Related papers: A Sub-linear Time Framework for Geometric Optimiza…
In machine learning or statistics, it is often desirable to reduce the dimensionality of a sample of data points in a high dimensional space $\mathbb{R}^d$. This paper introduces a dimensionality reduction method where the embedding…
We propose the first general and practical framework to design certifiable algorithms for robust geometric perception in the presence of a large amount of outliers. We investigate the use of a truncated least squares (TLS) cost function,…
This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…
Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance),…
Outlier-robust estimation is a fundamental problem and has been extensively investigated by statisticians and practitioners. The last few years have seen a convergence across research fields towards "algorithmic robust statistics", which…
Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have…
DBSCAN is a popular density-based clustering algorithm that has many different applications in practice. However, the running time of DBSCAN in high-dimensional space or general metric space ({\em e.g.,} clustering a set of texts by using…
Incorporating a non-Euclidean variable metric to first-order algorithms is known to bring enhancement. However, due to the lack of an optimal choice, such an enhancement appears significantly underestimated. In this work, we establish a…
Estimating structures in "big data" and clustering them are among the most fundamental problems in computer vision, pattern recognition, data mining, and many other other research fields. Over the past few decades, many studies have been…
We propose a new randomized optimization method for high-dimensional problems which can be seen as a generalization of coordinate descent to random subspaces. We show that an adaptive sampling strategy for the random subspace significantly…
Suppose that there is a ground set which consists of a large number of vectors in a Hilbert space. Consider the problem of selecting a subset of the ground set such that the projection of a vector of interest onto the subspace spanned by…
Discriminative learning effectively predicts true object class for image classification. However, it often results in false positives for outliers, posing critical concerns in applications like autonomous driving and video surveillance…
Quadratic programming is a ubiquitous prototype in convex programming. Many machine learning problems can be formulated as quadratic programming, including the famous Support Vector Machines (SVMs). Linear and kernel SVMs have been among…
In this paper, we present a new iterative rounding framework for many clustering problems. Using this, we obtain an $(\alpha_1 + \epsilon \leq 7.081 + \epsilon)$-approximation algorithm for $k$-median with outliers, greatly improving upon…
The goal of Feature Selection - comprising filter, wrapper, and embedded approaches - is to find the optimal feature subset for designated downstream tasks. Nevertheless, current feature selection methods are limited by: 1) the selection…
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…
Bayesian optimization is a sequential method for minimizing objective functions that are expensive to evaluate and about which few assumptions can be made. By using all gathered data to train a Gaussian process model for the function and…
With the sweeping digitalization of societal, medical, industrial, and scientific processes, sensing technologies are being deployed that produce increasing volumes of time series data, thus fueling a plethora of new or improved…
The paper considers the minimization of a separable convex function subject to linear ascending constraints. The problem arises as the core optimization in several resource allocation scenarios, and is a special case of an optimization of a…
Constrained optimization problems appear in a wide variety of challenging real-world problems, where constraints often capture the physics of the underlying system. Classic methods for solving these problems rely on iterative algorithms…