Related papers: Algorithms and Hardness for Robust Subspace Recove…

Robust model fitting is a core algorithm in a large number of computer vision applications. Solving this problem efficiently for datasets highly contaminated with outliers is, however, still challenging due to the underlying computational…

Subspace clustering is the unsupervised grouping of points lying near a union of low-dimensional linear subspaces. Algorithms based directly on geometric properties of such data tend to either provide poor empirical performance, lack…

Many real-world problems can be formulated as geometric optimization problems in high dimensions, especially in the fields of machine learning and data mining. Moreover, we often need to take into account of outliers when optimizing the…

Robust parameter estimation is a crucial task in several 3D computer vision pipelines such as Structure from Motion (SfM). State-of-the-art algorithms for robust estimation, however, still suffer from difficulties in converging to…

Phase retrieval in real or complex Hilbert spaces is the task of recovering a vector, up to an overall unimodular multiplicative constant, from magnitudes of linear measurements. In this paper, we assume that the vector is normalized, but…

We propose methods for estimating correspondence between two point sets under the presence of outliers in both the source and target sets. The proposed algorithms expand upon the theory of the regression without correspondence problem to…

Neural networks (NNs) can achieved high performance in various fields such as computer vision, and natural language processing. However, deploying NNs in resource-constrained safety-critical systems has challenges due to uncertainty in the…

Subspace clustering is the problem of clustering data that lie close to a union of linear subspaces. In the abstract form of the problem, where no noise or other corruptions are present, the data are assumed to lie in general position…

Recovering a sparse signal from outlier-contaminated measurements is a fundamental challenge in many applications. While existing algorithms predominantly address scenarios with bounded noise or assume known signal sparsity, few methods…

The vast majority of theoretical results in machine learning and statistics assume that the available training data is a reasonably reliable reflection of the phenomena to be learned or estimated. Similarly, the majority of machine learning…

This paper addresses the robust estimation of linear regression models in the presence of potentially endogenous outliers. Through Monte Carlo simulations, we demonstrate that existing $L_1$-regularized estimation methods, including the…

In this paper, we study the adversarial robustness of subspace learning problems. Different from the assumptions made in existing work on robust subspace learning where data samples are contaminated by gross sparse outliers or small dense…

Robust estimation is much more challenging in high dimensions than it is in one dimension: Most techniques either lead to intractable optimization problems or estimators that can tolerate only a tiny fraction of errors. Recent work in…

In many linear inverse problems, we want to estimate an unknown vector belonging to a high-dimensional (or infinite-dimensional) space from few linear measurements. To overcome the ill-posed nature of such problems, we use a low-dimension…

Missing data often exists in real-world datasets, requiring significant time and effort for data repair to learn accurate models. In this paper, we show that imputing all missing values is not always necessary to achieve an accurate ML…

The task of outlier detection is to find small groups of data objects that are exceptional when compared with rest large amount of data. In [38], the problem of outlier detection in categorical data is defined as an optimization problem and…

Outlier detection is a significant area in data mining. It can be either used to pre-process the data prior to an analysis or post the processing phase (before visualization) depending on the effectiveness of the outlier and its importance.…

The goal of ordinal embedding is to represent items as points in a low-dimensional Euclidean space given a set of constraints in the form of distance comparisons like "item $i$ is closer to item $j$ than item $k$". Ordinal constraints like…

We propose statistically robust and computationally efficient linear learning methods in the high-dimensional batch setting, where the number of features $d$ may exceed the sample size $n$. We employ, in a generic learning setting, two…

We introduce the notion of a reproducible algorithm in the context of learning. A reproducible learning algorithm is resilient to variations in its samples -- with high probability, it returns the exact same output when run on two samples…