are statistically rare, irrespective of whether the detected instances have real-world significance or not. In this paper, we are interested in…
One key challenge in Out-of-Distribution (OOD) detection is the absence of ground-truth OOD samples during training. One principled approach to address this issue is to use samples from external datasets as outliers (i.e., pseudo OOD…
Under normality and homoscedasticity assumptions, Linear Discriminant Analysis (LDA) is known to be optimal in terms of minimising the Bayes error for binary classification. In the heteroscedastic case, LDA is not guaranteed to minimise…
We propose the first near-optimal quantum algorithm for estimating in Euclidean norm the mean of a vector-valued random variable with finite mean and covariance. Our result aims at extending the theory of multivariate sub-Gaussian…