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Optimal transport (OT) has become exceedingly popular in machine learning, data science, and computer vision. The core assumption in the OT problem is the equal total amount of mass in source and target measures, which limits its…
Sufficient dimension reduction (SDR) is a popular tool in regression analysis, which replaces the original predictors with a minimal set of their linear combinations. However, the estimated linear combinations generally contain all original…
How can we compute the pseudoinverse of a sparse feature matrix efficiently and accurately for solving optimization problems? A pseudoinverse is a generalization of a matrix inverse, which has been extensively utilized as a fundamental…
Difference imaging is a technique for obtaining precise relative photometry of variable sources in crowded stellar fields and, as such, constitutes a crucial part of the data reduction pipeline in surveys for microlensing events or…
Optimal transport (OT) is a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been made in designing OT variants which are either…
This paper proposes a fast and accurate method for sparse regression in the presence of missing data. The underlying statistical model encapsulates the low-dimensional structure of the incomplete data matrix and the sparsity of the…
We consider a general nonlinear regression problem where the predictors contain measurement error. It has been recently discovered that several well-known dimension reduction methods, such as OLS, SIR and pHd, can be performed on the…
Aligning partially overlapping point sets where there is no prior information about the value of the transformation is a challenging problem in computer vision. To achieve this goal, we first reduce the objective of the robust point…
Iterated sampling importance resampling (i-SIR) is a Markov chain Monte Carlo (MCMC) algorithm which is based on $N$ independent proposals. As $N$ grows, its samples become nearly independent, but with an increased computational cost. We…
Domain generalization asks for models trained over a set of training environments to perform well in unseen test environments. Recently, a series of algorithms such as Invariant Risk Minimization (IRM) has been proposed for domain…
The explosion of large-scale data in fields such as finance, e-commerce, and social media has outstripped the processing capabilities of single-machine systems, driving the need for distributed statistical inference methods. Traditional…
Outlier detection is critical in real applications to prevent financial fraud, defend network intrusions, or detecting imminent device failures. To reduce the human effort in evaluating outlier detection results and effectively turn the…
Current metric learning approaches for image retrieval are usually based on learning a space of informative latent representations where simple approaches such as the cosine distance will work well. Recent state of the art methods such as…
Background modeling is a critical component for various vision-based applications. Most traditional methods tend to be inefficient when solving large-scale problems. In this paper, we introduce sparse representation into the task of large…
This paper revisits the classic iterative proportional scaling (IPS) from a modern optimization perspective. In contrast to the criticisms made in the literature, we show that based on a coordinate descent characterization, IPS can be…
Online sparse linear regression is an online problem where an algorithm repeatedly chooses a subset of coordinates to observe in an adversarially chosen feature vector, makes a real-valued prediction, receives the true label, and incurs the…
In this paper, we consider regression models with a Hilbert-space-valued predictor and a scalar response, where the response depends on the predictor only through a finite number of projections. The linear subspace spanned by these…
Reverse engineering (RE) of user interfaces (UIs) plays an important role in software evolution. However, the large diversity of UI technologies and the need for UIs to be resizable make this challenging. We propose ReverseORC, a novel RE…
Most linear dimension reduction methods proposed in the literature can be formulated using an appropriate pair of scatter matrices, see e.g. Ye and Weiss (2003), Tyler et al. (2009), Bura and Yang (2011), Liski et al. (2014) and Luo and Li…
Supervised Deep-Learning (DL)-based reconstruction algorithms have shown state-of-the-art results for highly-undersampled dynamic Magnetic Resonance Imaging (MRI) reconstruction. However, the requirement of excessive high-quality…